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Methodology for Operational Performance Assessment of Two-Lane Highway Facilities


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METHODOLOGY FOR THE OPERATIONAL PERFORMANCE ASSESSMENT OF TW O-LANE HIGHWAY FACILITIES By QINGYONG YU A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2006

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Copyright 2006 by Qingyong Yu

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ACKNOWLEDGEMENTS First I would like to say thank you to the many people who generously supported me, both directly and indirectly, throughout my graduate studies at University of Florida and in the process of completing my dissertation. Secondly, I would like to express my deepest gratitude to Dr. Scott Washburn, my advisor and dissertation committee chairman. It was with his guidance, his encouragement and his financial support that helped me to finish my dissertation. I will never forget the many weekends he gave up with his family to discuss the research with me; I will always remember his encouragement and praise when I made any little improvement; and many thanks go to him for his instructive comments to my proposal and dissertation. Without his help I would not be where I am today. I would also like to express my appreciation to my committee members, Dr. Lily Elefteriadou, Mr. William M. Sampson, Dr. Charles R. Glagola, and Dr. Ruth Steiner for their insight, guidance and patience throughout my studies and in the preparation of the dissertation. Finally, I dedicate this dissertation to my loving parents. Every call from them made me feel that I was surrounded by their love. Here I would like them to share my success with me. iii

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TABLE OF CONTENTS page ACKNOWLEDGEMENTS ...........................................................................iii LIST OF TABLES ........................................................................................vii LIST OF FIGURES .......................................................................................ix ABSTRACT .................................................................................................xii CHAPTER 1 INTRODUCTION ....................................................................................1 1.1 Background ...............................................................................................................1 1.2 Problem Statement ....................................................................................................1 1.3 Objectives and Tasks ................................................................................................4 1.4 Organization of the Document ..................................................................................7 2 OVERVIEW OF ANALYSIS METHODS .............................................9 2.1 Analytical Methods ...................................................................................................9 2.1.1 HCM Methodology for Two-Lane Highways ...................................................9 2.1.2 HCM Methodology for Signalized and Unsignalized Intersections ................11 2.1.3 HCM Methodology for Urban Streets .............................................................12 2.1.4 Performance Measure Definition .....................................................................12 2.1.5 FDOT HIGHPLAN Software ..........................................................................13 2.2 Simulation Methods ................................................................................................14 2.2.1 TWOPAS Software ..........................................................................................14 2.2.2 TRARR Software .............................................................................................17 2.2.3 CORSIM Software ...........................................................................................18 2.3 Effect of Upstream Signal on Two-Lane Highway PTSF ......................................20 3 CONCEPTUAL OVERVIEW OF TWO-LANE HIGHWAY FACILITY ANALYSIS METHODOLOGY.........................................22 3.1 Conceptual Framework for Facility Evaluation Methodology ...............................22 iv

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3.1.1 The Definition of a Two-Lane Highway with Signalized/Unsignalized Intersections ..............................................................................................................22 3.1.2 Service Measure Consistency ..........................................................................26 3.1.3 Impacts of Signalized Intersection on Adjacent Highway Segments ..............29 3.1.3.1 Effects of intersections on the upstream two-lane highway operation .....30 3.1.3.2 Effects of intersections on the downstream two-lane highway operation 33 3.2 Methodological Approach ......................................................................................37 3.2.1 Service Measure Selection ...............................................................................37 3.2.2 Facility Segmentation ......................................................................................42 3.2.3 Overview of Computational Methodology ......................................................46 4 DEVELOPMENT OF FACILITY SEGMETNATION COMPUTATION...................................................................................53 4.1 Effective Length of the Influence Area Upstream of the Signalized Intersection ..54 4.1.1 Recommended Length in FDOTs 2002 Level/Quality of Service Handbook 54 4.1.2 Components of the Signal Influence Area .......................................................55 4.1.2.1 Determining stopping sight distance .........................................................59 4.1.2.2 Determining average queue length ...........................................................61 4.1.2.3 Determining acceleration distance ............................................................63 4.1.3 Simulation and Regression Analysis ...............................................................67 4.1.3.1 Contributing factor selection .....................................................................68 4.1.3.2 Simulation model selection .......................................................................70 4.1.3.3 Simulation model experimental design .....................................................72 4.1.3.4 Regression model development ................................................................73 4.2 Effective Length of the Influence Area Downstream of Signalized Intersection ...77 4.2.1 Entering Percent Following of TWOPAS ........................................................77 4.2.2 Headway Distribution ......................................................................................78 4.2.2.1 Shifted negative exponential distribution .................................................79 4.2.2.2 Composite distribution ..............................................................................80 4.2.3 Determining Entering Percent Following ........................................................85 4.2.4 Effective Length of a Signalized Intersection on the Downstream Segment ..89 4.2.5 Evaluation Based on CORSIM Simulation ......................................................96 5 ESTIMATION OF SERVICE MEASURE VALUES ........................100 5.1 Free-Flow Speed Estimation .................................................................................100 5.1.1 Field Measurement of Free-Flow Speed ........................................................101 5.1.2 Estimating Free-Flow Speeds ........................................................................102 5.2 Performance Measure on the Unaffected Two-Lane Highway Segment .............103 5.3 Performance Measure on an Affected Two-Lane Highway Segment ..................105 5.4 Service Measure on a Two-Lane Highway with a Passing Lane ..........................112 5.5 Service Measure at a Signalized Intersection .......................................................115 5.6 Service Measure at a TWSC Unsignalized Intersection .......................................117 5.7 Level of Service Thresholds .................................................................................125 v

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6 APPLICATION EXAMPLES .............................................................127 6.1 Input Parameters ...................................................................................................127 6.2 Example 1 .............................................................................................................128 6.2 Example 2 .............................................................................................................137 7 SUMMARY AND RECOMMENDATIONS .....................................161 7.1 Summary ...............................................................................................................161 7.2 Further Research ...................................................................................................164 APPENDIX A PASSING PERCENTAGE AND AVERAGE TRAVEL SPEED ON TWO-LANE HIGHWAYS.................................................................167 B HEADWAY DISTRIBUTION ...........................................................171 C ENTERING PERCENT FOLLOWING CALCULATION ...............180 C.1 Methods to Calculate EPF Downstream of Signal ...............................................180 C.2 Method to Calculate EPF Without Signal ............................................................189 D VISUAL BASIC CODE .....................................................................196 D.1 Calculate Entering Percent Following .................................................................196 D.2 Extract Average Travel Speed From CORSIM Output .......................................199 D.3 Determine Upstream Effective Length ................................................................203 E PLOTS OF DIFFERENCE IN AVERAGE TRAVEL SPEED FROM TWOPAS.............................................................................................207 F PLOTS OF DIFFERENCE IN AVERAGE TRAVEL SPEED FROM CORSIM..............................................................................................212 G NOMENCLATURE TABLE .............................................................217 H LIST OF REFERENCES ....................................................................221 I BIOGRAPHICAL SKETCH ...............................................................223 vi

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LIST OF TABLES Table page 3-1. Traffic simulation conditions .....................................................................................30 3-2. Service measure evaluation .......................................................................................41 3-3. Summary of programs used at each step ...................................................................51 3-4. Simulation model evaluation .....................................................................................52 4-1. Normal acceleration rates, distance, and elapsed time ..............................................65 4-2. Regression model summary .......................................................................................66 4-3. Variable input values (with a left-turn bay) ...............................................................73 4-4. Variable input values (without a left-turn bay) .........................................................73 4-5. Regression model (with a left-turn bay) ....................................................................75 4-6. Regression model (without a left-turn bay) ...............................................................76 4-7. Upstream effective length with low traffic volume (ft) .............................................76 4-8. Composite headway distribution calculation (volume = 1500-1740 veh/h) ..............83 4-9. Chi-Squared test calculation ......................................................................................85 4-10. Entering Percent Following .....................................................................................88 4-11. Recommended default values for desired speed by vehicle type ............................90 4-12. Regression model for the downstream effective length ..........................................95 4-13. Comparison of downstream effective length ...........................................................98 5-1. Adjustment (fLS) for lane width and shoulder width ................................................103 5-2. Adjustment (fA) for access-point density ................................................................103 vii

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5-3. Adjustment factor, fATS, to ATS for a segment downstream of a signal ..................111 5-4. Downstream length of roadway affected by passing lane .......................................114 5-5. Factors for estimation of average travel speed within a passing lane .....................115 5-6. Variable input values (TWSC intersection) .............................................................122 5-7. Simulation results on the queue length of the TWSC intersection ..........................123 5-8. LOS criteria for two-lane highway facilities ...........................................................126 6-1. Input data needs for the facility-wide operational analysis .....................................128 6-2. Average travel speed for the unaffected two-lane segments ...................................152 6-3. Average travel speed for the affected downstream two-lane segments ...................153 6-4. Average travel speed for the affected passing lane segments .................................154 6-5. Control delays at signalized intersections ...............................................................154 B-1. Time headway distribution (traffic flow rate = 900 veh/h ~ 1140 veh/h) ..............171 B-2. Chi-Square test calculation (based on Table B-1) ..................................................173 B-3. Time headway distribution (traffic flow rate = 1200 veh/h ~ 1440 veh/h) ............174 B-4. Chi-Square test calculation (based on Table B-3) ..................................................176 B-5. Time headway distribution (traffic flow rate = 1500 veh/h ~ 1740 veh/h) ............177 B-6. Chi-Square test calculation (based on Table B-5) .................................................179 C-1. Entering Percent Following with a signalized intersection .....................................192 C-2. Entering Percent Following with no signalized intersection ..................................195 viii

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LIST OF FIGURES Figure page 2-1. Screenshot from TWOPAS road editor .....................................................................15 2-2. Screenshot from Traffic Analysis Module of IHSDM ..............................................16 2-3. Screenshot from TRARR road editor ........................................................................18 2-4. Screenshot from CORSIM simulation animation (TRAFVU) ..................................19 3-1. Typical basic two-lane, two-way highway segment ..................................................24 3-2. Typical two-lane, two-way highway with a passing lane ..........................................24 3-3. Typical two-lane, two-way highway with an unsignalized intersection ...................25 3-4. Typical two-lane, two-way highway with a signalized intersection .........................26 3-5. Effect of a signalized intersection on average travel speed .......................................32 3-6. Platoon dispersion, 300 ft from the upstream signalized intersection .......................35 3-7. Platoon dispersion, 5280 ft from the upstream signalized intersection .....................35 3-8. Platoon dispersion, 10560 ft from the upstream signalized intersection ...................36 3-9. Segment division of a two-lane highway with multiple isolated signalized intersections ..............................................................................................................44 3-10. Facility segmentation of a two-lane highway with multiple isolated signalized intersections ..............................................................................................................45 3-11. Flow diagram of two-lane highway facility operational analysis methodology .....50 4-1. Length of intersection area ........................................................................................55 4-2. Schematic distance-time diagram at a signalized intersection ..................................58 4-3. Queue length estimation ............................................................................................59 ix

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4-4. Average travel speed along the two-lane highway with signal .................................74 4-5. TWOPAS traffic data input interface ........................................................................78 4-6. Composite time headway distribution .......................................................................84 4-7. Two-lane highway traffic flow downstream of a signalized intersection .................87 4-8. Difference in the average travel speed between with and without signalized intersection along the downstream two-lane highway ..............................................93 4-9. Difference in the average travel speed with traffic volume = 1100 veh/h ................94 4-10. Average travel speed variation with traffic volume = 220 veh ...............................99 5-1. Downstream operational effects of a signalized intersection on AT .......................110 5-2. Effect of a passing lane on average travel speed .....................................................114 5-3. Traffic streams at a TWSC intersection ..................................................................118 5-4. Guideline for determining the need for a major-road left-turn bay at a two-way stop-controlled intersection .............................................................................................124 5-5. Length of TWSC intersection area ..........................................................................125 6-1. A two-lane highway with an isolated signalized intersection .................................131 6-2. Segmentation for a two-lane highway facility .........................................................143 6-3. Traffic flow rates at three intersections ...................................................................144 6-4. A view of a typical passing lane ..............................................................................149 A.1. Passing percentage for various levels of advancing and opposing traffic volume on two-lane highways ..................................................................................................168 A-2. Average travel speed for various levels of advancing and opposing traffic volume on two-lane highways ..................................................................................................169 A-3. Percent time-spent-following for various levels of advancing and opposing traffic volume on two-lane highways ................................................................................170 B-1. Composite time headway distribution (based on Table B-1) ..................................172 x

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B-2. Composite time headway distribution (based on Table B-3) ..................................175 B-3. Composite time headway distribution (based on Table B-5) ..................................178 C-1. Two-lane highway traffic flow downstream of a signalized intersection ...............181 E-1. Difference in the average travel speed with traffic volume = 440 veh ...................207 E-2. Difference in the average travel speed with traffic volume = 660 veh/h ................208 E-3. Difference in the average travel speed with traffic volume = 880 veh/h ................209 E-4: Difference in the average travel speed with traffic volume = 1110 veh/h ..............210 E-5. Difference in the average travel speed with traffic volume = 1320 veh/h ..............211 F-1. Difference in the average travel speed with traffic volume = 220 veh/h ................212 F-2. Difference in the average travel speed with traffic volume = 440 veh/h ................213 F-3. Difference in the average travel speed with traffic volume = 660 veh/h ................214 F-4. Difference in the average travel speed with traffic volume = 880 veh/h ................215 F-5. Difference in the average travel speed with traffic volume = 1100 veh/h ..............216 xi

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ABSTRACT Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy METHODOLOGY FOR THE OPERATIONAL PERFORMANCE ASSESSMENT OF TWO-LANE HIGHWAY FACILITIES By Qingyong Yu May 2006 Chair: Scott. S. Washburn Major Department: Civil and Coastal Engineering Traffic engineers have indicated that a facility-based evaluation methodology for two-lane highways would be much more useful and practical to them than just the individual segment and point analysis methodologies. A facility level analysis will allow the various features (e.g., isolated intersections, continuous grades, passing lanes) that are typical to an extended length of two-lane highway to be addressed in a combined analysis with a single performance measure and level of service value resulting. Currently there is not any operational analysis methodology to address two-lane highways with different segment types at the facility level. The scope of analysis provided in the Highway Capacity Manual (HCM) 2000 for two-lane highway is limited to separated segment within the facility. In this dissertation, a methodology is developed to assess the operational performance of an extended length of a two-lane highway facility, which might include an occasional signalized intersection and other control or roadway segments. xii

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The methodology maintains some fidelity to the HCM 2000 by using the existing methodologies for the two-lane highway segments and signalized intersections. Meanwhile, the individual segment in the whole facility is not regarded as an isolated object, and the impacts between segments are taken into account. A common time/delay based measure (percent time-delayed) is used for each segment and point of the entire facility. The primary contribution of this dissertation is the development of analytical relationships to determine the upstream and downstream boundary points that define the transition between basis tow-lane highway segments and the effective influence area of the signalized intersection and the TWSC intersection, as well as the corresponding method for calculation of an overall facility service measure based upon percent time-delayed and then translating it to a Level Of Service (LOS) grade. The dissertation focuses the efforts on developing the methodology for operational analysis of a two-lane highway with an isolated signalized intersection at the facility level. Nonetheless, this research also provides a model for the basic structure of a facility-level analysis that will be amenable to the incorporation of a variety of segment types. Finally the methodology has been incorporated into the existing HIGHPLAN software program. xiii

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CHAPTER 1 INTRODUCTION 1.1 Background Two-lane highways, which account for approximately 80 percent of all paved rural highways in the United States and carry about 30 percent of all traffic, are important facilities in our transportation network system [1]. With the increased development in rural areas, more signals are being installed on two-lane highways typically when these highways travel through small towns. Additionally, there are a number of other design and operational treatments developed on extended lengths of two-lane highways, such as passing lanes, two-way stop-controlled intersections, driveway turnouts, and two-way left-turn lanes. They can be effective in alleviating some operational problems on two-lane highways. Because these design and operational treatments significantly affect traffic operations on two-lane highways, there is ongoing demand for analysis methodologies with which to analyze the operating effectiveness of the entire length of two-lane highway, that is, the facility as a whole. This is consistent with the fact that drivers typically evaluate the quality of their trip over its entire length, not just in separate segments. 1.2 Problem Statement Personnel with the Florida Department of Transportation (FDOT) Systems Planning Office have indicated that a facility-based evaluation methodology for two-lane highways would be much more useful to them than just the individual segment and point 1

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2 analysis methodologies. Segment is a stretch of roadway with homogenous conditions. Facility is composed of different segments. A facility level analysis will allow the various features (e.g., isolated intersections, continuous grades, passing lanes) that are typical to an extended length of two-lane highway to be addressed in a combined analysis with a single performance measure and level of service value resulting. Frequently, a traveler is less concerned about the quality of service offered by a particular segment than the service over a facility that may be served by more than one segment type. For example, on a two-lane highway with several isolated intersections, most travelers are concerned about the operation of the whole facility and not just the operation of a particular intersection, or a particular two-lane highway segment. From the viewpoint of travelers or transportation engineers, a facility level analysis on a two-lane highway facility, instead of the segment level, is more practical and meaningful. Currently, there is not any operational analysis methodology to address two-lane highways with different segment types at the facility level. In the Highway Capacity Manual (HCM) 2000 [1], the basic two-lane highways with or without passing lane can be evaluated with the methodology in Chapter 20, Two-Lane Highways. Isolated signalized intersections on two-lane highways can be evaluated with the methodology in Chapter 16, Signalized Intersections. The scope of analysis provided in the HCM 2000 for two-lane highways is mainly limited to separate segments within the facility, while the methodology to evaluate the facility as a whole is of much more practical value to transportation engineers. In the HCM 2000, Chapter 15, Urban Streets, presents the methodology for evaluating arterials in urban and suburban areas with multiple signalized intersections at a

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3 spacing of 2.0 miles or fewer. To some degree, the analysis procedure is performed at the facility level, which combines the segment running time and control delay at the signalized intersection when determining the performance measure (average travel speed) for the entire facility. However, this methodology has some obvious drawbacks. They are the following: 1. The potential impacts between roadway segments and signalized intersections are not taken into account in this methodology. Continuing research has shown that the installation of signalized intersections can significantly affect traffic operations on the two-lane highways, such as decreasing average travel speed, and increasing percent time-spent-following. The impact between different segment types is a big issue differentiating the facility-level analysis from the segment-level analysis. 2. In this methodology, the urban street is divided into multiple segments, which is the full distance from one signalized intersection to the next. The signalized intersection is regarded as a typical point location within a traffic network, and control delay is regarded as a typical point performance measure without covering any distance. In the HCM 2000 [1], by definition, control delay includes movements at slower speeds and stops on intersection approaches as vehicles move up in queue position or slow down upstream of an intersection, as well as delay due to re-acceleration downstream of a signal after stopping or slowing. It implies that control delay happens not at a point, but actually within a certain distance. Although the time lost due to slow movement before and after a stop is technically part of the running time, it is also included in control delay. Segment division in this methodology causes the problem of double-counting the

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4 deceleration-acceleration delay. Segment division introduces error due to the segment between intersections being longer than they should. In this dissertation, a methodology for the operational performance assessment of two-lane highways with isolated signalized intersections (spacing of signalized intersections is 3 miles or more) will be explored, in addition to a way to combine a number of different segments (two-way stop-controlled intersection, passing lanes, basic segment, etc.). 1.3 Objectives and Tasks The objective of this research is to develop a methodology that can be used to assess the operational performance of an extended length of a two-lane highway facility, which might include occasional signalized intersections, unsignalized intersection, and other control or roadway treatments. This two-lane highway would then be comprised of multiple segments, with segment delineations occurring with a change in either roadway or control attribute. The most common types of two-lane highway segments are the following: Basic segmentthis is a segment that consists of a simple two-lane cross section, either level or rolling terrain Basic segments with a continuous specific up or down grade Three-lane cross section segments, with the additional lane being a passing lane Three-lane cross section segments, with the additional lane being a center left-turn lane Three-lane cross section segments, with the additional lane being a right-turn only lane Segments terminating with an isolated signalized intersection Segments terminating with an unsignalized intersection

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5 Segments terminating into a multilane highway This research focuses on developing the methodology for operational analysis of a two-lane highway with isolated signalized/un-signalized intersections at the facility level. Nonetheless, it is intended that this research will also provide a model for the basic structure of a facility level analysis that will be amenable to the incorporation of a variety of segment types. The tasks required to accomplish the research study objectives are as follows. Task 1: Perform a literature review on current analytical and simulation methods for evaluating the performance of basic two-lane segments and signalized intersections, along with previous research on the effects of signalized intersections on a two-lane highway. Task 2: Define the basic conceptual framework, from a segmentation and service measure perspective, for combining two-lane highway segments with intersections into a facility-wide operational analysis. Task 3: Investigate traffic operations at the boundary of a two-lane segment and a signalized intersection (upstream of the signal) and develop a method that can be used to determine the effective length of the signals influence area upstream of the signal. The conceptual approach being taken is that the effective upstream length of the signals influence area is a function of average queue length on the approach to the signal and some portion of perception/reaction time and braking distance before the queue. The combination of the stopping sight distance (SSD) equation, from the AASHTO Green Book [2], and average queue length formulas from Chapter 16 of the HCM 2000, are compared to simulation output from CORSIM. A comprehensive experimental design

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6 for simulation is utilized to fully explore the relationship between influence area and the appropriate traffic and control variables. These results are reconciled against those from the SSD + Average Queue Length results to arrive at an appropriate relationship. Task 4: Investigate traffic operations downstream of a signalized intersection and develop a method that can be used to determine the effective length of the signals influence area downstream of the signal. The conceptual approach being taken is that the effective downstream length of the signals influence area is a function of vehicle acceleration and platoon dispersion. Thus, three types of areas are investigated: Simple vehicle dynamics equations related to vehicle acceleration. Platoon dispersion downstream of a signal, such as the model currently used in the TRANSYT-7F program. Changes in the vehicle headway distribution downstream of a signal. Previous work performed by Dixon et al. [3] related to this issue is investigated, with two main differences being: o A composite headway distribution model is used for headways instead of a simple negative exponential model, and o The EPF (Entering Percent Following) measure as used by Dixon et al. is related to downstream vehicle speeds as opposed to percent time-spent-following. Task 5: Investigate traffic operations at the boundary of a two-lane segment and a two-way stop-controlled intersection (without sharing left-turn lanes), and develop a method that can be used to determine the effective length of the two-way stop-controlled intersection on through traffic on the major street and right-turn traffic from the major street behind it. Task 6: Join the components (basic two-lane segment, upstream signal influence area, signal delay, and downstream signal influence area) into an integrated methodology

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7 for the operational analysis of a two-lane highway facility. This methodology will be predicated upon the use of an aggregated percent-time-delayed measure as the facility-wide service measure. As part of this, two example problems are presented. Task 7: Determine LOS thresholds that maintain a reasonable relationship with existing LOS thresholds in Chapter 20 (two-lane highways) of the HCM 2000. For example, with the use of a new service measure for the facility analysis, it should not be possible to get a better level of service for the two-lane highway when installing a signal compared to the previous LOS method. Task 8: Provide a qualitative overview of how the method of analysis for multilane highways might be modified to fit into this framework such that combinations of two-lane highway segments, multilane highway segments, and occasional traffic signals can be analyzed as an overall facility. Task 9: Modify HIGHPLAN program to include this new methodology for a facility-level analysis. This will require the addition of a new screen for segment and intersection data inputs, as well as a new result. 1.4 Organization of the Document This document is organized into six chapters in addition to the Introduction. Each of the chapters covers a different aspect of the issue of assessing the operational performance of a two-lane highway facility consisting of different segment type. In Chapter 1, the background, objectives, and tasks of this research are introduced and the stage is set for the organization of the rest of the document. Chapter 2, the literature review gives a review of the current methodologies for evaluating the operational performance of basic two-lane segments, and signalized intersections. It also provides a brief overview of the simulation models and their potential ability to contribute to the

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8 performance evaluation for the two-lane highway facility. Chapter 3 presents the conceptual framework of the operational analysis procedure for a two-lane highway facility, and puts forward the methodology of operational analysis for the two-lane highway facilities. The first two steps of the selection of facility-wide service measure and facility segmentation are also explored in this chapter. Chapter 4 describes the procedures for determining component segment lengths of the facility, mainly including the length of a signalized intersection influence area, and the length of the downstream segment affected by the upstream signal. Chapter 5 describes the methods for calculating the service measure value of each segment type. They include the free-flow speed, and average travel speed on three kinds of two-lane highway segments, and control delay at the signalized and unsignalized intersections. In Chapter 6, two examples are provided to illustrate the application of the developed methodology. Finally, Chapter 7 provides summary and recommendations for future research.

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CHAPTER 2 OVERVIEW OF ANALYSIS METHODS This chapter summarizes current methodologies for evaluating the operational performance of basic two-lane segments, and signalized intersections. It also provides a brief overview of the TWOPAS, TRARR, and CORSIM simulation models and their potential ability to contribute to the performance evaluation for the two-lane highway facility. Finally previous research on effects of signalized intersections on a two-lane highway segment is presented. 2.1 Analytical Methods The following sections give an overview of analytical methodologies presented in the HCM 2000. They are for two-lane highways, signalized intersections, and urban streets. Finally the adjustment method used in the FDOT HIGHPLAN software for the facility level analysis is presented. 2.1.1 HCM Methodology for Two-Lane Highways The Highway Capacity Manual (HCM) published by the Transportation Research Board (TRB) presents the widely accepted standards for analysis of two-lane highway capacity and quality of service. In the 1950 HCM, the first version of HCM, the procedure for analysis of two-lane highway capacity developed by O. K. Norman was presented. The capacity of a two-lane road was determined by comparing the demand for passing with observed actual passing 9

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10 rates at various flow rates. In the subsequent editions of 1965, 1985, and 2000 [1], the capacity and quality-of-service analysis procedure of a two-lane highway and their related service measures were revised. In the 1965 HCM, the capacity of a two-lane highway was estimated for both directions of travel combined, regardless of the direction split of traffic, and the two service measures for the operational analysis were the operating speed of traffic over a roadway section and the volume-to-capacity ratio. A great improvement in analysis of two-lane highway capacity and quality of service was achieved in the 1985 HCM. The capacity of a two-lane highway was determined to be a function of the directional split of traffic, ranging from a capacity of 2800 pc/h in both directions of travel combined for a 50/50 directional split to 2,000 pc/h for a 100/0 split. In this version, a new level of service measure named percent time delay was developed. Percent time delay is measured as the percentage of vehicles traveling at headway of 5 sec or less at one or more representative points within the analyzed roadway. In Chapter 20 of the HCM 2000, an improved operational analysis procedure for two-lane highway was presented. Key features of the improved operational analysis procedure are revised factors for the effects of grades and heavy vehicles, separate computational procedures for two-lane and directional segments, provision of operational analysis procedures for passing lanes in level and rolling terrain, climbing lanes on steep upgrades, and steep downgrades on which some trucks must use crawl speeds [1]. The combination of average travel speed and percent time-spent-following was determined as the level of service measure (i.e., the performance measures used to base level of service upon).

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11 The above discussion reviews the historical development of the HCM procedure for analysis of two-lane highway capacity and quality of service. The analysis procedure has been limited to the segment level. The operational analysis methodologies in this chapter do not address two-lane highways with signalized intersections or with other types of segments. 2.1.2 HCM Methodology for Signalized and Unsignalized Intersections In the HCM 2000, Chapter 16 Signalized Intersections contains a methodology for analyzing the capacity and level of service of signalized intersections [1]. The methodology addresses the capacity, LOS, and other performance measures for lane groups and intersection approaches and the LOS for the intersection as a whole. The ratio of demand flow rate to capacity is used as a capacity utilization measurement. The capacity analysis methodology for signalized intersections is based on known or projected signalization plans, and traffic characteristics. The control delay per vehicle is used as the service measure. In this methodology, the signalized intersection is regarded as an isolated point location. It does not take into account the potential impact of downstream congestion on intersection operation. In the HCM 2000, Chapter 17 Unsignalized Intersections contains a methodology for analyzing the capacity and level of service, lane requirements, and effects of traffic and design features of unsignalized intersections [1]. The analyzed unsignalized intersections include two-way stop-controlled (TWSC), all-way stop-controlled (AWSC) intersections, and roundabouts. For a TWSC intersection, LOS is determined by the computed or measured control delay and is defined for each minor movement. For an AWSC intersection, control delay is also used to determine LOS.

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12 2.1.3 HCM Methodology for Urban Streets In the HCM 2000, Chapter 15 Urban Streets contains a methodology used to access the mobility function of the urban street [1]. Four urban street classes are defined and reflect unique combinations of street function and street design. The degree of mobility provided is assessed in terms of average travel speed for the through-traffic stream. Computing the urban street or section speed requires the total time that a vehicle spends on the urban street. The total time consists of the segment running time and the intersection control delay of the lane group for through traffic. The methodology may be used to analyze urban streets that have a traffic signal spacing of 2 miles or less. To some degree, the analysis procedure is performed at the facility level, which combines the segment running time and control delay at the signalized intersection when determining the performance measure (average travel speed) for the entire facility. However, the potential impacts between roadway segments and signalized intersections are not taken into account in this methodology. 2.1.4 Performance Measure Definition Each facility type has a defined method for assessing capacity and level of service using performance measures. These measures reflect the operating conditions of a facility, given a set of roadway, traffic, and control conditions. Service measures are the performance measures used to base level of service upon. In this dissertation, a methodology of operational performance analysis is developed for the two-lane highway facility composed of different types of segments. A special service measure will be selected for this facility to determine its level of service. The definitions of some performance measures often used in the HCM are summarized here.

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13 Volume to Capacity Ratio (v/c) The v/c ratio is defined as the volume to capacity ratio, often used as a measure of the sufficiency of existing or proposed capacity. Average Travel Speed (ATS) ATS is defined as the length of the roadway segment under consideration divided by the average total travel time for all vehicles to traverse that segment during some designed time interval. Percent Time-Spent-Following (PTSF) PTSF is defined as the average percentage of travel time that vehicles on a given roadway segment must travel in platoons behind slower vehicles due to the inability to pass during some designed time interval. Travel Time Travel time is defined as the time spent traversing a section of highway. Percent Free Flow Speed (PFFS) Percent free flow speed is defined as the ratio of vehicle average travel speed to free flow speed. Density Density is the number of vehicles occupying a given length of highway or lane and is generally expressed as vehicles per mile per lane. Control Delay Control delay includes Movements at slower speed and stops on intersection approaches as vehicles move up in queue position or slow down upstream of an intersection [1]. It includes deceleration delay, stopped delay, and acceleration delay. Percent Time-Delayed Percent time-delayed is defined as the percentage of the travel time that vehicles on a given roadway segment must travel at speeds less than their desired speed (typically the free-flow speed) due to inability to pass or to delays caused by traffic control. 2.1.5 FDOT HIGHPLAN Software HIGHPLAN, designed for uninterrupted flow highway level of service analysis for planning applications, is FDOTs software for two-lane and multilane uninterrupted flow

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14 highways [4]. HIGHPLAN maintains fidelity to the HCM 2000 two-lane and multilane procedures to the extent possible. However due to some unique characteristics in the State of Florida, HIGHPLAN incorporates a number of concepts and calculations that differ significantly from the basic procedures in the HCM 2000. HIGHPLAN includes an adjustment to account for whether the analysis is at the segment level or the facility level. If a segment level analysis is performed, it is assumed that the highway section under consideration is short enough that it does not include any capacity reducing effects due to the presence of intersecting driveways or cross streets. If a facility level analysis is chosen, a 10% reduction is applied to the base capacity to account for driveway and cross street friction. This value is consistent with the capacity reducing effects of interchanges experienced on Florida freeways [5]. Nonetheless, this is a gross adjustment necessitated by the lack of a specific facility-level methodology. 2.2 Simulation Methods The following section provides a brief overview of the TWOPAS, TRARR and CORSIM simulation models and their potential ability to contribute to the performance evaluation for the two-lane highway operations. 2.2.1 TWOPAS Software TWOPAS (TWO-lane PASsing) rural highway simulation software is used for modeling traffic conditions on two-lane two-way roadways. This software was used extensively in developing the two-lane analysis methodology in the HCM 2000. TWOPAS was first developed in the 1970s by Mid-West Research Institute for the US Federal Highway Administration (FHWA). TWOPAS was revised most recently in 1998, and was contained in a graphic interface, UCBRURAL, developed by the University of California-Berkeley. UCBRURAL provides a menu-driven interactive

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15 graphical interface with comprehensive input checking, carefully selected default values, and user-selected output options including graphic depictions of traffic performance, which is more convenient for users to run TWOPAS model. Figure 2-1 shows a view of the UCBRURAL road editor. Recently the TWOPAS traffic simulation model is built in the Traffic Analysis Module (TAM) of the Interactive Highway Safety Design Model (IHSDM) to estimate traffic quality-of-service measures for an existing or proposed design. The TAM facilitates use of TWOPAS by feeding it the roadway geometry data stored by IHSDM. Figure 2-2 shows a view of TAM input interface in IHSDM. Figure 2-1. Screenshot from TWOPAS road editor As a microscopic, stochastically based model, TWOPAS simulates traffic operations on a two-lane highway by reviewing the position, speed, and acceleration of each individual vehicle along the roadway at 1-second intervals. The operation of each

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16 vehicle is also influenced by the characteristics of the vehicle and its driver, by the geometric of the roadway, and by the surrounding traffic simulation in a realistic manner as it advances along the road [6]. TWOPAS incorporates the major features: Highway Geometry specified in terms of grades, horizontal curves, lane and shoulder width, along with passing and climbing lanes. Traffic control specified by users, especially passing and no-passing zones, and reduced speed zones. Driver Characteristics and preferences including desired speeds, preferred acceleration levels, limitations on sustained use of maximum power, passing and pass-abort decisions, and realistic behavior in passing and climbing lanes. Entering Traffic streams generated in response to user-specified flow rate, vehicle mix, immediate upstream alignment, and the percent of traffic platooned. Driver speed choices in unimpeded traffic based on user-specified distribution of desired speeds; in the impeded traffic based on a car-following model that simulates driver preferences for following distances, relative leader/follower speeds, and desire to pass the leader [6]. Figure 2-2. Screenshot from Traffic Analysis Module of IHSDM

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17 TWOPAS has the capability to simulate both conventional two-lane highways and two-lane highways with added passing lanes. However, TWOPAS does not have the ability to simulate traffic turning on or off the highway at driveways, unsignalized intersections, or signalized intersections. 2.2.2 TRARR Software TRARR (TRAffic on Rural Roads) was developed in the 1970s and 1980s by the Australian Road Research Board. TRARR is designed for two-lane rural highways, with occasional passing lane sections. It is a microscopic simulation model, that is, it models each vehicle individually. Each vehicle is randomly generated, placed at one end of the road and monitored as it travels to the other end. Various driver behaviors and vehicle performance factors determine how the vehicle reacts to changes in alignment and other traffic. TRARR uses traffic flow, vehicle performance, and highway alignment data to establish, in detail, the speeds of vehicles along rural roads. This determines the driver demand for passing and whether or not passing maneuvers may be executed [7]. Figure 2-3 shows an interface of the TRARR road editor. TRARR is designed for two-lane rural highways, with occasional passing lane sections. TRARR can be used to obtain a more precise calculation of travel time, frustration (via time spent following), and benefits resulting from passing lanes or road realignments. For strategic assessment of road links, TRARR can also be used to evaluate the relative benefits of passing lanes at various spacing. Similar to TWOPAS, TRARR has no ability to handle varying traffic flows down the highway, particularly due to major side roads or signalized intersections. However, TWOPAS was developed with U.S. data and, therefore, was better representative of U.S. conditions than TRARR.

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18 Figure 2-3. Screenshot from TRARR road editor 2.2.3 CORSIM Software CORSIM (CORridor SIMulation), developed by the Federal Highway Administration, is the core simulation engine in the TSIS (Traffic Software Integrated System) suite [8]. CORSIM is a comprehensive traffic simulation program, applicable to surface streets, freeways, and integrated networks with a complete selection of control devices, such as stop/yield signs, traffic signals, and ramp metering. CORSIM is a microscopic, discrete time, stochastic, state-of-the-practice model used to simulate traffic operations. It integrates two microscopic traffic simulation models: the arterial network model, NETSIM, and the freeway model, FRESIM. CORSIM is able to simulate existing or proposed conditions on very large networks. CORSIM has been applied by thousands of practitioners and researchers worldwide over the past 30 years and

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19 embodies a wealth of experience and maturity [8]. Figure 2-4 shows an interface simulating traffic operations at a signalized intersection. CORSIM has expanded the capabilities of NETSIM and FRESIM with the following major enhancements: HOV lanes in FRESIM Freeway ramp metering Vehicle-type-specific turn percentages Support Larger Networks Path Following Capacity Figure 2-4. Screenshot from CORSIM simulation animation (TRAFVU) CORSIM can simulate traffic and traffic control system using commonly accepted vehicles and driver behavior models. However, it does not have the ability to simulate vehicle passing operations on a two-lane highway using the opposing lane.

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20 2.3 Effect of Upstream Signal on Two-Lane Highway PTSF In the research of Dixon et al. [3], they developed a methodology to estimate the effects of a simple isolated signalized intersection on a downstream two-lane highway segment in terms of percent time-spent-following. In their research, the effect of an upstream signalized intersection on the two-lane highway segment was to modify the distribution of entering headways. The condition with no signalized intersection is represented by assuming the negative exponential distribution of headways for entering traffic, which is derived from the Poisson distribution for random arrivals. However, the upstream signalized intersection will modify the headway distribution of the traffic stream entering the downstream two-lane highway segment. In TWOPAS, the distribution of headways is defined through the input variable, Entering Percent Following (EPF), which is the percent of the total number of vehicles in the direction of travel that are following in platoons, defined as headways less than 3.0 seconds, as they enter the road being analyzed. In Dixon et al.s research, it was assumed that as long as the percentage of vehicles following, immediately downstream of the signalized intersection, could be determined, it was appropriate to represent the effects of the signalized intersection through the EPF parameter. Vehicle headways were assumed to follow a random distribution, and EPF was calculated using a cumulative exponential distribution of headways less than 3.0 seconds. The analysis procedure of two-lane highway segment affected by the upstream signalized intersection operations was broken down into four steps. Step 1: Determine the percentage of vehicle following (EPF) downstream of the signalized intersection. Step 2: Determine the Percent Time Spent Following (PTSF) for the downstream highway section without the upstream signalized intersection.

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21 Step 3: Estimate the PTSF for the downstream highway section with the upstream signalized intersection. In this step, two methods can be used. One method is using TWOPAS and another method is using the HCM 2000 two-lane highway directional analysis procedures and deterministic adjustment factors. Step 4: Estimate the level of service based on the criteria suggested in the HCM 2000 two-lane highway analysis procedure.

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CHAPTER 3 CONCEPTUAL OVERVIEW OF TWO-LANE HIGHWAY FACILITY ANALYSIS METHODOLOGY This chapter describes the development of operational analysis procedures for two-lane highway facilities. The developed methodology would maintain some fidelity to the HCM by using the existing methodologies for two-lane highway segments and signalized intersections. This chapter begins with a discussion of the conceptual framework of the operational analysis procedure for a two-lane highway facility. It then puts forward a methodology of operational analysis for two-lane highway facilities and presents an overview of this methodology. Finally, the chapter discusses the selection of a facility-wide service measure and the first step of this methodologyfacility segmentation. 3.1 Conceptual Framework for Facility Evaluation Methodology To develop a methodology for the operational analysis of a two-lane highway facility, a two-lane highway with an isolated signalized intersection will be used as a model. This section discusses the conceptual framework of the operational analysis procedure for such a configuration. Aspects of the conceptual framework addressed are the definition of the two-lane highway facility, segment types, the features of operational analysis at the facility level, and the proposed methodologies. 3.1.1 The Definition of a Two-Lane Highway with Signalized/Unsignalized Intersections In the HCM 2000, the primary highway system structure consists of points, segments, facilities, corridors and areas. A facility is a length of roadway composed of 22

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23 points and segments. A point is a boundary between segments, in other words, points are where modal users enter, leave, or cross a facility, or where roadway characteristics change. A segment is a portion of a facility defined by two end points. Segments are the primary building blocks of facility analyses. In addition, a sub-segment is a further division of a segment. Whereas segments are delineated by points (e.g., intersections) or changes in geometric conditions, sub-segments for the purpose of discussion in this document are delineated only by changing operational conditions. For example, an isolated signalized intersection on a two-lane highway produces operational effects on the upstream segment. The upstream two-lane highway segment can be divided into the upstream sub-segment within the effective length of the signalized intersection, and the upstream sub-segment beyond the effective length of the signalized intersection. Although both sub-segments have homogenous geometric conditions, their operational features are different. One sub-segment is affected by the downstream signal; the other is not affected. The potential segment types on a two-lane highway could include the following: Basic segment, this is a segment that consists only of a two-lane across section. Figure 3-1 shows a typical view of this type of segment. Basic segment with continuous specific upgrade or downgrade Three-lane cross section segment, with the additional lane being a passing lane. Figure 3-2 shows a typical view of this type of segment. Segment with an unsignalized intersection. Figure 3-3 shows a typical view of this type of segment. Three-lane cross section segment, with the additional lane being a center left-turn lane or a right-turn lane Segment terminating into a multilane highway Segment with an isolated signalized intersection

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24 Figure 3-1. Typical basic two-lane, two-way highway segment Figure 3-2. Typical two-lane, two-way highway with a passing lane

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25 A two-lane highway with signalized intersections is a type of facility composed of isolated signalized intersections, and the basic two-lane highway. A two-lane roadway generally extends from one signalized intersection to the next signalized intersection. This type of facility is typically located in a rural area, but the signal may be present in a small town. Figure 3-3. Typical two-lane, two-way highway with an unsignalized intersection Figure 3-4 shows a typical view of a two-lane highway with a signalized intersection. The main features are as follows: Roadside development is not intense. Density of traffic access point is not high. Signalized intersections are more than 2 miles apart. These conditions result in a smaller number of traffic conflicts, smoother flow, and dissipation of the platoon structure.

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26 Figure 3-4. Typical two-lane, two-way highway with a signalized intersection 3.1.2 Service Measure Consistency LOS is a qualitative designation of the operational conditions within a traffic stream based on performance measures such as speed, travel time, freedom to maneuver, traffic interruptions, comfort, and convenience. Six levels of service are defined in the HCM, using the letters A through F for each type of facility, where A is good, and F is bad. The performance measure chosen to base LOS upon is referred to as a service measure. For application in the segment LOS analysis, every type of segment has its own service measure based on to determine its LOS. When performing the facility-level operational analysis, occasional inconsistencies can arise because of different service measures being applied. For example, in the two-lane highway with an isolated intersection, the combination of average travel speed and percent time-spent-following is used as the service measure to evaluate the level of

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27 service on the basic two-lane highway segment, however the service measure for a signalized intersection is based on control delay. In the HCM 2000, the measure of operational quality used for point locations is not related to highway segment. Thus, anomalies are possible when changing from one facility type to another. Therefore selecting an appropriate service measure is a key issue in the development of operational analysis for the two-lane highway at the facility level. There are basically two methodological approaches that can be taken for an operational analysis of a facility composed of different types of segment. They are: 1. Each segment uses the service measure(s) already specified for it in the HCM 2000. The LOS of the entire facility is determined by combining the LOS of each segment in some manner. 2. A common service measure is used for each segment and point. LOS of the entire facility is determined by the aggregated service measure. With the first methodology, no unified facility-wide service measure is applied for the segments of the entire facility. Each segment or point uses its own service measure(s) defined in the HCM 2000. Because of different service measures (e.g., ATS, PTSF, or control delay) being applied, inconsistencies can arise. For example, when determining the level of service of a two-lane highway with multiple signals, the combination of average travel speed and percent time-spent-following is used as the service measure to evaluate the level of service on an uninterrupted flow two-lane highway segment; however the service measure for a signalized intersection is based on control delay. Thus, anomalies are possible when changing from one segment type to another. Another drawback of this methodology is the aggregation of the point and segment LOS grades into an estimate of the LOS grade for the entire facility. In the HCM 2000, the measure of operational quality used for point locations is not related to highway

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28 segments. It is very difficult to combine the LOS of points with that of segments. Equation 3-1 gives an example method of aggregating the LOS grades of segments and points weighted by the segment length. niiniiiLLLOSLOS11 (3-1) Where: LOS: the level of service of the entire facility, LOS i : the level of service of segment i, L i : the length of segment i, ft, and n: the number of segments. With this approach, segment LOS values are weighted by the segment length; however, LOS is not a quantitative value. It is simply a measure of user satisfaction for that service along the roadway. It is difficult to accurately convert the LOS grade into the corresponding numerical value for aggregation. Even though a certain conversion method is available, because each segment type has its own strategy to determine the LOS, every segment type needs a unique conversion method, which makes the LOS combination method somewhat complicated and possibly subjective. In the HCM 2000, Chapter 15, the average travel speed is used as the service measure on the urban street with multiple signalized intersections at a spacing of 2.0 miles or less. The method using a common service measure for a facility consisting of multiple different segment types is a good reference. In the second methodology, a common service measure would be applied to every segment of the entire facility. The service measures at each segment are aggregated to obtain an estimate of service measure

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29 for the entire facility. The LOS of the entire facility is determined by this aggregated service measure. The unified facility-wide service measure not only avoids many disadvantages of the application of multiple service measures, but also provides a Measure of Effectiveness (MOE) describing traffic operations in terms discernible by motorists from the scope of the entire facility. The proposed second method would also maintain some fidelity to the Highway Capacity Manual by using the existing methodologies for two-lane highway segments and signalized intersections. For the two-lane methodology (HCM Chapter 20), the method for calculation of average travel speed (ATS) is utilized; however, percent time-spent-following (PTSF) is not utilized. For signalized intersections (HCM Chapter 16), the current method for the calculation of control delay is utilized. By using a time/delay based service measure, this method will be similar to the current HCM methodology for urban streets. For transportation agencies looking to analyze the impacts of adding a lane (or lanes) to a two-lane highway, along with adding some signalized intersections, thus possibly changing the classification to an urban arterial in some sections, this will provide for consistency in the analyses (assuming the LOS thresholds are set accordingly). This methodology will be completely presented and explained in Section 3.2. 3.1.3 Impacts of Signalized Intersection on Adjacent Highway Segments Another important issue in the development of an operational analysis at the facility level is the impacts with different segment types. Continuing research has shown that installing a signalized intersection on a two-lane highway can produce effects on traffic operations of the upstream and downstream two-lane highway segment.

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30 To illustrate the potential effects of an isolated signalized intersection on the two-lane highway operation, CORSIM and TRANSYT-7F programs are used to simulate the operations of a two-lane highway with an isolated signalized intersection. 3.1.3.1 Effects of intersections on the upstream two-lane highway operation When vehicles approach the signalized intersection facing a red signal indication, drivers will safely stop their vehicles with sufficient sight distance to avoid entering the intersection or colliding with queued vehicles. Here CORSIM is used to model the variation of average travel speed as vehicles approach the upstream signalized intersection. Six CORSIM simulations are made with 30 replicate runs for each. The six conditions are as follows: Table 3-1. Traffic simulation conditions Traffic Volume (veh/h) With or Without Signal 1 600 With 2 600 Without 3 1000 With 4 1000 Without 5 1400 With 6 1400 Without The operational effects of a signalized intersection on the two-lane highway based on average travel speed are shown in Figure 3-5. This figure is directly derived from preliminary simulation runs. Figure 3-5 shows a comparison of the modeled average speed as it varies along a two-lane highway with an isolated signalized intersection and with no isolated signalized intersection under different traffic flow levels. As seen in Figure 3-5, on the two-lane highway segment upstream of the signalized intersection, when vehicles enter the basic two-lane highway segment, the difference in the values of

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31 average travel speed is very small. The average travel speeds along the two-lane highway with an isolated signalized intersection are very much in agreement with those with no isolated signalized intersection. When near to the signalized intersection (about 1000 ft before the stop line of signalized intersection), the difference in average travel speed becomes very large. The average travel speed under the condition with an isolated signalized intersection drops dramatically because of queuing in front to the signal. After the signalized intersection, average traffic speed quickly increases and returns to its former level. So installing a signalized intersection on a two-lane highway significantly affects traffic operations on the upstream two-lane highway segment based on average travel speed, and the effective length of a signalized intersection is greater than its actual length. The effective length of the upstream influence area of a signalized intersection is defined from the dividing point, at which vehicles begin decelerating to the stop line of this signalized intersection

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Operational Effects of an Isolated Signalized Intersection on Average Travel Speed051015202530354045500500100015002000250030003500Position Along Roadway (ft)Average Travel Speed (mph) Traffic Flow = 600 vph Traffic Flow = 1000 vph Traffic Flow = 1400 vph Without Signalized Intersection Intersection Two-lane highway segment Upstream influence area of a signal 32 Figure 3-5. Effect of a signalized intersection on average travel speed

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33 3.1.3.2 Effects of intersections on the downstream two-lane highway operation After passing through the signalized intersection, the vehicle platoon will go into the downstream two-lane highway. The platoon dispersion pattern is affected not only by the upstream signalized intersection, but also by the right-turn vehicles and left-turn vehicles from minor streets. There are three movements that contribute to the flow profile, as follows: through movement from the major street right-turn movement from the minor street left-turn movement from another minor street The start-and-stop operation of signals on the two-lane highways tends to create platoons of vehicles that travel along a two-lane highway link. Here TRANSYT-7F is used to model the dispersion of these platoons as they progress along the downstream two-lane highway segment. In TRANSYT-7F, for each time interval (step), t, the arrival flow downstream is found by the following recurrence equation [9]: )1()()1( TttTtvFvFv (3-2) Where: )(Ttv : predicted flow rate (in time interval of the predicted platoon); v t : flow rate of the initial platoon during step t; : an empirical factor, generally 0.8; T: the cruise travel time on the link in steps; and F: a smoothing factor (3-3) 1)1(TF Where:

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34 : platoon dispersion factor (PDF) Equation 3-3 is based on field studies by Hillier and Rothery [10]. The factor has been found by researchers to best represent measured dispersion on typical urban streets in the U.S. when it was set at 0.35. This PDF will vary to consider site-specific factors such as grades, opposing flow interference and other sources of impedance. The diagrams below illustrate the nature of platoon dispersion on the downstream two-lane highway of a signalized intersection. As traffic moves downstream, the initially tight platoon formed from the departing queue tends to disperse the farther downstream it travels. Because drivers tend to maintain safe headways, or spacing, between vehicles and often travel at different speeds, the platoon tends to spread out a few moving ahead and some dropping back. The flow rate decreases with time as the platoon reaches each point of observation. They are the snapshots of the traffic flow at the different observation stations of the downstream link (the average traffic flow is 1200 veh/h). The first diagram (Figure 3-6) illustrates a platoon after it has traveled 300 feet after being stopped at the upstream signalized intersection. The most intense portion of the platoon is at a rate higher than 1870 veh/h, and the lowest portion is at a rate near 0 veh/h. The platoon has spread out extremely unevenly. At this point, the timing plan of the upstream signal and traffic streams from the minor streets produce significant effects on the pattern of platoon dispersion. As traffic moves downstream, the initially tight platoon formed from the departing queue tends to disperse the farther downstream it travels. The second diagram (Figure 3-7) illustrates the same platoon after traveling one-full mile, or 5280 feet. Notice that after a full-mile, the most intense portion of the platoon is a rate slightly higher than 1500

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35 veh/h, whereas after 300 feet the most intense portion of a platoon is approximately 1900 veh/h. At this point, the platoon has spread out to cover the whole portion of the cycle. The effect produced by the upstream signal on the platoon dispersion becomes smaller. Figure 3-6. Platoon dispersion, 300 ft from the upstream signalized intersection Figure 3-7. Platoon dispersion, 5280 ft from the upstream signalized intersection

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36 Figure 3-8. Platoon dispersion, 10560 ft from the upstream signalized intersection The same phenomenon can be observed from the third diagram (Figure 3-8), which illustrates the same platoon after traveling 2 miles, or 10560 feet. The platoon has spread out more evenly and covered the whole portion of the cycle. The most intense portion of the platoon is about 1400 veh/h, which is near to the average flow rate of 1200 veh/h. At this point, the effect produced by the upstream signal on the platoon dispersion is negligible. Based on the above analysis, it can be determined that the upstream signalized intersection and traffic streams from the cross street alter the pattern of platoon dispersion. The degree of platoon dispersion in turn directly affects vehicle delay, speed, queuing, and other measures of effectiveness. Given the potential impact of a signalized intersection on downstream two-lane highway operations, it is necessary to investigate the effects further when performing an operational performance assessment of two-lane highway facilities. To quantify the

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37 effect of a signalized intersection on the downstream two-lane highway segment, a key issue is to determine this effective length of influence area, downstream segment of the signalized intersection. 3.2 Methodological Approach Based on the discussion in the former section, using a common service measure for the entire facility is preferred. A two-lane highway with an isolated signalized intersection will be used as a model. This section begins with a discussion of service measure selection, facility segmentation for a two-lane highway with isolated intersections. Next the section presents an overview of the operational analysis procedures for a two-lane highway with an isolated signalized intersection. 3.2.1 Service Measure Selection In this methodology, a common service measure is applied to every segment of the entire facility. The LOS of the entire facility is determined by this aggregated service measure. One of the key steps in the methodology is the selection of a service measure(s) used to define the overall level of service for the facility. Based on the features of the two-lane highway with occasional signalized and unsignalized intersection, some candidate service measures are estimated. They are described as follows: Volume to Capacity Ratio (v/c) The v/c ratio is often used as a measure of the sufficiency of existing or proposed capacity. According to the 2000 HCM, this v/c ratio measure of capacity sufficiency of the overall intersection is a good indication of whether the physical geometry design features and the signal design provide sufficient capacity for the intersection. But the ratio is not sensitive to speeds and travel time. With an acceptable LOS grade, a v/c ratio may indicate that the same facility is operating at or near all capacity.

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38 Conversely, road segments operating at deficient levels of service may have an acceptable v/c ratio in cases where the adjoining intersections are not operating efficiently. Generally, the v/c ratio is used as a measure of the sufficiency of existing or proposed capacity. The ratio however, is not sensitive to speeds and travel time. The v/c ratio is better as a measure of the capacity sufficiency, but not good as a measure of the quality of service. The combination of v/c ratio and other performance measures may be better. Average Travel Speed (ATS) ATS reflects the mobility function of traffic facilities. Speed, as represented by ATS, is a very important part of the LOS definition and is also easy for the public to understand. And it is easily calculated using the data that is already being collected. As a space-average measure, ATS can be estimated in the field by travel time studies or by measure of spot speeds. One potential drawback to the use of average travel speed as the single service measure for two-lane highways is that it is not as sensitive as PTSF to the relative balance between passing demand and passing supply. Percent Time-Spent-Following (PTSF) Given the platooned nature of traffic on the two-lane highway, PTSF represents freedom to maneuver and the comfort and convenience of travel on a two-lane highway. However, some researchers [5] think this measure is not appropriate for application to developed, tourist-oriented sections, such as US Route 1 in the Florida Keys, on which motorists are more concerned about the ability to maintain a reasonable speed. PTSF is also a space-averaged measure, which is difficult to measure directly in the field. While the HCM suggests that it be estimated as the

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39 percentage of vehicles traveling at a headway of 3 seconds or less at a representative point, the LOS estimation is very sensitive to the headway threshold [11]. Both ATS and PTSF are measured over a section of roadway. In the highway structure system of the HCM, the signalized intersection is regarded as a point, or a segment with a short length, so ATS, PTSF, or their combination is a conceptually adequate service measure for two-lane highway segments, but a poor one for the signalized intersection by itself. So ATS, PTSF, or their combination is not a good facility-wide service measure for the facility consisting of two-lane highway segments and signalized intersections. Travel Time Travel time, particularly in the context of reliability, is gaining momentum as a performance and service measure for some types of facilities. Travel time is essentially the same performance measure as speed (it is simply the reciprocal). However, just like speed, travel time alone is not sufficient as a service measure over a length of two-lane highway facility. It would also need to be qualified per some unit distance (e.g., min/mi). In this situation, it is generally a simple task to convert to other time-based measures if so desired. Currently, for the purposes of the HCM 2000 methodologies, speed is still generally used in preference to travel time. Percent Free Flow Speed (PFFS) PFFS is defined as the ratio of vehicle average travel speed to free flow speed. Washburn, et al. [5] proposed percent free flow speed as the primary performance measure for two-lane highways in developed areas. This measure makes some sense for these areas due to the fact that drivers probably do not have much expectation for

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40 passing in these areas and they are willing to tolerate following other vehicles as long as their speed is close to the desired free-flow speed. Density Density is used as the primary service measure for the types of uninterrupted flow facilities, such as freeway and multilane highway. Given the platooned nature of traffic on a two-lane highway, density is much less evenly distributed on a two-lane highway than on a freeway or multilane highway [11]. Density is not a good service measure for the two-lane highway facility. Percent time-spent-following does a much better job of representing density; percent time-spent-following is the percentage of the total travel time that drivers spend traveling in local high-density conditions. An additional difficulty with density is that direct measurement of it in the field is difficult, requiring a vantage point for photographing, videotaping, or observing significant lengths of highway. Furthermore, conceptually it does not work for signalized intersections. Control Delay Control delay includes Movements at slower speed and stops on intersection approaches as vehicles move up in queue position or slow down upstream of an intersection [1]. It is the principal service measure for evaluating LOS at intersections, which are point locations within a traffic network. However, the measure of operational quality of effectiveness used for point locations can not be used for highway segments, such as two-lane highway segments. Percent Time-Delayed Percent time-delayed is defined as the percentage of the travel time that vehicles on a given roadway segment must travel at speeds less than their desired speed due to

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41 inability to pass or traffic control during some designated time interval. Percent time-delayed is a good performance measure for interrupted-flow facilities, such as two-lane highways with occasional signalized intersections. It reflects the effects of speed reductions by motorists due to restrictive roadway geometry, traffic control, and other traffic, and represents the degree to which drivers are forced to travel at speeds less than their desired speed. Just like other delay-related performance measures, percent time-delayed also has a direct economic interpretation and can be used in economic studies if the monetary value of a travlers delay can be established. The primary drawback of percent time-delayed as a performance measure is the difficulty of measuring it in the field. Table 3-2. Service measure evaluation Undeveloped uninterrupted two-lane segments Developed uninterrupted two-lane segments Intersection influence area Facility incorporating two-lane highway and signalized intersection Volume/Capacity Ratio F F F F Average Travel Speed G G P P Percent Time-Spent-Following E F P P PTSF and ATS E E P P Travel Time G G P P Percent Free-Flow-Speed G E P P Density F F F F Control Delay P P E P Percent Time-Delayed G G G G Note: E = excellent, G = good, F = Fair, P = poor Table 3-2 summarizes the evaluation of potential service measures for a two-lane highway with signalized intersections. Based on a review of the advantages and disadvantages of candidate service measures discussed above, it is concluded that percent time-delayed is an appropriate selection as the single service measure for the interrupted-flow facility of a two-lane highway with signalized intersections. Percent time-delayed is a measure that directly relates to the drivers experience. It not only represents freedom to

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42 maneuver and the comfort and convenience of travel on a two-lane highway, but also reflects the effects of speed reductions due to traffic control (e.g., signalized intersection, stop sign), and due to restrictive geometric features (e.g., vertical grade, horizontal curve, no-passing zone), and other traffics (e.g., opposite traffic flow, heavy vehicles). 3.2.2 Facility Segmentation To perform an operational analysis for a facility consisting of different segment types, and obtain the LOS of the facility, the entire facility is divided into several segments. Thus, the analysis methodology must prescribe how to segment the facility. In the HCM 2000, Chapter 15, Urban Streets, presents the methodology for evaluating arterials in urban and suburban areas with multiple signalized intersections at a spacing of 2.0 miles or less. In this methodology, the urban street is divided into segments, which is the full distance from one signalized intersection to the next. Figure 3-9 illustrates the segmentation method for this methodology. Running time is computed for each segment, along with control delay at each signalized intersection. In this methodology, the signalized intersection is regarded as a point location within a traffic network, and control delay is regarded as a typical point performance measure without covering any distance. In the HCM 2000 [1], the definition of control delay implies that control delay happens not at a point, but actually within a certain distance. Although the time lost due to slow movement before and after a stop is technically part of the running time, it is also included in control delay. Thus, this segment division method introduces error due to the segment between intersections being longer than they should. In the HCM 2000, Chapter 16, Signalized Intersections, presents the methodology for evaluating isolated signalized intersections. In this methodology, the signalized intersection is regarded as a single isolated traffic control installation. So the length of the

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43 signal influence area is not a key factor in determining control delay, or in the decision of LOS based on control delay. When evaluating highways with multiple signalized intersections, the signalized intersection should not be regarded as an isolated point. The impacts between signalized intersections and highway segments should be taken into account. In Sections 3.1.3.1 and 3.1.3.2, it has been shown that the installation of a signalized intersection actually affects the operations on the highway segments, and the signal influence area does extend a certain length. So when evaluating a two-lane highway with signalized intersections, the signalized intersection is not regarded as a single point, but as a segment with a certain length. Figure 3-10 shows the division of a two-lane highway with multiple isolated signalized intersections. The whole facility is divided into three types of segments, described as follows: Type 1: the basic two-lane highway This type of segment may be located in the upstream or downstream of the signalized intersection, but beyond the signal effective length. These segments are not affected by signalized intersections. Type 2: the signal influence area In the highway structure system of HCM 2000, the signalized intersection is defined as a point; the boundary between segments. In this operational analysis methodology, it will be regarded as a segment with a certain length, which is composed of not only its own actual length, but also the deceleration and acceleration lengths. The length of the signal influence area corresponds to the three components of control delaydeceleration delay, stop delay, and acceleration delay. Type 3: the affected downstream segment This type of segment is still the two-lane highway, but affected by the upstream signalized intersection. Potential operational effects on this segment are produced by the upstream signalized intersection and traffic flows coming from the cross street. Note the length of this type of segment does not include the acceleration length of the signal influence area. The lengths of these different segment types should add up to the total length of the analyzed facility.

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Roadway Segments Figure 3-9. Segment division of a two-lane highway with multiple isolated signalized intersections 44

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Figure 3-10. Facility segmentation of a two-lane highway with multiple isolated signalized intersections 45

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46 3.2.3 Overview of Computational Methodology In this methodology, a common service measure would be applied to every segment of the entire facility. The service measures at each segment are aggregated to obtain an estimate of the overall service measure for the entire facility. The LOS of the entire facility is determined by this aggregated service measure. An example of analyzing a two-lane highway with signalized intersections using this methodology is provided here. Percent time-delayed is applied as the common service measure for the whole facility composed of two-lane highway segments and signalized intersections. The first step in this analysis is to segment the facility based on the features of segment type. The second step is to determine the free-flow speed. The free-flow speed is used to determine the average travel speed and delay time at each segment. The basic free-flow speed for the two-lane highway is observed at basic conditions and ranges from 45 to 65 mile/h, depending on the highways characteristics. The speed study should be conducted at a representative site within the study section. The best location to measure free-flow speed on the two-lane highway is mid-block and as far as possible from the nearest signalized or stop-controlled intersection. If field observation of free-flow speed is not practical, free-flow speed on the two-lane highway may be estimated using the method presented in the HCM 2000. The next step in the analysis is to perform operational analysis at the point and segment levels. At the first type of segment, which is the basic two-lane highway sections, and not affected by the signalized intersection, the average travel speed can be calculated using the two-lane highway procedure presented in Chapter 20 of HCM 2000.

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47 The length of the conventional two-lane highway segment is determined by the actual placement of the signalized intersection within the analysis section. At the second type of segment, which is the signalized intersection influence area, the control delay is the portion of the total delay for a vehicle approaching and entering a signalized intersection. Control delay concludes the delays of initial deceleration, move-up time in the queue, stops, and acceleration. It can be calculated using the signalized intersection procedure presented in Chapter 16 for the through-traffic lane group. The length of the signal influence area includes the deceleration length, stopping length, and acceleration length. The third type of segment is the downstream segment, affected by the upstream signalized intersection, and the traffic flow coming from the cross streets. The potential impacts of the signalized intersection on this segment will be assessed further in the term of average travel speed. The effective length of influence area downstream of the signalized intersection is also decided. For the analysis of this type of segment, statistical methods and TWOPAS simulation model will be used to quantify the impacts. The methodology will be presented in Chapter 4. Once average travel speed on the two-lane highway segments and control delay within the signalized intersection are determined, the delay time on the two-lane highway segments and the signalized intersection can be calculated using the following equations. Delay time on the two-lane highway segment: FFSLSLDHHHH (3-4) Where: : delay on the two-lane highway segment, s/veh HD

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48 HL : length of two-lane highway segment, ft FFS : free flow speed for the two-lane highway segment, ft/s HS : average travel speed for two-lane highway segment, ft/s Control delay at the signalized intersection: 321)( ddPFdDS (3-5) Where: : control delay per vehicle at the signalized intersection, s/veh SD : uniform control delay, s/veh 1d : incremental delay, s/veh 2d : initial queue delay, s/veh 3d PF: uniform delay progression adjustment factor After estimates of delay time at the segment and point levels are obtained, segment and point delays are then added together to obtain the entire facility estimate. Percent time-delayed is then computed through dividing total delay time on the entire facility by the total travel time at the free-flow speed on the entire facility. Equation 3-6 shows the aggregation of point and segment results to obtain an estimate of percent time-delayed for the entire facility. After the facility-wide performance measure, percent time-delayed is obtained, the facilitys LOS grade can be determined based on the LOS table. An initial set of thresholds will be established as part of this research, but further research on this issue will likely be warranted. Figure 3-11 illustrates the analysis procedure for determining LOS on the two-lane highway with signalized intersections.

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49 SHSHSHSSHHSHSHLLLFFSLFFSLDDPTD,,, )()( (3-6) Where: PTD: percent time-delayed per vehicle for the entire facility, % D H : delay time per vehicle for the two-lane highway segment, s/veh D S : delay time per vehicle for the signalized intersection influence area, s/veh FFS H : free flow speed for the two-lane highway segment, ft/s FFS S : free flow speed for the signalized intersection influence area, ft/s L: length of the entire facility, ft L H : length of the two-lane highway segment, ft and L S : length of the signalized intersection influence area, ft

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50 Input ----Roadway data----Traffic data----Control data Free-Flow Speed (FFS)----Determine free-flow speed Divide the facility into segments Type 2:Signalized or Unsignalized Intersection Influence Area Type 3: Affected Downstream Segment Compute ATS Compute EPF Compute control delay Determine effective length on ATS Type 1: Basic Two-lane Highway Segment Determine effective factor on ATS Determine Percent time-delayed-----By segment-----Over entire facility Compute ATS Determine LOS over entire facility Determine effective length of the intersection influence area Determine segment length Figure 3-11.Flow diagram of two-lane highway facility operational analysis methodology

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51 In developing this methodology, some simulation and analysis methods were used at each methodological step. Table 3.3 summarizes those programs and methods used. Table 3-3. Summary of programs used at each step Step 1: Divide the facility into segments. Facility is divided into segments based on its geometric conditions. Segments in the facility are not regarded as isolated. The interactions between different segments are also taken into account. Step 2: Determine the free-flow speed. The methods presented in the HCM 2000 are used field measurement, or estimating free-flow speed. (Chapter 20, Page 20-4, 20-5) Step 3: Determine segment length. 3.1 Determine the length of the signalized intersection influence area The length of signal influence area is the sum of three components, deceleration distance, queue length, and acceleration distance. Acceleration distance can be determined using the linearly-decreasing acceleration model. The deceleration distance and queue length are determined using the CORSIM simulation program and regression analysis. 3.2 Determine the length of the affected downstream segment The length of the affected downstream segment is determined using the TWOPAS simulation program and regression analysis. The method is built upon work done previously by Dixon, et al. 3.3 Determine the length of the TWSC intersection influence area The length of TWSC influence area is the sum of three components, deceleration distance, queue length, and acceleration distance. The Synchro/SimTraffic program was used to determine the queue length. Step 4: Calculate the unaffected average travel speed on basic two-lane highway segments. The analysis methods presented in Chapter 20 of the HCM 2000 are used to calculate the average travel speed on basic two-lane highway segments. Step 5: Calculate control delay at the signalized or unsignalized intersection influence area. The analysis methods presented in Chapter 16 of the HCM 2000 are used to calculate control delay at the signalized intersection. The analysis methods presented in Chapter 17 of the HCM 2000 are used to calculate control delay at the Two-Way Stop-Controlled intersection. Step 6: Determine average travel speed on the affected downstream segment. An adjustment factor is used to account for the effects of the upstream signalized intersection on the downstream highway segment. The values of adjustment factor are determined using the TWOPAS simulation program and regression analysis. Step 7: Determine the delay time at every segment. The delay time at every segment is calculated using Equations 3-4 and 3-5. Step 8: Determine the percent time-delayed and LOS of the entire facility. The percent time-delayed is calculated using Equation 3-6. LOS is determined from Table 5-8 (Chapter 5).

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52 In this methodology, three simulation programs are selected to simulate traffic operations on the two-lane highway in the vicinity of an intersection. The reasons why they were selected are presented in Table 3-4. Table 3-4. Simulation models evaluation Simulation Model Evaluation CORSIM CORSIM, developed by the Federal Highway Administration, is the most widely used and accepted traffic simulation model in the U.S. It has the ability to simulate traffic operations on a two-lane roadway and includes detailed modeling of traffic signal operations. In addition, the CORSIM simulation model simulates the traffic system on a vehicle-by-vehicle basis by updating roadway position, speed, acceleration, and other state variables in discrete time steps. The ability to calibrate, modify, and manipulate these parameters is a key characteristic of the CORSIM simulation model amenable for use to determine the effective length of the signal influence area. CORSIM cannot simulate passing maneuvers using the on-coming lane of traffic. However, experience shows that drivers usually do not undertake passing maneuvers in the vicinity of a traffic signal. Under this assumption, it is feasible to use a program such as CORSIM to model vehicular operations on a two-lane roadway in the vicinity of a traffic signal, and determine the effective length of the signal influence area on the upstream two-lane highway segment. TWOPAS TWOPAS is the only simulation program that is able to simulate the passing maneuver operation on the two-lane highway using the opposing lane, and was developed with U.S. data. Meanwhile the input variable, Entering Percent Following reflects the potential effects of a signalized intersection on the downstream two-lane highway operations. In this study, TWOPAS was used to simulate the effects of the signalized intersection on the downstream segment. Synchro and SimTraffic Synchro is a complete software package for modeling and optimizing traffic signal timing. SimTraffic is a companion product to Synchro for performing microscopic simulation and animation. SimTraffic uses a Synchro file for input. It is very convenient to obtain the queue information from its simulation output. In Synchro, there are two options for reporting the intersection statistical information, the Synchro method or the HCM method. The HCM method is used to determine the queue length to maintain fidelity to the existing HCM.

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CHAPTER 4 DEVELOPMENT OF FACILITY SEGMENTATION COMPUTATIONS The methodology developed in Chapter 3 divides the entire facility into three types of segments. They are the basic two-lane highway, the signalized intersection influence area, and the affected downstream two-lane highway segment. In this methodology, the overall LOS for the facility is calculated by aggregating the service measure values of the segments, as weighted by segment length. The focus of this chapter is the determination of the length of each of the component segments of a two-lane highway facility. Here the relation of the signalized intersection influence area and the affected segment downstream of the signalized intersection is clarified again. The components of the signal influence area include deceleration distance, stopping distance, and acceleration distance, which are consistent with those of control delay defined in the HCM 2000deceleration delay, stop delay, and acceleration delay. The segment delay time for the signalized intersection influence area is determined by the intersection control delay. The affected downstream segment is still affected by the upstream signalized intersection. As the traffic stream discharges from the upstream intersection into the downstream highway segment, it will take some distance for traffic to return to the same flow condition as before the influence of the signal. The delay time for the affected downstream segment is determined by the difference in free-flow travel time and actual travel time. This chapter includes two sections. Section 1 presents three methods to determine the length of a signalized intersection influence area and their advantages and 53

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54 disadvantages are evaluated. Section 2 explores the methodology to determine the length of the downstream segment affected by the upstream signal. How to accurately define the headway distribution and calculate the parameter of EPF is discussed in this section. Finally, this methodology is verified by comprehensive comparisons with other simulation programs. 4.1 Effective Length of the Influence Area Upstream of the Signalized Intersection This section discusses the methodology of determining the effective length of the signalized intersection influence area. Three methods are presented. The first method is to apply the recommended length in FDOTs 2002 Level/Quality of Service Handbook; the second one determines the length of a signalized intersection influence area using the HCM equations; the third one is to apply simulation method. 4.1.1 Recommended Length in FDOTs 2002 Level/Quality of Service Handbook In FDOTs 2002 Level/Quality of Service Handbook, for a preliminary engineering analysis FDOT recommends breaking the facility into uninterrupted and interrupted flow segments [4]. The interrupted flow intersection segments, intersection influence areas, extend 0.5 miles in length centered on the midpoint of the crossing facility. The LOS for this influence area is determined by the intersection LOS. Figure 4-1 shows an example of how to determine the intersection length in the two-lane highway facility with signalized intersections. In this example, a two-lane highway with a signalized intersection extends 10 miles, and the isolated intersection is located at the 6-mile point. The first 5.75 miles would be regarded as a two-lane highway segment, the next 0.5 miles would be regarded as the intersection area, and the last 3.75 miles would be regarded as a two-lane highway segment.

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55 The recommended length in FDOTs 2002 Level/Quality of Service Handbook is only a simplified value. It does not take into account any actual factors such as traffic conditions and signal timing plans in the field. A new method to determine the effective length of the signalized intersection influence area under specific conditions is presented here from a component-based perspective. Two-lane Highway Segment Two-lane Highway Segment Intersection 5.750.250.253.75 Figure 4-1. Length of intersection area 4.1.2 Components of the Signal Influence Area The signalized intersection influence area is the place where control delay happens. Control delay is defined as the total delay due to the signalized intersection and includes deceleration delay, stop delay, and acceleration delay. The length of the signalized intersection influence area should be consistent with control delay, and its components correspond to those of the control delay. That is, the components of the signalized influence are deceleration length, stopping length, and acceleration length. The detailed distance-time diagram shown in Figure 4-2 is useful for defining the general shape of the

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56 relationship of control delay (Time), and the length of the signalized intersection area (Distance) associated with a specific vehicle. Figure 4-2 shows the main delay terms at a signalized intersection, and components of the signal influence area. Before Point 1 on the time-distance diagram, the vehicle is moving at a relatively uniform speed. From Point 1 to Point 2, the vehicle decelerates until it stops at Point 2 to join the standing queue before the signalized intersection. The vehicle remains stopped between Points 2 and 3. Between Points 3 and Point 4, the vehicle accelerates until it reaches a uniform speed again at Point 4. Notice that Point 3 is the stop bar. In Figure 4-2, the deceleration distance L D is given by 12LLLD (4-1) Similarly, the stopping distance L S is given by 23LLLS (4-2) Similarly, the acceleration distance L A is given by 34LLLA (4-3) To determine the overall length of the signal influence area, the lengths of each of the three components must be determined. The method to determine the lengths of these three components will be discussed in the following section. Figure 4-3 illustrates several kinds of conditions for which vehicles pass through a signalized intersection. Figure 4-3(a) shows the condition for which vehicles are near the intersection facing a red signal indication and a queue exists in front of the intersection, so drivers will safely stop their vehicles within sufficient sight distance to avoid entering the intersection or colliding with queued vehicles. For this condition, the effective length

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57 is equal to the sum of stopping sight distance (SSD) and queue length. At the end of the red period, the queue length increases to the maximum value. Figure 4-3(b) shows the condition for which vehicles are near the intersection facing a green signal indication, a queue exists in front of the intersection, and drivers do not need to stop their vehicle completely, but still need to decelerate. For this condition, the effective length is still equal to the sum of SSD and queue length. At the end of the green period, the queue length decreases to the minimum value. Vehicle approaches the signal under different conditions. Here the average queue length is used. Figure 4-3(c) shows the condition for which vehicles are near the intersection facing a green signal indication, and no queue exists in front of the intersection. In this case, the effective length is equal to SSD only. When a vehicle randomly arrives at the intersection, it may encounter any condition, where queue length is at a maximum, median, or not present. Based on the above discussion, the upstream effective length of the signalized intersection influence area can be calculated as the summation of stopping sight distance and average queue length. That is, QSSDLU (4-4) Where: L U : effective length of influence area upstream of signalized intersection, ft SSD: Stopping Sight Distance, ft Q : average queue length, ft In the above equation, SSD corresponds to the distance traveled during perception/reaction time plus the braking/deceleration distance, and Q corresponds to the stopping distance (i.e., distance over which queued vehicles are stopped).

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Control delayStopped delayStop barDeceleration beginsAcceleration endsFree flow speedtrajectorySpeed = 0Approach delayVehicletrajectoryTimeDistance12345t1t2t4t5t3L1L2L4L3 Decelerationdistance AccelerationdistanceQueuelength Figure 4-2. Schematic distance-time diagram at a signalized intersection 58

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59 ( a )( b )( c ) Queue Length Safe Braking Distance Queue Length Safe Braking Distance Safe Braking Distance Signal is RedSignal is Green Figure 4-3. Queue length estimation 4.1.2.1 Determining stopping sight distance The stopping sight distance can be calculated using Equation 4-5, as follows: GgagVtVSSDr2211 (4-5) Where: SSD: Stopping Sight Distance, ft V 1 : initial vehicle speed, ft/s t r : perception-reaction time, sec a: deceleration rate, ft/s

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60 g: gravitational constant, ft/s G: roadway grade (+for uphill and for downhill), percent/100 This equation is from AASHTOs Green Book [2]. In this equation, the perception-reaction time is taken as 2.5 seconds and a deceleration rate of 11.2 ft/s 2 (3.4 m/s 2 ) is assumed. Perception-reaction time and initial vehicle speed are two important elements in calculating the stopping sight distance. The perception-reaction time is the time it takes to initiate the physical response, which includes the detection, identification, and decision elements involved in responding to a stimulus. The perception-reaction time used to calculate the stopping sight distance, when vehicles are near to the signalized intersection should be analyzed from the features of actions taken by drivers when near the signalized intersection. Vehicle deceleration when approaching an intersection is an expected event. Perception-reaction time varies depending on whether the event is expected or unexpected, with expected events logically requiring less time. Vehicle deceleration when approaching an intersection is a relatively simple task. Perception-reaction time varies with the complexity of the task. The simpler the task, the shorter the time required for a response. Decelerating vehicles approaching the signalized intersection is an expected event, and it is also a fairly simple task. At the first part of perception-reaction time, vehicles still keep the initial speed; at the ending part of perception-reaction times, drivers begin taking actions to decelerate the vehicles. The AASHTO Green Book [2] suggests a perception-reaction time of 2.5 seconds, which is a design recommendation, accounting for unexpected events or obstacles in the roadway. Based on this recommended value and the characteristics of actions taken by drivers nearing a signalized intersection, the perception-reaction time is assumed to be in the range of 1 second (1 second is typically

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61 used for yellow interval timing calculations). It is also assumed that the latter part of this perception-reaction time will consist of some vehicle deceleration as a driver will lift their foot off the accelerator in preparation for applying the vehicles brakes. Initial vehicle speed is another important element of stopping sight distance. The travel speed is generally inversely proportional to the traffic volumes. When the traffic volume is lower, vehicles approach the intersection at a higher speed; when the traffic volume is higher, vehicles approach the intersection at a relatively lower speed. 4.1.2.2 Determining average queue length Appendix G of Chapter 16 in the HCM 2000 puts forward the concept of the average back-of-queue measure [1] at signalized intersections. In this model the back of queue is the number of vehicles that are queued depending on arrival patterns of vehicles and vehicles that do not clear the intersection during a given green phase. The average back of queue is used as the average queue length, and can be calculated using Equation 4-6: 21QQQ (4-6) Where: Q : maximum distance in vehicles over which queue extends from stop line on average signal cycle, veh 1Q : first-term queued vehicles, veh, and 2Q : second-term queued vehicles, veh The first term, Q, represents the number of vehicles that arrive during the red phases and during the green phase until the queue has dissipated. The first term is calculated using equation 4-7. 1

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62 CgXCgCVPFQLL),0.1min(11360021 (4-7) Where: PF 2 : adjustment factor for effects of progression V L : lane group flow rate per lane, veh/h C: cycle length, sec g: effective green time, sec, and X L : ratio of flow rate to capacity Q 1 represents the number of vehicles that arrive during the red phases and during the green phase until the queue has dissipated. The adjustment factor for effects of progression is calculated by Equation 4-8. LLPLLPsvRCgsvCgRPF11112 (4-8) Where: PF 2 : adjustment factor for effects of progression, veh v L : lane group flow rate per lane veh/h s L : lane group saturation flow rate per lane, veh/h C: cycle length, sec g: effective green time, sec, and R p : platoon ratio The second term, Q, is an incremental term associated with randomness of flow and overflow queues that may result because of temporary failures. This value can be an 2

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63 approximate cycle overflow queue when there is no initial queue at the start of the analysis period. The second term of the average back of queue can be computed using Equation 4-9. 222)(168)1()1(25.0TcQkTcXkXXTcQLbLBLLBLLL (4-9) Where: c L : lane group capacity per lane, veh/lane T: length of analysis period, h k B : second-term adjustment factor related to early arrivals, and : initial queue at start of analysis period, veh bLQ The second term adjustment factor related to early arrivals is calculated using Equation 4-10: ) (360010.0) (360012.06.07.0signalsactuatedgsIksignalspretimedgsIkLBLB (4-10) Where: k B : second-term adjustment factor related to early arrivals s L : lane group saturation flow rate per lane, veh/h g: effective green time, sec I: upstream filtering factor for platoon arrivals 4.1.2.3 Determining acceleration distance Another component of the signal influence area, acceleration distance after the signalized intersection stop bar, can be determined using a linearly-decreasing

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64 acceleration model. Continuing research [12] has shown that the linearly-decreasing acceleration model better represents both maximum vehicle acceleration capacities as well as actual motorist behavior. The linearly-decreasing acceleration model can be rewritten as a differential equation and integrated to derive the following relationships (treating a grade as being constant), as Equation 4-11 through 4-14. It should be noted that this is only part of the full derivation. The full derivation can be found in most traffic flow theory textbooks, for example [13]. Ggvtv (4-11) toevGgaGgav)( (4-12) Ggavvdt0 (4-13) )1()(toevGgatGgad (4-14) Where: v: speed at the end of the acceleration cycle, ft/s v 0 : speed at the beginning of the acceleration cycle, ft/s : acceleration model parameters, based on the design vehicle type g: gravitational constant, ft/s G: roadway grade (+for uphill and for downhill), percent/100 t: time for vehicle to accelerate from beginning speed, v 0 to ending speed, v, sec d: distance for vehicle to accelerate from beginning speed, v 0 to ending speed, v, ft

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65 The equations presented above arising from the linearly-decreasing acceleration model are not quite as simple or as easy to apply as their counterparts based on constant acceleration rates, but they are processed readily by a computer. Transportation and Traffic Engineering Handbook [14] also contained one of the most comprehensive summaries of previous research and field studies of maximum and normal acceleration and deceleration rates. Table 4-1 summarizes acceleration rates, distances traveled, and elapsed time for passenger vehicles on level terrain and under normal operating conditions. Table 4-1. Normal acceleration rates, distance, and elapsed time Final Speed (mph) Initial Speed 15 30 40 50 60 Acceleration Rate (mph/s) 3.3 3.3 3.3 3.1 2.9 Elapsed Time (sec) 4.5 9.1 12.1 15.9 20.9 0 Distance Traveled (ft) 49 200 354 574 929 Acceleration Rate (mph/s) 3.3 2.9 2.5 Elapsed Time (sec) ----3.0 6.8 11.8 30 Distance Traveled (ft) 154 374 729 Acceleration Rate (mph/s) 2.6 2.3 Elapsed Time (sec) ------3.8 8.8 40 Distance Traveled (ft) 220 575 Acceleration Rate (mph/s) 2.0 Elapsed Time (sec) --------5.0 50 Distance Traveled (ft) 355 Source: Reference 14. After the SSD, back of queue, and acceleration length are determined, the length of the signalized intersection influence area can be calculated as the summation of the three components. That is, ASLQSSDL (4-15)

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66 Where: L S : length of a signalized intersection influence area, ft L A : acceleration length, ft The components of the signal influence area, SSD, back of queue, and acceleration length, are consistent with those of control delay defined in the HCM 2000, which are deceleration delay, stop delay, and acceleration delay. A regression model was developed for the relationship of control delay calculated using the methodology presented in the HCM 2000, and the length of the signal influence area as the summation of SSD, average back of queue, and acceleration length. The results indicate that the assumption of a linear relationship is reasonable with an adjusted R-squared value of 0.895. The regression model summary is presented in Table 4-2. Table 4-2. Regression model summary 1.SUMMARY OUTPUT: Regression Statistics Multiple R 0.9469 R Square 0.8966 Adjusted R Square 0.8946 Standard Error 23.9621 Observations 54.0000 2. ANOVA: df SS MS F Regression 1.0000 258814.8753 258814.9 450.7529 Residual 52.0000 29857.5439 574.1835 Total 53.0000 288672.4193 Coefficients Standard Error t Stat P-value Intercept -114.408 8.80784 -12.9893 5.94E-18 X Variable 1 0.105078 0.00495 21.23094 2.79E-27 Lower 95% Upper 95% Lower 95.0% Upper 95.0% -132.082 -96.7335 -132.082 -96.7335 0.095146 0.115009 0.095146 0.115009

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67 In this methodology, the length of a signal influence area is calculated as the summation of its components. In determining the length of each component, especially the SSD and back of queue, several significant factors are not reflected in the calculation formulas, such as the availability of a left-turn bay, the directional distribution of traffic flow, and the percentage of left-turn vehicles in the traffic flow. A new methodology is explored in the next section to fully take into account all major contributing factors, which can affect the length of a signalized intersection influence area. 4.1.3 Simulation and Regression Analysis To fully account for all significant contributing factors affecting the length of a signalized intersection influence area, the method of regression analysis method is applied. Ideally, field data would largely be used to develop the regression model. However, in many cases, available study sites are either too limited and/or data cannot be collected without great complication. Additionally, it is often difficult to collect enough field data to provide a statistically valid sample size. In this study, the simulation method is applied to simulate the operations of a two-lane highway with a signalized intersection. The overall procedure consists of the following four major steps: 1. Select the potential contributing factors that are expected to have an impact on the effective length. 2. Select the appropriate simulation model. 3. Develop the simulation model to simulate the effects of contributing factors on effective length. 4. Develop the regression model. These steps are discussed in detail in the following sections.

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68 4.1.3.1 Contributing factor selection The contributing factors considered include those that are expected to affect the effective length. Many factors can produce effects on the effective length of a signalized intersection. In the following section, traffic data, geometric data, and signal data are discussed, respectively. Traffic Data Traffic data include the hourly traffic volume, a Peak-Hour Factor (PHF), the proportion of trucks and recreational vehicles in the traffic stream, and the directional split (D-factor). Traffic flow rate can be used to represent the traffic conditions by making adjustments to the hourly traffic demand. These adjustments are the PHF, the heavy-vehicle adjustment factor, and the grade adjustment factor. The conversion can be made using Equation 4-16 [1]: HVGPffPHFVv (4-16) Where: v p : passenger-car equivalent flow rate for peak 15-min period, pc/h V: demand volume for the full peak hour, veh/h PHF: peak-hour factor f G : grade adjustment factor f HV : heavy-vehicle adjustment factor Traffic data also include the proportions of through vehicles, left-turn vehicles and right-turn vehicle in the traffic stream. The left-turning vehicles may have a negative effect on the flow of the through movements, particularly when higher percentage of left-turning vehicles may result in lane overflow or obstruction of the through

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69 movements. The directional distribution of traffic flow is another important characteristic of traffic stream. On two-lane highways, lane changing and passing are possible only in the face of oncoming traffic in the opposite lane. There is a strong interaction between the directions of travel on a two-lane highway because passing opportunities are reduced and eventually eliminated as the opposing traffic volume increases. At an intersection, left-turn vehicles execute their turning maneuvers through the gaps of the opposing through traffic stream. When the opposing through traffic volume is high, left-turn vehicles have less opportunity to execute their turning movements. Geometric Data Geometric data include the two-lane highway geometry and intersection geometry. The basic geometric conditions of the two-lane highway and intersection are used to determine the effective length. The existence of exclusive left-or right-turn lanes, along with the storage lengths of such lanes should be noted, as these are important factors in determining the effective length. Signal Data The signalization conditions include control mode (i.e., pre-timed, semi-actuated, and fully-actuated), the phase plan, cycle length, green time, and clearance intervals. In this study, the simplest and most widely used form of signalization, the two-phase pre-timed signal, is used. All left-turn and right-turn movements are made on a permitted basis from shared or exclusive lanes. The cycle length and effective green time are selected as contributing factors to determine the effective length.

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70 Based on the above discussion on traffic, geometric, and signalization conditions, contributing factors are selected for calibration of the upstream length of roadway affected by the signalized intersection. They are: peak volume D-factor percentage of left-turn and right-turn movements cycle length ratio of effective green time to cycle length availability of a left-turn bay 4.1.3.2 Simulation model selection The next step is to select a simulation model to simulate traffic operations on a two-lane highway with a signalized intersection. As reviewed in Chapter 2, TWOPAS rural highway simulation model has the ability to simulate traffic operations on a conventional two-lane roadway. However, the model has no ability to simulate traffic turning on or off the highway at driveways and does not handle signalized intersections. Therefore, the TWOPAS simulation model is not appropriate to determine the effective length of the influence area upstream of the signalized intersection. CORSIM, developed by the Federal Highway Administration, is the most widely used and accepted traffic simulation model in the U.S. It has the ability to simulate traffic operations on a two-lane roadway and includes detailed modeling of traffic signal operations. However, CORSIM cannot simulate passing maneuvers using the on-coming lane of traffic. Before making a decision, TWOPAS was used to simulate the traffic operations on the basic two-lane roadway to study the relation of passing demand, passing capacity, the

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71 percentage of passing zones, the advancing traffic volume, and the opposing traffic volume. CORSIM was used to determine the features that affected performance measure variation on the two-lane highway segment upstream the signalized intersection. These results are presented in Appendix A. After large quantities of simulations, the following conclusions can be drawn from the study: Although on the two-lane highway, passing operations can be performed using the opposite lane in the face of oncoming traffic, the percentage of vehicles undertaking passing maneuvers is rarely more than 6% of the traffic volume under different conditions of advancing traffic flow rate and opposing traffic flow rate. At the same advancing traffic volume level, the difference in average travel speed at the different opposing traffic volume levels is very small, less than 2%; the difference in the average travel speed between 100% no-passing zones and 0% no-passing zones is also small. As the advancing traffic flow rate increases, the difference decreases and gradually becomes negligible. The variance in travel speed due to a downstream signalized intersection is much larger than due to following a slower leading vehicle. As vehicles approach a signal (i.e., within the influence area of the signalized intersection), the spacing between vehicles decreases, and following vehicles are unlikely to pass leading vehicles. Experience has shown that as drivers approach a signal, they generally will be more cautious; thus usually not undertaking passing maneuvers and possibly slowing down even if the signal indication is green. The roadway is also often marked with solid yellow dividing lines (i.e., no passing) in the vicinity of traffic signals. Under this assumption, it is feasible to use a program such as CORSIM to model vehicular operations on a two-lane roadway in the vicinity of a traffic signal, and determine the effective length of the signal influence area on the upstream two-lane highway segment. In addition, the CORSIM simulation model typically simulates the traffic system on a vehicle-by-vehicle basis by updating roadway position, speed, acceleration, and other state variables in discrete time steps. The ability to calibrate,

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72 modify, and manipulate these parameters is a key characteristic of the CORSIM simulation model amenable for use to determine the effective length of the signal influence area. 4.1.3.3 Simulation model experimental design A two-way, two-lane roadway network with an isolated fixed-time signalized intersection was simulated using CORSIM. It extended 3 miles, and the isolated intersection was located at the 1-mile point. The attributes of the simulated network were set to fulfill the basic conditions for a two-lane highway and signalized intersection according to the HCM 2000. These were defined as: Design speed greater than or equal to 60 mi/h Lane widths greater than or equal to 12 ft Clear shoulder wider than or equal to 6 ft Level terrain All passenger cars in traffic stream Two phase pre-timed signal Two sets of CORSIM base road network were developed. One is the signalized intersection with a 250-foot left-turn bay; the other is the signalized intersection without a left-turn bay. Once the base road networks were developed, the values for the contributing variables were systematically changed to model different scenarios. The values for each contribution variable are displayed in Table 4-3 and Table 4-4. The different inputs resulted in a combination of 243 (33333=243) simulation scenarios for the base network without a left-turn bay. Ten simulation runs were made for each scenario to account for the variability in stochastic micro-simulation program output. A

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73 total of 2430 simulated runs were performed. The length of simulation time for each run was 15 minutes. Table 4-3. Variable input values (with a left-turn bay) Peak Volume (pc/h) Cycle length (sec) g/C Percentage of left-turn and right-turn vehicles 400 60 0.55 5% 800 75 0.65 10% 1200 90 0.75 15% Table 4-4. Variable input values (without a left-turn bay) Peak Volume (pc/h) D-Factor Cycle length (sec) g/C Percentage of left-turn and right-turn vehicles 400 0.50 60 0.55 5% 700 0.55 75 0.65 8% 1100 0.60 90 0.75 11% At an intersection, left-turn vehicles execute their turning maneuvers through the gaps of the opposing through traffic stream. When the opposing through traffic volume is lower, the left-turn vehicles can execute their turning movements. When the opposing through traffic volume is very high and left-turn vehicles cannot execute their turning movements, the left-turn vehicles can stay temporarily at the left-turn bay, and will not block the advancing through traffic behind them. So when developing the effective length model for the signalized intersection with a left-turn bay, the D-factor is not included as a contributing factor. 4.1.3.4 Regression model development After simulation, average travel speeds at the interval of 0.025 miles along the two-lane roadway were obtained from the CORSIM output file. Figure 4-4 illustrates the variations of average travel speed along the two-lane highway with an isolated signalized intersection.

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74 Based on the variation of average travel speed, the effective length of the signalized intersection on the upstream two-lane highway segment can be measured from the bifurcation point, at which point vehicles begin decelerating to the stop line of the signalized intersection, such as the section AO in Figure 4-4. After extracting the needed data, regression analysis was performed to establish the model of the upstream effective length with contributing factors. 05101520253035404550051015202530Position Along Roadway (1/40 mi)Average Travel Speed (mph) Two-lane Highway With Signal Two-lane Highway Without Signal Upsteam Effective LengthIntersection O A Figure 4-4. Average travel speed along the two-lane highway with signal The regression model for the upstream effective length of a signalized intersection with a left-turn bay is developed as follows: (4-17) CgCycleLTVCycleVLenupeff_2444.5%)100/(3041.57 2178.5)100/(2688.42463.432_ Where: Len eff_up : upstream effective length of a signalized intersection, ft V: traffic flow rate, veh/h Cycle: cycle length, sec

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75 g_C: ratio of effective green time to the cycle length, and %LT: percentage of left-turn vehicles in the directional traffic flow The statistical results for the effective length model for the signalized intersection with the left-turn bay (250 ft) are presented in Table 4-5. For a significance level of 0.05 (or 95% confidence), =0.05, and the degrees of freedom, n (k + 1) = 30 5 = 25 df. The critical t value obtained from t-Distribution Table is t 0.05 = 1.708. All the t-stat absolute values are greater than 1.711, so all the variables used in the chosen model are useful. Table 4-5. Regression model (with a left-turn bay) R 2 = 0.95743; Adj R 2 = 0.95519 Coefficient t-stat Intercept 43.2463 4.84765 V/100(Q) 4.2668 29.38653 Cycle (L) 5.2178 11.41796 V/100(L) %LT(L) -57.3041 -3.05196 Cycle (L) gCRatio (L) -5.2444 -9.45781 (L) Linear; (Q) Quadratic The regression model for the upstream effective length of a signalized intersection without a left-turn bay is developed as follows: (4-18) 222_)(%)100/(1171.01 )_(52.4758_59.733669.1 00.440)100/(89.549.3074LTVCgCgCycleDFactorVLenupeff Where: Len eff_up : upstream effective length of a signalized intersection, ft V: traffic flow rate, veh/h DFactor: percentage of traffic traveling in the peak direction Cycle: cycle length, sec

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76 g_C: the ratio of effective green time to the cycle length, and %LT: the percentage of left-turn vehicles in the directional traffic flow The statistical results for the effective length model for the signalized intersection without a left-turn bay are presented in Table 4-6. For a significance level of 0.05 (or 95% confidence), =0.05, and the degrees of freedom, n (k + 1) = 30 5 = 24 df. The critical t value obtained from t-Distribution Table is t 0.05 = 1.711. All the t-stat absolute values are greater than the value of 1.711, so all the variables used in the chosen model are useful. Table 4-6. Regression model (without a left-turn bay) R 2 = 0.77764; Adj R 2 = 0.77199 Coefficient t-stat Intercept 3074.49 3.97573 V/100(Q) 5.89 20.44190 Dfactor (L) -440.00 -2.08639 Cycle (L) 1.69 2.40322 gCRatio (L) -7336.59 -3.08700 gCRatio (Q) 4758.52 2.60546 V/100(L) %LT(Q) 1171.01 3.98667 (L) Linear; (Q) Quadratic When calculating the upstream effective length, Table 4-7 is used for the following conditions: (1): The maximum g/C value for this regression model is 0.8. (2): When the traffic flow rate is less than or equal to 300 veh/h Table 4-7. Upstream effective length with low traffic volume (ft) g/C V (veh/h) 0.5 0.6 0.7 0.8 100 160 130 110 90 200 180 150 130 110 300 210 180 160 140

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77 4.2 Effective Length of the Influence Area Downstream of the Signalized Intersection After passing through the signalized intersection, the vehicle platoon will travel into the downstream two-lane highway. The platoon dispersion pattern is affected not only by the upstream signalized intersection, but also by the right-turn vehicles and left-turn vehicles from minor streets. This section begins with the discussion of Entering Percent Following (EPF) in the TWOPAS model and headway distribution. Then the effect of the signalized intersection on the downstream two-lane highway segment is quantified through the parameter of EPF. Next, the methodology using TWOPAS simulation to determine the effective length of a signalized intersection on the downstream segment is presented. Finally CORSIM simulation is used to validate this methodology. 4.2.1 Entering Percent Following of TWOPAS A study by Dixon et al. [3] concluded that the potential effect of a signalized intersection on the downstream two-lane highway operations was to modify the distribution of headways. The condition with no signalized intersection is represented by assuming randomly distributed headways for entering traffic. However, the signalized intersection in the upstream will modify the headway distribution of the traffic stream entering the two-lane highway. The TWOPAS model is used to simulate the effects of a signalized intersection on the downstream two-lane highway. In TWOPAS, the distribution of headway is defined through the input variable, Entering Percent Following (EPF), which is the percentage of the total vehicles in the direction of travel that are following in platoons when they enter the road being analyzed. Figure 4-5 illustrates an interface of TWOPAS for inputting

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78 traffic data. In this interface, EPF is identified in the text, % Traf in Platoons in Dixon et al.s study, it was assumed that it was appropriate to represent the effects of a signalized intersection through the EPF parameter, the percentage of vehicles following immediately downstream of a signalized intersection. To analyze the potential effect of a signalized intersection on the downstream two-lane highway operation, the key point is how to accurately decide the EPF at the point immediately downstream of a signalized intersection. Figure 4-5. TWOPAS traffic data input interface 4.2.2 Headway Distribution The time headway distribution between vehicles is an important flow characteristic that affects the safety, level of service, driver behavior, and capacity of a transportation system. Previous research [15] has established that the shape of the time headway distribution varied considerably as the traffic flow rate increased. In Dixon et al.s study, the negative exponential distribution is used to define the headway distribution for the different traffic flow levels. For example, for the basic two-lane highway without a

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79 signalized intersection, the EPF parameter is calculated using a cumulative exponential distribution for headways less than or equal to 3.0 seconds, using Equation 4-19: )1100 %3600tqe(Platooned (4-19) Where: q: hourly flow rate of traffic entering the two-lane highway, veh/h t: headway criteria used to define when vehicles are following, (3.0 sec) The simple negative exponential distribution could not completely capture the features of headway distribution. To accurately quantify the effect of an isolated signalized intersection on the downstream two-lane highway segment, the shifted negative exponential distribution and composite distribution are introduced into the Dixon et al. methodology to calculate the EPF parameter. 4.2.2.1 Shifted negative exponential distribution Under very low volume conditions, all the vehicles may be thought of as traveling independent of one another. Any point in time is as likely to have a vehicle arriving as any other point in time. This situation will be classified as the random headway state. The negative exponential distribution can be used to define the time headway distribution for this condition. However, drivers typically maintain a minimum time headway for safety considerations, although their perception of the minimum safe headway is often too low. Thus, the shifted negative exponential distribution can better define the time headway distribution under very low volume conditions. The probability density function of the shifted negative exponential distribution is given by equation 4-20: (4-20) )()(tetf Where:

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80 f(t): probability density function, : user-selected parameter greater than or equal to zero that affects the shift of the distribution, sec, and : parameter that is a function of the mean time headway and can be calculated as: t1 (4-21) The percentage of vehicles in platoon with the shifted negative exponential distribution can be calculated using Equation 4-22: )t)/((tt)(t-e dte t)P(hplatoon 1 11% (4-22) 4.2.2.2 Composite distribution As the traffic flow rate increases, there is increasing interaction between vehicles. Gerlough et al. [16] proposed that the traffic flow consisted of two classes of vehicles: constrained vehicles and free-moving vehicles. According to May [15], the random headway state (Negative exponential distribution) is best suited for very low flow conditions, while the nearly-constant headway state (Normal distribution) is best suited for very high flow conditions. The intermediate headway state lies between the two boundary conditions of the randomand constant-headway states. The composite model is a better alternative to represent the headway distribution as the traffic flow level increases. The composite model approach utilizes the combination of a normal headway distribution for these constrained cars that are in the car-following or platoon mode and a shifted negative exponential distribution for those free-moving vehicles. The composite

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81 distribution represents the time headway distribution well when the traffic flow rate is higher. The percentage of vehicles in platoon with the composite distribution can be calculated using Equation 4-23. t)stt(P)t)/((tNPdtesPeP t)P(hPlatoonedPNP2212111% (4-23) Where: P p : proportion of vehicles in platoon, % P NP : proportion of vehicles not in platoon, % pt : mean headway of the vehicles in platoon, sec Npt : mean headway of the vehicles not in platoon, sec : the minimum time headway for vehicles not in platoon, sec s: standard deviation of normal distribution t: time headway being investigated, sec t : mean headway, sec/veh In the composite distribution, there are four independent parameters that need to be specified: mean and standard deviation of the normal distribution, the proportion of vehicles in platoon, and the minimum time headway for vehicles not in platoon. Numerous calculations and sensitivity analyses of a matrix of the four independent parameters need to be conducted to find the best composite model distribution for each traffic flow level. An example is given here to show how to find an appropriate composite distribution for the traffic flow of 1636 veh/h. Detailed calculations of the theoretical time headway for this traffic flow level are shown in Table 4-8. The

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82 theoretical shifted negative exponential headway distribution, normal headway distribution, composite headway distribution, and the measured time headway distribution are presented graphically in Figure 4-6. The Chi-Squared test is used to access statistically how closely the measured distribution is similar to the theoretical composite distribution. An example is given to compare the measured time headway distribution for the traffic flow level of 1636 veh/h with a composite distribution. The Chi-Squared test calculations are shown in Table 4-9. The individual Chi-Squared contributions are summed, and the calculated Chi-Squared value is found to be 13.94. The number of degrees of freedom is determined to be 10 based on 15 time intervals and 4 parameters required for the composite distribution. Assuming a 0.05 significance level the reference Chi-Squared value is determined to be 18.30. Since the calculated Chi-Squared value is less than the reference Chi-Squared value, the hypothesis is not rejected and the conclusion is that there is no evidence of a statistical difference between the two distributions. Although the composite distribution is the combination of a normal headway distribution and a shifted negative exponential distribution, when the traffic flow rate is lower, a larger difference occurs between the composite distribution and the measured distribution. So in this study, the shifted negative exponential distribution and composite distribution are used together to mathematically describe time headway distribution, including boundary conditions of random headway state and nearly-constant headway state, and the intermediate headway state. Detailed calculations of the theoretical time headway for all four traffic flow levels are presented in tabular form and figure in Appendix B.

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Table 4-8. Composite headway distribution calculation (volume = 1500-1740 veh/h) 6818.0sec,5.0sec,5.1,3182.0sec,5.1sec,2.2sec,7.3 ppPNPNPNPPsEPst 83

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Composite Distribution ( Mean Headway = 2.2 sec)-0.050.000.050.100.150.200.250.01.02.03.04.05.06.07.08.09.010.0Headway (sec)Probability Shifted Negative Exponential Distribution Normal Distribution Composite Distribution Measured Distribution Figure 4-6. Composite time headway distribution 84

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85 Table 4-9. Chi-Squared test calculation Time Headway Group f 0 f t f 0 f t 20)(tff ttfff20)( 0.0 0.5 22 19 3 10 0.4934 0.5 1.0 140 122 18 310 2.5355 1.0 1.5 312 307 4 19 0.0616 1.5 2.0 294 307 -13 164 0.5342 2.0 2.5 209 198 10 102 0.5158 2.5 3.0 125 117 9 74 0.6293 3.0 3.5 78 71 7 47 0.6638 3.5 4.0 46 50 -4 15 0.2955 4.0 4.5 30 36 -5 30 0.8433 4.5 5.0 21 26 -5 21 0.8143 5.0 5.5 13 18 -5 27 1.4748 5.5 6.0 7 13 -7 43 3.2939 6.0 6.5 7 9 -3 8 0.8607 6.5 7.0 7 7 0 0 0.0044 7.0 7.5 3 5 -2 5 7.5 8.0 3 3 -1 1 8.0 8.5 0 2 -2 6 8.5 9.0 2 2 0 0 9.0 9.5 1 1 0 0 > 9.5 3 1 -2 4 1.9678 0.4183 1320 1320 0 41.152CALC n = (I 1 p) = (16 1) 4 = 11. Significance Level = 0.05, 70.192ref 70.1941.15,22refCALC ; Therefore, do not reject null hypothesis 4.2.3 Determining Entering Percent Following Dixon et al. [3] concluded that it was appropriate to represent the effects of a signalized intersection on the downstream two-lane highway operations through the EPF parameters, as long as the percent following immediately downstream of a signalized intersection can be determined. In this study, the methodology for determining Entering Percent Following is based on Dixon et al.s methodology. The main difference from their methodology is the application of distributions for time headway. As discussed in

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86 Section 4.2.2, the shifted negative exponential distribution and composite distribution are introduced into this methodology. Estimation of the percentage of entering traffic following is based on a flow profile immediately downstream of the signalized intersection. A flow profile immediately downstream of the signalized intersection at location A is shown in the Figure 4-7. The A denotes a location immediately downstream of the signalized intersection. As shown in Figure 4-7, there are three movements that contribute to the flow profile: Movement 1: Primary contributing movement. They are through movements from the upstream major street; Movement 2: Secondary contributing movement. They are right-turn movements from the minor street; and Movement 3: Secondary contributing movement. They are left-turn movements from the minor street. As shown in the Figure 4-7, the total cycle-length is divided into three states. The above three movements are charged through the three states. They are: First state: Discharged from the through movement queue during the first phase Second state: Discharge from the through movement without a queue plus any right-turn on red executed during the first phase Third state: Discharge from the right and left turn movements during the second phase Entering percent following at location A can be estimated using equation 4-24: iiaaaaVFVFVVFEPF (4-24) Where: EPF a : percent of vehicles following at Point A, immediately downstream of a

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87 signalized intersection, VF a : total number of vehicles following per cycle at location A, veh VF i : total number of vehicles following per cycle from movement i, veh, and V a : total number of vehicles per cycle at location A, veh Figure 4-7. Two-lane highway traffic flow downstream of a signalized intersection Source: Dixon, Michael P., Michael Kyte, and Satya Sai Kumar Sarepali. Effects of Upstream Signalized Intersections on Two-Lane Highway Operations, Transportation Research Board, Washington D.C., 2004 To determine the EPF a the key point is to decide on the value of the denominator, V a and numerator, VF a Because V a is the summation of the cycle-by-cycle volumes from movements 1, 2, and 3, it can be determined if volumes for movements 1, 2 and 3 and the cycle length are known. This leaves the estimation of VF a the number of vehicles

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88 following at location A, which can be estimated by each movement. The detailed procedure for calculating EPF is presented in Appendix C. Table 4-10 summarizes the values of EPF under different traffic conditions and signal timing plans. Due to the complexity of the calculations, a Visual Basic program was developed to calculate the EPF values. The Visual Basic codes programmed for this research are presented in Appendix D. Table 4-10. Entering Percent Following g/C=0.6 Cycle Length (sec) 60 90 120 Without signal 220 0.2069 0.2978 0.3433 0.1458 440 0.4515 0.4969 0.5197 0.2778 660 0.5988 0.6291 0.6442 0.3962 880 0.7213 0.7441 0.7554 0.5015 Traffic Volume 1100 0.8435 0.8617 0.8708 0.5941 g/C=0.7 Cycle Length (sec) 60 90 120 Without signal 220 0.1192 0.2101 0.2556 0.1458 440 0.3662 0.4117 0.4344 0.2778 660 0.5149 0.5452 0.5803 0.3962 880 0.6372 0.6599 0.6713 0.5015 1100 0.7789 0.7980 0.8071 0.5941 Traffic Volume 1320 0.8657 0.8808 0.8884 0.6745 g/C=0.8 Cycle Length (sec) 60 90 120 Without signal 220 0.0324 0.1233 0.1687 0.1458 440 0.2826 0.3281 0.3508 0.2778 660 0.4334 0.4637 0.4789 0.3962 880 0.5582 0.5789 0.5903 0.5015 1100 0.7184 0.7366 0.7475 0.5941 1320 0.8030 0.8182 0.8258 0.6745 Traffic Volume 1540 0.8915 0.9045 0.9110 0.7434

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89 After estimating EPF a the percent following immediately downstream of a signalized intersection is determined and then input into the TWOPAS model. A series of runs of TWOPAS model are performed to determine the effective length of a signalized intersection on the downstream two-lane segment, and performance measures (average travel speed and percent time-spent-following) of the downstream two-lane highway segment. The detailed procedure is presented in the next section. 4.2.4 Effective Length of a Signalized Intersection on the Downstream Segment In this section, the input variable, EPF will be entered into the TWOPAS simulation model to illustrate the potential downstream effects of a signalized intersection on the two-lane highway operations. Two types of TWOPAS run were made with 10 replicate runs for each. The two conditions are as follows: A traffic stream of 600 veh/h travels along a two-lane highway with no signalized intersection. A traffic stream composed of through vehicles from the main street, left-turn vehicles and right-turn vehicles from the minor streets disperses from the signalized intersection into the downstream two-lane highway. The volumes of these three movements are 400 veh/h, 100 veh/h and 100 veh/h, respectively. A value of EPF = 36.83% was used for the condition with no signalized intersection, assuming a volume of 600 veh/h. A higher value of EPF = 48.04% is used to represent the situation where a signalized intersection is present and modifying the headway distribution of a traffic stream consisting of 400 through vehicles from the main street, 100 left-turn vehicles from one minor street, and 100 right-turn vehicles from the cross-street entering the downstream two-lane highway segment. A 5-mile section of two-lane highway was simulated using TWOPAS with the following conditions: Through movement saturation flow rate, s 1 = 1800 veh/h

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90 PHF = 1.0 100% passenger cars 0% no-passing zones 0% reduced speed zone Level terrain Lane width = 12 ft 50/50 directional split Two-phase timing plan Inter-green time is equal to the lost time per phase Desired speed and speed standard deviation using the recommended default values presented in Table 4-11. Table 4-11. Recommended default values for desired speed by vehicle type Passenger Car Recreational Vehicle Truck Mean Desired Speed (mi/h) 61.5 59.5 59.5 Standard Deviation (mi/h) 5.0 4.0 3.5 When establishing the TWOPAS model, a series of data collection stations were set along the two-lane highway at 100 ft intervals. After simulation, the average travel speed at each data collection station was obtained from the TWOPAS output file. ATS sig,i denotes the average travel speed at the i th data collection station on the two-lane highway with a signalized intersection. ATS wo_sig,i denotes the average travel speed at the i th data collection station on the two-lane highway without a signalized intersection. Figure 4-8 shows the difference between ATS sig,i and ATS wo_sig,i along the two-lane highway downstream of the signalized intersection. Point O in Figure 4-8 is the location of the stop line of the signalized intersection. Point C is the end of the two-lane highway downstream segment. The black thick line is the trendline of the difference between ATS sig,i and ATS wo_sig,i along the roadway. As observed from Figure 4-8, when the traffic stream travels into the downstream segment

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91 from Point O, the difference between ATS sig,i and ATS wo_sig,i becomes larger until it reaches the peak point (Point A). In the section (OA), vehicles in the tight platoon have no opportunity to pass the slow leading vehicles and travel at the desired speed, mainly due to the initially tight platoon formed from the upstream signalized intersection. As traffic moves downstream, the initially tight platoon formed from the departing queue tends to disperse the farther downstream it travels. The platoon tends to spread out a few moving ahead and some dropping back. After the peak point, it can be observed that the difference between ATS sig,i and ATS wo_sig,i drops dramatically. It is mainly because the initially tight platoon formed from the signalized intersection has spread out and its effect is becoming smaller and smaller. Point B can be considered as the transition point, at which point the decreasing slope changes from steep to fairly level. After Point B, the difference between ATS sig,i and ATS wo_sig,i becomes negligible, near to 0.2 miles per hour. It still keeps dropping, but the decreasing rate becomes extremely small. After a certain distance, the platoon has spread out, and the impacts produced by the upstream signal on the platoon dispersion gradually disappear. Based on the above discussion, the effective length of a signalized intersection on the downstream two-lane highway segment can be determined from the stop line of this signalized intersection to the point, at which the difference between ATS sig,i and ATS wo_sig,i becomes negligible, and its decreasing rate becomes smaller. To estimate the downstream effective length of a signalized intersection, a key issue is to measure the variation of the difference between ATS SIG and ATS W_SIG Ideally, the downstream effective length of a signalized intersection can be measured from the on-site observation. However, available study sites are often too limited.

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92 Furthermore, it is very difficult to get the information about the difference in average travel speed between the condition with signalized intersection and without signalized intersection at the same location. In this study, TWOPAS is used to simulate traffic operations on the two-lane highway under different traffic conditions, and it is assumed that it is appropriate to represent the effects of a signalized intersection through the entering percent following parameter. The average travel speed at the interval of 100 ft along the downstream two-lane highway can be obtained from the TWOPAS simulation output. Figure 4-9 illustrates the difference in the average travel speed between the condition of with a signalized intersection and with no signalized intersection. The traffic volume is 1100 veh/h. When the signalized intersection is present, the cycle length is 60 seconds, 90 seconds, and 120 seconds, respectively. The ratio of effective green time to the cycle length is 0.6, 0.7, and 0.8 respectively. Similar figures for the other levels of traffic volume are plotted and presented in Appendix E. On observing these figures, the following conclusions can be drawn: The traffic volume is the decisive factor for the downstream effective length of a signalized intersection. The bigger the traffic volume into the downstream segment, the shorter the downstream effective length. Cycle length and the ratio of effective green time to cycle length also have some effect on the downstream effective length of the signalized intersection influence area, but it is much smaller. Based on the above analysis, it was decided to develop a simplified model for the downstream effective length of a signalized intersection, that is, one that is just a function of directional traffic volume being served during the analysis period, as shown in Equation 4-25:

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00.10.20.30.40.50.60500010000150002000025000Position along Roadway (ft)Difference in Average Travel Speed (mph) AB O C Figure 4-8. Difference in the average travel speed between with and without signalized intersection along the downstream two-lane highway 93

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Traffic Flow Rate = 1100 vph-1-0.500.511.522.533.54050100150200250300Position (100ft)Speed Difference (mph) 60Sec_0.6 60Sec_0.7 60Sec_0.8 90Sec_0.6 90Sec_0.7 90Sec_0.8 120Sec_0.6 120Sec_0.7 120Sec_0.8 Downstream Effective Length Figure 4-9. Difference in the average travel speed with traffic volume = 1100 veh/h 94

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95 Len eff_down = 2.218584 0.122942 (V/100) (4-25) Where: Len eff_down : Downstream effective length of a signalized intersection, mi, and V: Directional traffic flow rate, veh/h Table 4-12. Regression model for the downstream effective length R 2 = 0.98645; Adj. R 2 = 0.98306 Variable Coeff. t-stat Intercept 2.218584 38.8479 Volume/100 -0.122942 -17.0642 From the above model, it can be seen that the downstream effective length is inversely proportional to the traffic volume. As traffic volume increases, the downstream effective length decreases. When the traffic volume is low, the headway between vehicles is relatively large; thus, vehicles are generally not traveling in platoons and the average travel speed is at or very near to the free-flow speed. The presence of a controlled intersection introduces platooning in the traffic stream in the vicinity of the intersection. As the traffic stream discharges from upstream of the intersection into the downstream section beyond the intersection, it will take a relatively longer distance to return to the free-flow state from the platooned state. However, when the traffic flow rate is high, the headway between vehicles is much smaller; thus, a high percentage of vehicles are already in the platooned state and the average travel speed is lower than the free-flow speed. As the traffic stream discharges from upstream of the intersection into the downstream section beyond the intersection, it will take a relatively shorter distance to return to a similar platoon state from the signal queued state.

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96 This method of determining the effective length of an isolated signalized intersection influence area on the downstream two-lane highway segment takes full advantage of TWOPASs ability to simulate traffic operations on the two-lane highway. It also applies the parameter of EPF at the immediate downstream point of a signalized intersection to reflect the potential effect of a signalized intersection on the downstream two-lane highway operation. The evaluation for this methodology will be done in the next section. 4.2.5 Evaluation Based on CORSIM Simulation TWOPAS is the only simulation software that is able to simulate the passing maneuver operation on the two-lane highway using the opposing lane, and was developed with U.S. data. In this study, TWOPAS was used to study the effects of the signalized intersection on the downstream segment with the reasonable Entering Percent Following input variables. In this section, a simulation approach is used to evaluate the methodology for determining the downstream effective length of a signalized intersection on the two-lane highway. The CORSIM simulation model was selected as the traffic simulator. It can analyze a wide range of traffic, geometric, and control conditions and produces a relatively rich set of performance measures. CORSIM is not able to simulate the passing operation on the two-lane highway using the opposing lane, but this drawback will be considered in the results analysis. A two-way, two-lane roadway network with an isolated fixed-time signalized intersection was simulated using CORSIM. It was a total of 5 miles in length, and the isolated intersection was located at the 0.5-mile point. Once the CORSIM base road network was developed, the values for the independent variables were systematically

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97 changed to model different scenarios. After simulation, average travel speeds at the interval of 0.025 miles along the two-lane roadway are obtained from the CORSIM output file. The downstream effective length of a signalized intersection based on average travel speed can be determined from its variation trend. Figure 4-10 shows the average travel speed variation along the downstream two-lane highway segment of a signalized intersection and the average travel speed variation under the condition with no signalized intersection, assuming the traffic flow rate is 220 veh/h. The red line represents the average travel speed variation with no signalized intersection. The other lines represent the average travel speed variation with a signalized intersection, which have different cycle lengths and g/C (the ratio of green time to the cycle length). Similar figures for the other levels of traffic volume are plotted and presented in Appendix F. As observed from this figure, after the signalized intersection, vehicles travel some distance to return to the speed at which they would have traveled under the condition of no signalized intersection. According to the average travel speed variation under the two conditions, the distance of OB in this figure is defined as the downstream effective length due to the influence of the signalized intersection. In addition, it can be observed that with the same traffic flow rate, there is not a large difference in the variation of average travel speed when the signalized intersections have different cycle lengths and g/C ratios. These phenomena are the same with the conclusion drawn from the methodology for determining the downstream effective length of a signalized influence area presented in Section 4.2.4. Similar figures are plotted for other levels of traffic volume. As observed from these figures, the downstream effective lengths from CORSIM simulation are presented in Table 4-13.

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98 Table 4-13. Comparison of downstream effective length Volume (veh/h) Effective Downstream Length from CORSIM, (mi) Effective Downstream Length Equation 4-26, (mi) Difference (mi) 200 2.05 1.972 0.078 400 1.60 1.728 -0.128 600 1.35 1.480 -0.130 800 1.05 1.234 -0.184 1000 0.65 0.988 -0.338 As observed from Table 4-13, the downstream effective length of a signalized intersection from CORSIM simulation is also inversely proportional to the traffic flow rate. Through comparing the results obtained from the TWOPAS methodology with those from CORSIM simulation, it can be seen that when the traffic flow rate is low (such as 200 veh/h, 400 veh/h), the results obtained from the CORSIM simulation are very much in agreement with those obtained from the verified TWOPAS methodology. Although CORSIM has no ability to simulate the passing maneuver on the two-lane highway using the opposing lane, the low passing percentage under the low traffic demand on the two-lane highway weakens the effect of this drawback. When the traffic flow rate increase, the effective lengths obtained from the CORSIM simulation models are shorter than those obtained from the TWOPAS methodology. As the traffic flow rate increases, the traffic passing percentage also increases. The passing demand on the condition without any signalized intersection is larger than with a signalized intersection. It is CORSIMs inability of simulating passing maneuvers on the two-lane highway using the opposing lane that makes vehicle speeds drop quickly for the condition without any signalized intersection than for the condition with a signalized intersection. Therefore, the downstream effective lengths obtained from the CORSIM simulation model are shorter than these from TWOPAS when the traffic volume is higher. Based on the above comparison, it can be concluded that the downstream effective lengths obtained from TWOPAS essentially match those obtained from the CORSIM simulation.

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Traffic Flow Rate = 220 veh/h01020304050607000.511.522.533.544.5Position Along the Downstream Segment (mi)Average Travel Speed (mi/h) C=120 sec; g/C=0.6 C=120 sec; g/C=0.7 C=120 sec; g/C=0.8 C=90 sec; g/C=0.6 C=90 sec; g/C=0.7 C=90 sec; g/C=0.8 C=60 sec; g/C=0.6 C=90 sec; g/C=0.7 With No Signal Downstream Effective LengthSignalized Intersection Figure 4-10. Average travel speed variation with traffic volume = 220 veh 99

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CHAPTER 5 ESTIMATION OF SERVICE MEASURE VALUES This chapter describes the methods for calculating the service measure values of each of these segment types. It begins with procedures for determining the free-flow speed on the two-lane highway segment. Next, it presents how to determine average travel speed on three kinds of two-lane highway segments: the basic two-lane highway segment that is unaffected by a signalized intersection, the downstream two-lane highway segment within the effects of the installed signalized intersection, and a two-lane highway with a passing lane. Next, the formulas for calculating control delay at the signalized intersection and the TWSC intersection are presented. Finally the recommend LOS table for the two-lane highway facility is provided. 5.1 Free-Flow Speed Estimation Free-Flow Speed (FFS) is the average speed of the traffic stream when the traffic volume is sufficiently low so that drivers are not influenced by the presence of other vehicles and when intersection traffic control is not present or is sufficiently distant as to have no effect on speed choice [1]. In estimating expected operating conditions of a two-lane highway facility, the free-flow speed is a significant variable. The chosen service measure for this facility analysis methodology, percent time-delayed, is defined as the percentage of the travel time that a vehicle on a given roadway segment must travel at speeds less than their desired speed due to the inability to traffic control during some designed time interval. 100

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101 There is actually no practical method by which to measure drivers desired speed in the field. In practice, the desired speed, on aggregate, is usually considered to be the free-flow speed. In addition, free-flow speed is a necessary variable when calculating the average travel speed on the two-lane highway segment. Two general methods are recommended in the HCM 2000 [1] to determine the FFS for a two-lane highway: field measurement, and estimation of free-flow speed. 5.1.1 Field Measurement of Free-Flow Speed The Free-flow-speed of a two-lane highway can be determined directly from a speed study conducted in the field. The speed study should be conducted at a representative site within the study section. The best location to measure free-flow speed on the two-lane highway is mid-block and as far as possible from the nearest signalized or stop-controlled intersection. The measurement should be made under low flow conditions (less than 200 veh/h). The most appropriate section for performing a field study for the free-flow speed is the segment, which is not affected by the installed signalized intersection. Free-flow speeds may be directly measured as follows: A representative speed sample of 100 or more vehicle should be obtained. Total two-way traffic flow should be 200 pc/h or less. All vehicle speeds should be observed during the study period, or a systematic sampling should be applied. When a two-direction analysis is considered, the speed sample should be selected from both directions of flow; when a one-direction analysis is considered, the speed sample should be selected only from the direction under study. If field measurements must be made at a total flow level higher than 200 pc/h, the free-flow speed may be estimated as:

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102 )(00776.0HVfmfvSFFS (5-1) Where: FFS: free-flow speed for the facility, mi/h S m : mean speed of the measure sample (where the total flow is greater than 200 veh/h), mi/h V f : observed flow rate for the period of the speed sample, veh/h f HV : heavy vehicle adjustment factor 5.1.2 Estimating Free-Flow Speeds If field observation of free-flow speed is available, the free-flow speed on a two-lane rural highway may be estimated indirectly. Because the free-flow speed of a two-lane highway can range from 45 to 65 mi/h, this is a greater challenge on two-lane highways than on other types of uninterrupted-flow facilities. The free-flow speed can be estimated by applying the adjustments to the base free-flow speed (BFFS) using Equation 5-2 [1]: ALSffBFFSFFS (5-2) Where: FFS: estimated free-flow speed for the facility, mi/h BFFS: base free-flow speed for the facility, mi/h f LS : adjustment for lane and shoulder width, mi/h f A : adjustment for access point density, mi/h There are three important variables in the above estimating formula; the base free-flow speed (BFFS), adjustment for lane and shoulder widths, and adjustment for access

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103 point density. Note that because of the broad range of speed conditions on two-lane highways and the importance of local and regional factors that influence drive-desired speeds, the HCM 2000 does not provide any detailed criteria for estimating the BFFS. It is limited to a range of 45-65 mi/h. The adjustment factors for lane and shoulder width are shown in Table 5-1. The adjustment factors for access point density are shown in Table 5-2. Table 5-1. Adjustment (f LS ) for lane width and shoulder width Reduction in FFS (mi/h) Shoulder Width (ft) Lane Width (ft) >= 0 < 2 >= 2 < 4 >= 4 < 6 >=6 9 < 10 6.4 4.8 3.5 2.2 >= 10 < 11 5.3 3.7 2.4 1.1 >= 11 < 12 4.7 3.0 1.7 0.4 >= 12 4.2 2.6 1.3 0.0 Source: HCM 2000, Chapter 20 Table 5-2. Adjustment (f A ) for access-point density Access Points per mi Reduction in FFS (mi/h) 0 0.0 10 2.5 20 5.0 30 7.5 40 10.0 Source: HCM 2000, Chapter 20 Generally field measurement is best option for determination of the free-flow speed, but if not, HCM estimation method can be used. However, if an estimate of the BFFS is not available, FFS could be calculated as posted speed + 5 with the FDOT guidance. 5.2 Performance Measure on the Unaffected Two-Lane Highway Segment The HCM 2000 Chapter 20 [1] presents operational analysis methodologies for two-way and directional segments of two-lane highways. On a two-lane highway with different types of segments, such as a signalized intersection, an unsignalized intersection, and/or a passing lane, two-way segments typically do not have

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104 homogeneous cross sections or relatively constant demand volumes and vehicle mix proportions in the two directions. Thus, a separate analysis by direction of travel is particularly appropriate. The segment directional methodology for determining the average travel speed on the basic two-lane highway segment is summarized as follows. Determining FFS The first step in the analysis of a directional segment is to determine FFS. FFS can be determined by field measurement or estimation, which has been reviewed in Section 5.1. Note that these methods should be applied on a directional basis rather than to both directions combined. Determining demand flow rate This demand flow rate should be based on the PHF, the traffic composition, and the terrain or actual grade in the specific direction of travel. The demand flow rate for the peak 15-min period in the direction analyzed is determined with Equation 5-3 [1]: HVGdffPHFVv (5-3) Where: v d : passenger-car equivalent flow rate for the peak 15-min period in the direction analyzed (pc/h) V: demand volume for the full peak hour in the direction analyzed (veh/h) f G : grade adjustment factor, and f HV : heavy-vehicle adjustment factor A directional analysis also requires consideration of the demand flow rate in the opposing direction. The opposing demand flow rate is computed using Equation 5-4 [1].

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105 HVGooffPHFVv (5-4) Where: v o : passenger-car equivalent flow rate for the peak 15-min period in the opposing direction of travel, and V o : demand volume for the full peak hour in the opposing direction of travel. Determining average travel speed The average travel speed is estimated from the FFS, the demand flow rate, and an adjustment factor for the percentage of no-passing zones. Average travel speed is then estimated using Equation 5-5 [1]. npodddfvvFFSATS )(00776.0 (5-5) Where: ATS d : average travel speed in the analysis direction (mi/h) FFS d : free-flow speed in the analysis direction (mi/h) v d : passenger-car equivalent flow rate for the peak 15-min period in the analysis direction (pc/h) v o : passenger-car equivalent flow rate for the peak 15-min period in the opposing direction (pc/h) f np : adjustment for percentage of no-passing zones in the analysis direction The detailed procedure is described in Chapter 20 (Two-lane Highways) of the HCM 2000. 5.3 Performance Measure on an Affected Two-Lane Highway Segment The presence of a signalized intersection on a two-lane highway can significantly affect traffic operations on the downstream two-lane highway segment, such as decreasing travel speed, and increasing percent time-spent-following. In this section, the

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106 methodology is described, by which the effects of an isolated signalized intersection on a downstream two-lane highway segment can be estimated in terms of average travel speed. That is, to quantify the decrease of average travel speed within the downstream effective length caused by the upstream signalized intersection. The procedure can be broken down into three steps. Step 1: Determine the average travel speed for the basic two-lane highway section without the signalized intersection, ATS 1 Step 2: Determine the adjustment factor for the effect of a signalized intersection on average travel speed within the downstream effective length,. ATSf Step 3: Determine the average travel speed within the downstream effective length, ATS 2 Step 1: Determine ATS without signalized intersection, ATS 1 Two methods can be used to estimate the directional ATS for the two-lane highway. One is by microscopic simulation, and the other is using the HCM 2000 directional analysis procedure. The HCM 2000 directional analysis procedure is recommended. Step 2: Determine the adjustment factor for the effect of a signalized intersection on average travel speed, ATSf This step can be broken down into three sub-steps. First, divide the downstream effective length of a signalized intersection influence area into multiple short equal-distance intervals, then determine the average travel speed within each interval. Second, divide the two-lane highway segment without an intersection into multiple short equal-distance intervals. Then determine the average travel speed within each interval. Note that the length of each interval is equal to the one above. Third, determine the adjustment

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107 factor for the effect of a signalized intersection on the average travel speed of its downstream two-lane highway segment. The first two sub-steps can be performed with TWOPAS simulation. The simulation procedure is similar to the one for deciding the downstream effective length of a signalized intersection described in the last chapter. The characteristics of the highway section used in the simulation are also the same as those used to determine the downstream effective length of a signal influence area. Here the third sub-step is discussed in detail. Figure 5-1 shows the difference between ATS and ATS along the facility. This figure is from the output of TWOPAS runs. ATS denotes the average travel speed of the ith interval within a two-lane highway with no signalized intersection. ATS denotes the average travel speed of the ith interval within a two-lane highway segment downstream of a signalized intersection. The line AB in this figure represents the downstream effective length of a signal influence area, which is divided into multiple equal-distance small intervals. The adjustment factor for ATS is calculated as the average difference between ATS 1,i 2,i 1,i 1,i and ATS 2,i along the facility, that is 2,i niiiATSATSATSnf1,2,1)(1 (5-6) Where ATSf : adjustment factor for the effect of a signalized intersection on average travel speed within the downstream effective length of the signal influence area, ATS 1,i : average travel speed of the ith section of a two-lane highway without a signalized intersection, mph,

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108 ATS 2,i: average travel speed of the ith section of a two-lane highway downstream of a signalized intersection, mph, and n: number of sections within the downstream effective length of a signal influence area. The difference in average travel speed (v) between a two-lane highway with a signalized intersection and without a signalized intersection of ith interval, lying between the ith observing station i and the (i+1)th observing station, can be simplified to the following formula: 2)1()()21( iviviv And can be donated in Figure 5-1 as the line, )21(iv Note that the assumption is that the average travel speed variation curve is a straight line over the interval between the ith observing station and the (i+1)th observing station This approximate solution is acceptable when the distance interval of is small. The adjustment factor for average travel speed can be calculated using Equation 5-7 or Equation 5-8, x 2)(2)(2)(2)(1113221nnnnATSvvvvvvvvnf (5-7) or )(211111nniiATSvvvnf (5-8) Step 3: Determine the average travel speed for the downstream highway section within the downstream effective length, ATS 2

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109 Average travel speed within the downstream effective length of a signalized intersection is generally lower than the average travel speed without a signalized intersection. The effect varies as a function of the directional flow rate and the timing plan of the signalized intersection. The adjustment factors are presented in Table 5-3.

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-0.500.511.522.533.50500010000150002000025000Position Along Roadway (ft)Difference in Average Travel Speed (mph)) AB )21(iv)(iv )1( iv Figure 5-1. Downstream operational effects of a signalized intersection on AT 110

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111 Within the downstream effective length, average travel speed is assumed to decrease evenly to the value without the effect of the upstream signalized intersection. Thus, the average travel speed within the downstream effective length of a signalized intersection can be computed using Equation 5-9: ATS 2 = ATS 1 f ATS (5-9) Where: ATS 2 : average travel speed within the downstream effective length of the upstream signalized intersection, mi/h, ATS 1 : average travel speed without the effect of a signalized intersection, mi/h, and f ATS : adjustment factor for the effect of a signalized intersection on the average travel speed within the downstream effective length, mi/h. Table 5-3. Adjustment factor, f ATS to ATS for a segment downstream of a signal Free Flow Speed (mi/h) Directional Demand Flow Rate, (pc/h) 60 55 50 45 Cycle Length=60, g/C=0.6 220 0.908 0.835 0.762 0.689 440 1.051 0.978 0.905 0.832 660 1.437 1.284 1.130 0.976 880 1.824 1.589 1.354 1.119 1100 2.210 1.894 1.579 1.263 Cycle Length=60, g/C=0.7 220 0.676 0.599 0.522 0.445 440 0.741 0.664 0.587 0.510 660 0.921 0.806 0.691 0.575 880 1.102 0.948 0.794 0.641 1100 1.282 1.090 0.898 0.706 Cycle Length=60, g/C=0.8 220 0.382 0.321 0.260 0.198 440 0.484 0.423 0.361 0.300 660 0.595 0.530 0.466 0.402 880 0.705 0.638 0.571 0.503 1100 0.816 0.746 0.675 0.605 Cycle Length=90, g/C=0.6 220 1.135 1.006 0.878 0.749

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112 440 1.320 1.191 1.062 0.933 660 1.800 1.573 1.345 1.117 880 2.281 1.954 1.628 1.302 1100 2.761 2.336 1.911 1.486 Cycle Length=90, g/C=0.7 220 0.814 0.703 0.592 0.482 440 0.912 0.801 0.691 0.580 660 1.107 0.964 0.821 0.678 880 1.303 1.127 0.952 0.777 1100 1.498 1.290 1.083 0.875 Cycle Length=90, g/C=0.8 220 0.432 0.371 0.310 0.248 440 0.534 0.473 0.411 0.350 660 0.645 0.580 0.516 0.452 880 0.755 0.688 0.621 0.553 1100 0.866 0.796 0.725 0.655 Cycle Length=120, g/C=0.6 220 1.229 1.060 0.892 0.724 440 1.485 1.317 1.148 0.980 660 1.945 1.709 1.472 1.236 880 2.404 2.100 1.797 1.493 1100 2.864 2.492 2.121 1.749 Cycle Length=120, g/C=0.7 220 0.855 0.812 0.769 0.726 440 0.929 0.886 0.843 0.800 660 1.128 1.043 0.959 0.874 880 1.326 1.200 1.074 0.948 1100 1.525 1.357 1.190 1.022 Cycle Length=120, g/C=0.8 220 0.505 0.454 0.403 0.352 440 0.583 0.532 0.481 0.430 660 0.718 0.648 0.578 0.508 880 0.852 0.763 0.675 0.587 1100 0.986 0.879 0.772 0.665 5.4 Service Measure on a Two-Lane Highway with a Passing Lane When traffic operational problems occur on a two-lane highway, one method for alleviating these problems is to provide passing lanes at regular intervals. Passing lanes cannot increase the capacity of a two-lane highway but can improve its level of service [1]. A passing lane is a lane added in one direction of travel on a conventional two-lane

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113 highway to improve opportunities for passing. The addition of a passing lane to a two-lane highway provides a three-lane cross section with two lanes in one direction of travel and one lane in the other. Chapter 20 in the HCM 2000 provides an operational analysis procedure for a passing lane on a two-lane highway. Here the procedure to determine average travel speed on the two-lane highway with a passing lane is presented. The first step in the operation analysis of a passing lane is to apply the procedure for directional segment to the normal cross section without the passing lane. The result is the average travel speed, ATS d for the normal two-lane cross section. Installation of a passing lane provides operational benefits for some distance downstream before average travel speed returns to its former level. Thus, the effective length of a passing lane is greater than its actual length. The second step is to divide the analysis segment into four regions. Figure 5-2 shows the segment division and variation in average travel speed in a two-lane highway segment with a passing lane. These divided regions are: 1. Upstream of the passing lane 2. The passing lane 3. Downstream of the passing lane but with its effective length 4. Downstream of the passing lane but beyond its effective length 5. These four lengths add up to the total length of the analysis segment. The HCM 2000 provides a table on the downstream length of roadway affected by passing lanes on directional segment, L de The lengths of other regions can be determined by the actual placement of the passing lane within the analysis section. Table 5-4 shows the downstream length of two-lane highway affected by a passing lane, based on the average travel speed.

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114 Position Along Highway (mi)Average Travel Speed(mi/h)ATSdLdLULdeLpl Figure 5-2. Effect of a passing lane on average travel speed Table 5-4. Downstream length of roadway affected by passing lane Downstream Length of Roadway Affected, L de (mi) Directional Flow Rate (pc/h) Average Travel Speed 200 1.7 400 1.7 700 1.7 1000 1.7 Source: HCM 2000, Chapter 20 The next step is to determine the average travel speed. Average travel speed with lengths L u and L d is assumed to equal ATS d as predicted by the directional segment procedure. Within the passing lane, average travel speed is generally 8 to 11 percent higher than its upstream value. This effect varies as a function of directional flow rate, as

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115 shown in Table 5-5. Within the downstream length, L de average travel speed is assumed to decrease linearly with distance from the within-passing lane value to its normal upstream value. Thus, the average travel speed with the passing lane in place can be computed using equation 5-10 [1]. pldepldutdplfLfLLLLATSATS12 (5-10) Where ATS pl : average travel speed for the entire segment including the passing lane (mi/h) ATS d : average travel speed for the entire segment without the passing lane f pl : factor for the effect of a passing lane on average travel speed Table 5-5. Factors for estimation of average travel speed within a passing lane Directional Flow Rate (pc/h) Average Travel Speed 0 300 1.08 300 600 1.10 > 600 1.11 Source: HCM 2000, Chapter 20 5.5 Service Measure at a Signalized Intersection The HCM 2000 uses control delay as the service measure for a signalized intersection. Control delay includes movements at slower speed and stops on intersection approaches as vehicles move up in queue position or slow down upstream of an intersection. The delay model incorporated in the HCM 2000 includes the uniform delay, a version of Akceliks [1] overflow delay model, and a term covering delay from an existing or residual queue at the beginning of the analysis period. The control delay per vehicle for a given lane group is given by the following formulas, directly from the HCM

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116 2000. Equation 5-12 gives an estimate of control delay assuming uniform arrivals and stable flow. It is based on the first term of Websters delay formulation. Equation 5-13 gives an estimate of the incremental delay due to non-uniform arrivals and individual cycle failures, as well as delay caused by sustained periods of over-saturation. Equation 5-14 gives an estimate of the initial queue delay from the previous period at the start of the analysis. 321)( ddPFdd (5-11) ]),1[min(1)1(5.021CgXCgCd (5-12) cTklXXXTd8)1()1(90022 (5-13) cTtuQdb)1(18003 (5-14) Where: d: control delay per vehicle, s/veh d 1 : uniform control delay, s/veh d 2 : incremental delay, s/veh d 3 : initial queue delay, s/veh PF: progression adjustment factor T: analysis period, h X: v/c ratio C: cycle length, s k: incremental delay factor for actuated controller settings I: upstream filtering/metering adjustment factor

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117 c: capacity, veh/h Q b : initial queue at the start of analysis period u: delay parameter t: duration of unmet demand in analysis period The progression adjustment factor is an important factor in calculating the control delay. It is an empirically calibrated adjustment to uniform delay that accounts for the effect of platooned arrival patterns or signal coordination. Progression primarily affects uniform delay, so the progression adjustment factor is applied only to d 1 The value of PF can be determined by Equation 5-15. CgfPPFPA 1)1( (5-15) Where: PF: progression adjustment factor P: proportion of all vehicles arriving during green g/C: effective green to cycle length ratio f PA : supplemental adjustment factor for platoon arrival during the green The procedure of calculating control delay at a signalized intersection is described in detail in the HCM 2000, Chapter 16, Signalized Intersections. 5.6 Service Measure at a TWSC Unsignalized Intersection Usually there are three types of unsignalized intersections: two-way stop-controlled (TWSC), all-way stop-controlled (AWSC), and roundabouts. On a two-lane highway, the TWSC intersection is the most common type of unsignalized intersection. Stop signs are used to control vehicle movements at such intersections. At a TWSC intersection, the

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118 intersection approaches that are not controlled by stop signs are referred to as the major street approaches. The stop-controlled approaches are referred to as the minor street approaches; they can be either public streets or private driveways. Source: Chapter 17, Highway Capacity Manual 2000 Figure 5-3. Traffic streams at a TWSC intersection In this study, the operational analysis methodology developed is for the traffic on the major two-lane highway. Figure 5-3 shows the right-of way hierarchy at a TWSC intersection. According to the right-of way hierarchy at a TWSC intersection, the major street through and right-turning movements are the highest-priority movements at a

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119 TWSC intersection. These movements have the right-of-way over all minor-street movements at a STOP sign. Left-turning vehicles from the major street onto the minor street yield to opposing through and right-turning vehicles on the major street. Even though the right-of-way hierarchy suggests that the highest-priority movements experience no delay as they travel through a TWSC intersection, experience shows that their right-of-way is sometimes preempted by other conflicting movements. For example, when no exclusive left-turn lane is provided on the major street of a TWSC intersection, a delayed left-turn vehicle may block through and right-turn traffic on the major street (called Rank 1 vehicle). This will delay not only Rank 1 vehicles but also lower-ranked streams. While the delayed Rank 1 vehicles are discharged from the queue formed behind a left-turning vehicle, they impede lower ranked movements with which they conflict. Chapter 17 of the HCM 2000 [1] provides a method to calculate the average delay to Rank 1 vehicles on the main-street approach. It is computed as follows: 1N )1(1N )1(,,02,1,1,,,01LTMjiiiLTMjRankdpvvNvdpd (5-16) Where d Rank1 : delay to Rank 1 vehicles, s/veh N: number of through lanes per direction on the major street : proportion of Rank 1 vehicles not blocked jp,0 d M, LT : delay to major street left-turning vehicles, s/veh v i,1 : major-street through vehicles in shared lane, veh/h, and v i,2 : major-street right-turning vehicles in shared lane, veh/h

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120 On a two-lane highway, the number of through lanes per direction on the major street is always 1. d M,LT in Equation 5-16 is estimated using Equation 5-17 [1]. 54503600119003600,,2,,,TcvccvcvTcdxmxxmxmxxmxxm (5-17) Where d: control delay, s/veh v x : flow rate for movement x, veh/h c m,x : capacity of movement x, veh/h T: analysis time period, h (T=0.25 for a 15-min period) The constant value of 5 s/veh included in Equation 5-17 accounts for the deceleration of vehicles from the free-flow speed to the speed of vehicles in queue and the acceleration of vehicles from the stop line to the free-flow speed [1]. The procedure to calculate the delay to Rank 1 vehicles is outlined in Worksheet 11 of Chapter 17 of the HCM 2000. The control delay for all vehicles on a particular approach of the major street can be computed as the weighted average of the control delay estimated for each movement on the approach. The approach delay in the major street can be calculated using Equation 5-18 [1]. ltrllttrrAvvvvdvdvdd (5-18) Where

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121 d A : control delay on the approach, s/veh d r : computed control delay for the right-turn movements, s/veh d t : computed control delay for the through movements, s/veh d l : computed control delay for the left-turn movements, s/veh v r : flow rate of right-turn traffic on the approach, veh/h v t : flow rate of through traffic on the approach, veh/h v l : flow rate of left-turn traffic on the approach, veh/h Here the influence length of the delayed left-turn vehicles on the through and right-turn traffic of the major street at the TWSC intersection without an exclusive left-turn lane is discussed. Just like the signalized intersection discussed in Chapter 4, the influence area of the TWSC intersection is also made up of deceleration distance, stopping distance (queue length), and acceleration distance. When calculating the average delay to Rank 1 vehicles on the main-street approach, the constant value of 5 s/veh is included to account for the deceleration of vehicles from the free-flow speed to the speed of vehicles in queue and the acceleration of vehicles from the stop line to the free-flow speed. The base free flow speed for a two-lane highway ranges from 45 to 60 mi/h. In 5 seconds, the distance for the deceleration of vehicles from the free-flow speed to the speed of vehicles in queue and the acceleration of vehicles from the stop line to the free-flow speed ranges from 260 ft to 370 ft. This estimate is based on an assumed acceleration/deceleration rate of 11.2 ft/s 2 Regarding the queue length of a TWSC intersection, the method of simulation is used to determine the queue length of a TWSC intersection. Synchro and SimTraffic are selected as the simulation programs. Synchro is a complete software package for

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122 modeling and optimizing traffic signal timing and unsignalized intersections. SimTraffic is a companion product to Synchro for performing microscopic simulation and animation. SimTraffic uses a Synchro file for input. In Synchro, a vehicle is considered queued whenever it is traveling at less than 10 ft/s. A vehicle will only become queued when it is either at the stop bar or behind other queued vehicles [17]. In Synchro, there are two options for reporting the intersection statistical information, the Synchro method or the HCM method. To maintain fidelity to the existing HCM 2000 the option of HCM Un-signalized is chosen to create the HCM Un-signalized Intersection Report. The queue length can be obtained from the report [17]. Contributing factors selected for the determination of the queue length of a TWSC intersection influence area on the major approach due to the left-turn vehicles are presented in Table 5-6. Table 5-6. Variable input values (TWSC intersections) Peak Volume (pc/h) D-Factor Percentage of left-turn vehicles (%) 400 0.60 5% 700 0.70 10% 1000 0.80 15% The simulation results on the queue length of the TWSC intersection are presented in Table 5-7. The preliminary simulation results show that the queue lengths of the TWSC intersection influence area on the major approach are less than 200 ft in most cases. Only when the left-turn vehicle volume on the major approach is much higher, and the opposing traffic volume is also much higher, the queue length on the main approach is above 200 ft.

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123 Table 5-7. Simulation results on the queue length of the TWSC intersection Peak Volume (pc/h) D-Factor Percentage of left-turn vehicles (%) Queue Length (ft) 400 0.6 5% 0 400 0.6 10% 0 400 0.6 15% 0 400 0.7 5% 0 400 0.7 10% 0 400 0.7 15% 0 400 0.8 5% 0 400 0.8 10% 0 400 0.8 15% 0 700 0.6 5% 30 700 0.6 10% 85 700 0.6 15% 169 700 0.7 5% 16 700 0.7 10% 86 700 0.7 15% 97 700 0.8 5% 11 700 0.8 10% 14 700 0.8 15% 17 1000 0.6 5% 83 1000 0.6 10% 221 1000 0.6 15% 432 1000 0.7 5% 60 1000 0.7 10% 69 1000 0.7 15% 185 1000 0.8 5% 21 1000 0.8 10% 36 1000 0.8 15% 49 When the percentage of left-turn vehicles on the major approach increases, the effective length also increases. However, when the percentage of left-turn vehicles on the major approach increases to some point, an exclusive left-turn lane is usually provided at the TWSC intersection. NCHRP REPORT 457 [18] provides the guideline for determining the need for a major-road left-turn bay at a two-way stop-controlled intersection. A left-turn lane is recommended on the major road of any intersection when the combination of intersection volumes intersect above or to the right of the appropriate trend line shown in Figure 5-4. When a left-turn bay is added to the major-road approach, the assumption is that there would be no delay for the Rank 1 vehicles.

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124 Figure 5-4. Guideline for determining the need for a major-road left-turn bay at a two-way stop-controlled intersection Source: Reference 18. The above analysis shows that the sum of deceleration distance and acceleration distance of the TWSC intersection on the major approach ranges from 260 ft to 370 ft, and the queue length is less than 200 ft. So the sum of deceleration distance, queue length, and acceleration distance of the TWSC intersection without a left-turn bay on the main approach due to left-turn vehicles approaches 500 ft. In this dissertation, the effective length of the influence area due to left-turn vehicles at the TWSC intersection without an exclusive left-turn lane on the through and right-turn vehicles is recommend as extending 0.1 miles (528 ft) in length centered on the midpoint of the crossing facility.

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125 Figure 5-5 shows an example of how to determine the effective length on a two-lane highway facility of a TWSC intersection without an exclusive left-turn lane. In this example, a two-lane highway with a TWSC intersection extends 5 miles, and the isolated intersection is located at the 3-mile point. The first 2.95 miles would be regarded as a two-lane highway segment, the next 0.1 miles would be regarded as the intersection area, and the last 1.95 miles would be regarded as a two-lane highway segment. Two-lane Highway Segment Two-lane Highway Segment TWSC Intersection 2.950.050.051.95 Figure 5-5. Length of TWSC intersection area 5.7 Level of Service Thresholds To complete a level of service (LOS) methodology, it is necessary to define values of the service measure that serve to delineate between the various levels of service, A-F. The selected values, or thresholds, should be chosen such that they correspond to drivers level of satisfaction with the operating conditions for the given level of the service measure. However, without the benefit of research that directly investigates driver satisfaction on these facilities under varying levels of the service measure, there is no way to be sure that the chosen thresholds correlate with driver expectations. Nonetheless,

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126 threshold values must still be chosen such that a level of service value can be assigned to the analysis results. Although the selection of these threshold values is somewhat arbitrary without the benefit of driver perception-based research, there is some existing information that can be used to guide the threshold value selection. This information is the existing LOS thresholds for basic two-lane highway segments. It is important to recognize that adding a signalized intersection along a two-lane highway should not result in an improvement to the LOS that would be estimated for an equivalent two-lane highway with no signalized intersection(s) present. Preliminary LOS threshold values have been selected and are shown in Table 5-8. The application of these thresholds is demonstrated in the example problems of Chapter 6. Table 5-8. LOS criteria for two-lane highway facilities Level of Service Percent Time-Delayed A < 7.5% B 7.5%-15% C 15%-25% D 25%-35% E 35%-45% F > 45%

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CHAPTER 6 APPLICATION EXAMPLES The methodologies developed in this research can be used to assess the operational performance of an extended length of a two-lane highway facility, comprised of multiple segments, with segment delineations occurring with a change in either roadway or control attributes. A common application of the methodologies is to determine the LOS of a current or a changed facility in the near term or in the future. The primary outputs are the performance measure values of delay time and percent time-delayed, as well as a level of service ranking for the analyzed facility. This dissertation focuses the efforts on developing the methodology for operational analysis of a two-lane highway with an isolated signalized intersection at the facility level. It is intended that this research will also provide a model for the basic structure of a facility level analysis that will be amenable to the incorporation of a variety of segment types. In this chapter, two examples are provided to illustrate the application of the developed methodology. 6.1 Input Parameters Table 6-1 provides a summary of the input information required to conduct an operational analysis for the two-lane highway facility composed different types of segments. This information forms the basis for selecting computational values and procedures in the methodology developed in the dissertation. The data needed are detailed and varied and fall into two main categories: facility-wide data, and segment-wide data. The facility-wide data includes geometric and traffic conditions. 127

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128 Table 6-1. Input data needs for the facility-wide operational analysis Facility-wide information (1) Geometric Conditions (2) Traffic conditions Roadway length, (ft) Demand volume by movements, (veh/h) Lane width, (ft) Base saturation flow rate, (pc/h/ln) Shoulder width, (ft) Base FFS, (mi/h) Terrain Directional distribution Density of access points Peak-hour factor, PHF Proportion of no-passing zones, (%) Proportion of trucks and buses, (%) Proportion of RVs, (%) Segment-wide information (1) Signalized intersection (2) Unsignalized intersection Location of intersection Location of Intersection Traffic volume from minor streets, (veh/h) Traffic volume from minor streets, (veh/h) Existence of exclusive LT lane Existence of exclusive LT lanes Proportion of left-turn vehicles, (%) Proportion of left-turn vehicles, (%) Proportion of right-turn vehicles, (%) Proportion of right-turn vehicles, (%) Signal phasing plan Signal timing data (3) Passing lane Arrival type Location of the beginning of passing lane Area type Length of passing lane, (ft) Length of storage lanes, (ft) 6.2 Example 1 The Facility: A rural two-lane highway facility extends 7 miles with an isolated signalized intersection at the 3-mile point. Figure 6.1(a) illustrates the components of the facility. Determine: The percent time-delayed and level of service on this two-lane highway facility for the peak hour The Facts: Roadway Data Level terrain 6-ft shoulder width 5 access points/mi 60 mi/h base FFS 12-ft lane width 50% no-passing zones

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129 Downstream with 4-mile length Upstream with 3-mile length Traffic Data 1000 veh/h (two-way volume) 3 percent trucks and buses 0.95 PHF 60/40 split 2 percent RVs Control Data EB and WB HV = 5 percent 0.95 PHF EB-WB green = 54 s, NB-SB green = 26 s Cross street has one lane in each direction 6-ft shoulder width No parking at intersection NB and SB HV = 5 percent Two-phase signal Yellow = 4 s Main street has one lane and a left-turn bay in each direction. Movement lost time = 5 s 12-ft lane width Level terrain Outline of Solution: 1. Divide the facility into segments. 2. Determine segment lengths. 3. Calculate the free-flow speed. 4. Calculate the average travel speed on the two-lane highway segment upstream of the signal influence area. 5. Calculate control delay at the signalized intersection influence area. 6. Determine average travel speed on the affected downstream segment. 7. Determine average travel speed on the unaffected downstream segment. 8. Determine the delay of every segment. 9. Determine the percent time-delayed and LOS of the entire facility.

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130 INPUT WORKSHEET General Information Site Information Analyst Date Performed Analysis Time Period Intersection Area Type Analysis Year Facility Geometry Segment 4Segment 3Segment 2Segment 1 3 Mile4 Mile Grade = 0% Grade = 0% Grade = 0% Grade = 0%Main StreetCross Street Input Data of Two-Lane Highways Class II highway Two-way hourly volume 1000 veh/h Directional split 60/40 Peak-hour factor, PHF 0.95 Access points/mi 5 /mi % Trucks 3 % Base FFS 60 mi/h % Recreational vehicles 2 % Shoulder width 6 ft % No-passing zone 50 % Lane width 12 ft Upstream segment length 3 mi Downstream segment length 4 mi Terrain Level Input Data of Signalized Intersection Intersection Geometry ThroughLeftThrough+rightThrough+right+Left

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131 Volume and Signal Timing Input EB WB NB SB LT TH RT LT TH RT LT TH RT LT TH RT Volume, V (veh/h) 50 500 50 50 300 50 50 100 50 50 100 50 % heavy vehicle, %HV 5 5 5 5 5 5 5 5 5 5 5 5 Peak-hour factor, PHF 0.95 0.95 0.95 0.95 Pretimed(P), Actuated (A) P P P P Start-up Lost time, l (s) 2 2 2 2 Arrival type, AT 3 3 3 3 Parking (Y or N) N N N N Parking maneuvers, 0 0 0 0 Bus stopping 0 0 0 0 Signal Phasing Plan Diagram Phase 1 Phase 2 Time G= 54.0 Y+R=5.0 G= 26.0 Y+R=5.0 Cycle Length, C = 90.0 s Grade = 0 % Grade = 0 % Grade = 0 % Grade = 0 % 3 Mi 4 MIMain StreetCross Street S1 S2 S3 S4( A )( B ) Figure 6-1. A two-lane highway with an isolated signalized intersection

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132 Step 1: Divide the facility into segments The first step is to divide the facility into uninterrupted and interrupted flow segments. Each segment has homogenous characteristics. Figure 6-1 (B) shows the segmentation of a two-lane highway with an isolated signalized intersection. The whole two-lane highway facility is divided into four segments. These segments are: Segment 1: the basic two-lane highway segment. It is located upstream of the signalized intersection. This segment is not affected by the downstream signalized intersection. Segment 2: the influence area of the signalized intersection. It is composed of not only its own actual length, but also the deceleration distance, stopping distance and acceleration distance. Segment 3: the affected downstream two-lane highway segment. It is located downstream of the signalized intersection, and affected by the upstream signalized intersection. Note that this segment length does not include the acceleration distance of the signal influence area. Segment 4: the basic two-lane highway segment, it is located downstream of the signalized intersection. Just like Segment 1, this segment is not affected by the upstream signalized intersection. These four lengths add up to the total length of the analysis facility. Step 2: Determine segment lengths The length of the signalized intersection influence area, L 2 is calculated as the sum of upstream effective length and acceleration length. The upstream effective length is calculated using Equation 4-17. ft 355 6.0902444.5%3.8)100/600(3041.57 902178.5(600/100)4.268843.2463 _2444.5%)100/(3041.57 2178.5)100/(2688.42463.4322_CgCycleLTVCycleVLenupeff The acceleration length can be determined using the linearly-decreasing acceleration model, or obtained from the reference table in Transportation and Traffic

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133 Engineering Handbook, which is presented in Chapter 4, Table 4-1. Here the acceleration distance uses the value from this reference table. L A = 574 ft The length of Segment 2, L 2 is: mi18.0f t 929574355 _2AupeffLLL The length of the conventional two-lane highway segment upstream of the signalized intersection, L 1 is calculated by subtracting the upstream part of the signalized intersection influence area from the length of the two-lane highway upstream of the signalized intersection. That is, mi93.25280 / 3550.3 _11upeffULLL The length of the affected downstream segment of the signalized intersection, L 3 is calculated by subtracting the acceleration length of the signal influence area from the downstream effective length. The downstream effective length is calculated using Equation 4-25. Len eff_down = 2.218584 0.122942 (V/100) = 2.218584 0.122942 (600/100) = 1.48 mi The length of Segment 3, L 3, is, mi 37.1)5280/574(48.13_3LLLenLAdowneff Segment 4 is located downstream of the signalized intersection. The length of Segment 4 can be calculated by subtracting the total length of Segment 1, 2 and 3 from the total length of the facility. The length of Segment 4, L 4, is, )(3214LLLLLT

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134 mi 52.2)37.118.093.2()0.40.3(4 L Step 3: Calculate the free-flow speed mi/h 7.58 3.1060 ALSffBFFSFFS The above equation is Equation 20-2 in the HCM 2000. The f LS and f A values are from Exhibits 20-5 and 20-6, respectively, in Chapter 20 of the HCM 2000. Step 4: Calculate the average travel speed on the unaffected upstream segment. Use the HCM 2000 methodology to calculate the ATS (Chapter 20) ATS 1 = 48.4 mi/h Step 5: Calculate control delay at the signalized intersection influence area. Use the HCM 2000 methodology to calculate the control delay (Chapter 16) Control Delay = 12.8 sec/veh Step 6: Determine average travel speed on the unaffected downstream segment Use the 2000 HCM methodology to calculate the average travel speed. ATS 4 = 48.4 mi/h Step 7: Determine average travel speed on the affected downstream segment. For the affected downstream segment of the signalized intersection, an adjustment factor for the effect of a signalized intersection on average travel speed will be applied to the average travel speed without a signalized intersection to compute the average travel speed on the affected downstream segment of the signalized intersection. The adjustment factors can be obtained from Table 5-3 based on the traffic flow rate. The adjustment factor for Segment 4 can be interpolated as mi/h 669.1440660320.1800.1)440600(32.1 ATSf

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135 So the average travel speed of Segment 4 is mi/h73.46669.14.48 42 ATSfATSATS Step 8: Determine the delay of every segment. The delay at Segment 1, D 1 is sec/veh 38.24)3600)(7.5893.24.4893.2(mi/h 7.58mi/h 4.48mi 93.211111111FFSLSLDFFSSL The delay at segment 2, D 2 is sec/veh 8.12mi 18.022DL The delay at Segment 3, D 3 is sec/veh 52.21)3600)(7.5837.173.4637.1(mi/h 7.58mi/h 73.46mi 37.133333333FFSLSLDFFSSL The delay at Segment 4, D 4 is sec/veh 89.32)3600)(7.5852.24.4852.2(mi/h 7.58mi/h 4.48mi 52.244444444FFSLSLDFFSSL

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136 Step 9: Determine the percent time-delayed of the entire facility. 1. The total length of the facility Length of Segment 1, 1L miles 2.93 Length of Segment 2, 2L miles 18.0 Length of Segment 3, 3L miles 37.1 Length of Segment 4, 4L miles 2.52 Total Length, tL miles 752.237.118.093.24321 ttLLLLLL 2. The total delay of the facility Delay of Segment 1, 1D sec 38.24 Delay of Segment 2, 2D sec 80.12 Delay of Segment 3, 3D sec 52.21 Delay of Segment 4, 4D sec 89.23 Total Delay, TD sec/veh 45.10589.3252.218.1224.38 4321 DDDDDT 3. Calculate the total travel time of the facility based on the free flow speed sec/veh 429)3600(7.587FFSLTtFFS 4. Calculate the percent time-delayed of the facility %58.24429105.45 )()(,,FFSLDFFSLFFSLDDPTDtTSHSSHHSHSH

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137 From Table 5-8, this value of percent time-delayed gives an LOS value of C, albeit barely, as the value of 24.6% is just under the C/D threshold of 25.0%. By comparison, an average travel speed of 48.4 mph, for a two-lane highway with no signalized intersection, would also yield an LOS of C using the criteria in Exhibit 20-2 of the HCM 2000 (for ATS only). The LOS C range in this table is 45-50 mph. Although the level of service is the same in this situation, as opposed to being made worse due to the presence of the signal, it is still reasonable given that the average signal delay is only 12.8 seconds over a 7-mile length of highway. Thus, the relatively good signal conditions in this case are probably having a very minor impact on the overall trip quality over this length of highway. 6.2 Example 2 The Facility: A rural two-lane highway facility extends 20 miles with two isolated signalized intersections, a two-way stop-controlled intersection, and a passing lane. The first isolated signalized intersection is installed beginning at a location 3 mile downstream from the beginning of the 20-mile two-lane highway in the analysis direction; the second one is at the16-mile point. The two-way stop-controlled intersection is located at the 13-mile point. A 1.5-mile passing lane is also added at the 7-mile point. Figure 6.2-(a) illustrates the components of the facility. Determine: The percent time-delayed and level of service on this two-lane highway facility for the peak hour. The Facts:

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138 Two-lane highway segments 1200 veh/h (two-way volume) 3 percent trucks and buses 0.95 PHF Level terrain 6-ft shoulder width 5 access points/mi Three intersections and one passing lane 60/40 split 2 percent RVs 65 mi/h base FFS 12-ft lane width 40% no-passing zones 20-mile roadway Length The first signalized intersection is located 3 mi downstream A 1.5-mile length of passing lane including tapers at a location 7 mi downstream from the beginning of the 20-mile two-lane highway in the analysis direction A two-way stop-controlled intersection is located 13 mi downstream The second signalized intersection at a location 16 mi downstream The First Signalized intersection: EB and WB HV = 5 percent 0.95 PHF EB-WB green = 54 s, NB-SB green = 26 s Cross street has one lane in each direction 6-ft shoulder width No parking at intersection NB and SB HV = 5 percent Two-phase signal Yellow = 4 s Main street has one lane in each direction. Movement lost time = 5 s 12-ft lane width Level terrain The Second Signalized Intersection EB and WB HV = 5 percent 0.95 PHF EB-WB green = 63 s, NB-SB green = 17 s NB and SB HV = 5 percent Two-phase signal Yellow = 4 s Main street has one lane and a left

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139 Cross street has one lane in each direction 6-ft shoulder width No parking at intersection turn bay in each direction. Movement lost time = 5 s 12-ft lane width Level terrain The Two-Way Stop-Controlled Intersection Two-lane major street Two-lane minor street Stop-controlled on minor street approaches 5 percent HV No special intersection geometry No pedestrians Level grade Outline of Solution: 1. Divide the facility into segments. 2. Determine segment lengths. 3. Calculate the free-flow speed. 4. Determine the average travel speed on the unaffected basic two-lane segments (Segment 1, Segment 4, Segment 7, Segment 9, and Segment 12). 5. Determine the average travel speed of the affected downstream segments of the signalized intersection (Segment 3, Segment 11). 6. Determine the average travel speed within the passing lane and its affected downstream segment (Segment 5 and Segment 6). 7. Determine the control delay of the signal influence areas (Segment 2, and Segment 10). 8. Determine the delay of the unsignalized intersection (Segment 8). 9. Determine the performance measure of every segment. 10. Determine the performance measure and LOS of the entire facility.

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140 INPUT WORKSHEET General Information Site Information Analyst Date Performed Analysis Time Period Intersection Area Type Analysis Year Facility Geometry 3.0 Mi 4.0 MI 1.5 Mi 4.5 MI 4.0 Mi Grade = 0 % Grade = 0 % Grade = 0 % Grade = 0 % Grade = 0 % Grade = 0 % 3 Mi S S Input Data of Two-Lane Highways Class I highway Two-way hourly volume 1200 veh/h Directional split 60/40 Peak-hour factor, PHF 0.95 Access points/mi 5 /mi % Trucks and 3 % Base FFS 60 mi/h % Recreational vehicles 2 % Shoulder width 6 ft % No-passing zone 40 % Lane width 12 ft Facility length 20 mi Terrain Level Input Data of the First Signalized Intersection Intersection Geometry ThroughLeftThrough+rightThrough+right+Left

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141 Volume and Time Input EB WB NB SB LT TH RT LT TH RT LT TH RT LT TH RT Volume, v (veh/h) 50 620 50 50 230 50 40 50 115 115 90 40 % heavy vehicle, %HV 5 5 5 5 5 5 5 5 5 5 5 5 Peak-hour factor, PHF 0.95 0.95 0.95 0.95 Pre-time(P), Actuated (A) P P P P Start-up Lost time, l (s) 2 2 2 2 Arrival type, AT 3 3 3 3 Parking (Y or N) N N N N Parking maneuvers, 0 0 0 0 Bus stopping 0 0 0 0 Signal Phasing Plan Diagram Phase 1 Phase 2 Time G= 54.0 Y+R=5.0 G= 26.0 Y+R=5.0 Cycle Length, C = 90.0 s Input Data of the Second Signalized Intersection Signalized Intersection Geometry ThroughLeftThrough+rightThrough+right+Left Volume and Time Input EB WB NB SB LT TH RT LT TH RT LT TH RT LT TH RT Volume, v (veh/h) 100 700 50 120 240 120 60 100 85 85 120 60 % heavy vehicle, %HV 5 5 5 5 5 5 5 5 5 5 5 5 Peak-hour factor, PHF 0.95 0.95 0.95 0.95

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142 Pre-time(P), Actuated (A) P P P P Start-up Lost time, l (s) 2 2 2 2 Arrival type, AT 3 3 3 3 Parking (Y or N) N N N N Parking maneuvers, 0 0 0 0 Bus stopping 0 0 0 0 Signal Phasing Plan Diagram Phase 1 Phase 2 Time G= 63.0 Y+R=5.0 G= 26.0 Y+R=5.0 Cycle Length, C = 90.0 s Input Data of the TWSC Intersection Geometrics and Movements V1V2V3 V6V5V4 V7V8V9 V12V11V10V13V14V15V16 Vehicle Volumes and Adjustments Vehicles Volumes and Adjustments Movement 1 2 3 4 5 6 7 8 9 10 11 12 Volume (veh/h) 120 700 30 65 250 45 40 40 80 70 40 40 Peak-hour factor, PHF 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 Hourly flow rate, (veh/h) 100 630 30 30 360 80 40 40 90 80 40 50 Proportion of heavy vehicles, P HV 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 Pedestrian Volume and Adjustments Movement 13 14 15 16 Flow, V X (ped/h) 0 0 0 0

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3.0 Mi 4.0 MI 1.5 Mi 4.5 MI 4.0 Mi S1 S2 S3 S4 S5 S6 S7 S10 S11 S12 Grade = 0 % Grade = 0 % Grade = 0 % Grade = 0 % Grade = 0 % Grade = 0 % ( A )(B ) 3 Mi S8 S9 S S S S Figure 6-2. Segmentation for a two-lane highway facility 143

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S S 4090115405011550230505062050 4040704040452506512070030 601208560100120240120100700508085 Signalized Intersection ASignalized Intersection BTWSC Intersection ASignalized Intersection ASignalized Intersection BTWSC Intersection A Figure 6-3. Traffic flow rates at three intersections 144

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145 Step 1: Divide the facility into Segments To a two-lane highway with two isolated signalized intersections, one two-way stop-controlled intersection, and a passing lane, the signalized and unsignalized intersections affect the operations of the upstream and downstream two-lane highway segments; the added passing lane also has effects on the downstream two-lane highway segment. The first step is to break the facility into uninterrupted and interrupted flow segments. Each segment has the homogenous features. Figure 6-2 (B) shows the division of a two-lane highway with two isolated signalized intersections, one two-way stop-controlled intersection, and one passing lane. The whole two-lane highway facility is divided into twelve segments. These segments are: Segment 1: the unaffected two-lane highway segment. It is located upstream of the first signalized intersection. This segment is not affected by the downstream signalized intersection. Segment 2: the influence area of the first signalized intersection. It is composed of not only its own actual length, but also the deceleration distance, stopping distance and acceleration distance, which is needed for the vehicles through the first signalized intersection. Segment 3: the affected downstream two-lane highway segment. It is located downstream of the first signalized intersection, and affected by the upstream signalized intersection. Potential operational effects on this segment are produced by the first signalized intersection and traffic flows coming from the cross street at the first signalized intersection. Note this segment length does not include the acceleration length of the first signal influence area. Segment 4: the unaffected two-lane highway segment, it is located downstream of the first signalized intersection. This segment is not affected by the upstream signalized intersection, and the downstream passing lane. Segment 5: the passing lane. The passing lane length should include the length of the lane addition and lane drop tapers. Segment 6: the affected downstream segment. It is the downstream segment of the passing lane but within its effective length.

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146 Segment 7: the unaffected two-lane highway segment. It is located upstream of the two-way stop-controlled intersection. This segment is not affected by the upstream passing lane and the downstream unsignalized intersection. Segment 8: the influence area of the two-way stop-controlled intersection. Its length is longer than the actual length of this unsignalized intersection. Segment 9: the unaffected two-lane highway segment, it is located upstream of the second signalized intersection, and the downstream of the TWSC intersection. This segment is not affected by the upstream TWSC intersection and the downstream signalized intersection. Segment 10: the influence area of the second signalized intersection. It is composed of not only its own actual length, but also the deceleration lengths, stopping lengths and acceleration lengths, which is needed for the vehicles through the second signalized intersection. Segment 11: the affected downstream segment. It is located downstream of the second signalized intersection, and affected by the upstream signalized intersection. Potential operational effects on this segment are produced by the second signalized intersection and traffic flows coming from the cross street at the second signalized intersection. Note this segment length does not include the acceleration length of the second signal influence area. Segment 12: the unaffected two-lane highway segment. It is located downstream of the second signalized intersection. This segment is not affected by the upstream signalized intersection. These twelve lengths added up to the total length of the analysis facility. Step 2: Determine segment lengths Because there is not a left-turn bay present at the first signalized intersection, the upstream effective length of the first signalized intersection, is calculated using Equation 4-18. 1_upeffLen

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147 ft 620 )720/50()100/720(1171.01 )6.0(52.47586.059.73369069.1 6.000.440)100/720(89.549.3074 )(%)100/(1171.01 )_(52.4758_59.733669.1 00.440)100/(89.549.30742222221_LTVCgCgCDFactorVLenupeff The acceleration length can be determined using the linearly-decreasing acceleration model, or obtained from the reference table in Transportation and Traffic Engineering Handbook, which is presented in Chapter 4, Table 4-1. Here the acceleration distance uses the value from this reference table. L A = 574 ft The length of Segment 2, L 2 is: mi23.0f t 1194574620 1_2AupeffLLL The length of the unaffected two-lane highway segment upstream of the first signalized intersection, L 1 is calculated by subtracting the upstream part of the first signalized intersection influence area from length of the two-lane highway upstream of the first signalized intersection. mi88.25280 / 6200.3 1_1upeffUFSLLL The length of the affected downstream segment of the first signalized intersection, L 3 is calculated by subtracting the acceleration length of the first signal influence area from the downstream effective length of the first signalized intersection. The downstream effective length, Len eff_down1 is calculated using Equation 4-25. Len eff_down1 = 2.218584 0.122942 (V/100)

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148 = 2.218584 0.122942 (850/100) = 1.17 mi The length of Segment 3, L 3, is: mi 06.1)5280/574(17.131_3LLLenLAdowneff Segment 4 is located in the downstream of the first signalized intersection, and the upstream of the passing lane. The length of Segment 4 can be calculated by subtracting the total length of Segment 1, 2 and 3 from the total upstream length of the passing lane as shown in Equation 6-1. ) ()(3214LLLLLLUPUFS (6-1) Where: L UFS : upstream length of the first signalized intersection, mi, and L UP : the length between the stop line of the first signalized intersection and the beginning point of the passing lane, mi So the length of Segment 4, L 4 is: mi 83.2)06.123.088.2()0.40.3(4 L The length of the passing lane, L 5 includes the lengths of the lane addition and lane drop tapers. A typical passing lane is shown in Figure 6-4. In this analysis, the passing lane length, L 5 is: L 5 = 1.5 mi The length of the downstream highway segment within the effective length of the passing lane, L 6 is determined from Table 5-4. From this table, the downstream length of roadway affected by the upstream passing lane, L 6 is:

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149 L 6 = 1.7 mi Lane additionaltaperLane drop taper Passing lane Figure 6-4. A view of a typical passing lane Segment 8 is a two-way stop-controlled intersection. The effect of a shared lane on the major-street approach where left-turn vehicles may block Rank 1 through or right-turning vehicles can be significant. While the delayed Rank 1 vehicles are discharging from the queue formed behind a left-turning vehicle, they impede lower-ranked movements with which they conflict. Field observations have shown that such a blockage effect is very small [1]. CORSIM simulation runs have shown the same results. In this methodology, the interrupted flow unsignalized intersection segments, unsignalized intersection influence are, extend 0.1 miles in length centered on the midpoint of the crossing facility. The delay for this influence area is determined by the delay to Rank 1 vehicles. The length of the two-way stop-controlled intersection influence area, L 8 is: L 8 = 0.1 mi Segment 7 is an unaffected two-lane highway segment, located downstream of the passing plan, and upstream of the TWSC intersection. The length of Segment 7 can be calculated by subtracting the total length of Segment 1, Segment 2, Segment 3, Segment

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150 4, Segment 5, Segment 6, and half of Segment 8 from the total upstream length of the TWSC intersection as shown below. mi 2.75 )21.070.150.183.206.123.088.2()5.45.10.40.3()2()(86543217LLLLLLLLLLLLUTWSCPLUPUS The length of the second signalized intersection influence area, L 10 is also calculated as the sum of its upstream effective length and acceleration length. Because there is a left-turn bay present at the second signalized intersection, the upstream effective length of the second signalized intersection, is calculated using Equation 4-17. 2_upeffLen 434ft 7.0902444.5)850/100()100/850(3041.57 902178.5(850/100)4.268843.2463 _2444.5%)100/(3041.57 2178.5)100/(2688.42463.43222_CgCycleLTVCycleVLenupeff L A = 574 ft The length of Segment 10, L 10 is: mi19.0f t 1008574434 2_10AupeffLLL Segment 9 is an unaffected two-lane highway segment, located downstream of the two-way stop-controlled intersection and upstream of the signalized intersection. The length of Segment 9 can be calculated by subtracting the total length of Segment 1, Segment 2, Segment 3, Segment 4, Segment 5, Segment 6, Segment 7, Segment 8, and

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151 the upstream effective length of the second signal influence area from the total upstream length of the second signalized intersection. That is, mi 2.97 )5280/4341.075.270.150.183.206.123.088.2( )35.45.10.40.3( )( )(2_876543219upeffUSSUTWSCPLUPUFSLenLLLLLLLLLLLLLL (6-2) The length of the affected downstream segment of the signalized intersection, L 11 is calculated by subtracting the acceleration length of the second signal influence area from the downstream effective length. The downstream effective length, Len eff_down2 is calculated using Equation 4-25. Len eff_down2 = 2.218584 0.122942 (V/100) = 2.218584 0.122942 (870/100) = 1.15 mi The length of Segment 11, L 11, is: mi 04.1)5280/574(15.1112_11LLLenLAdowneff Segment 12 is located downstream of the second signalized intersection. The length of Segment 12 can be calculated by subtracting the downstream effective length of the second signalized intersection from the distance between the stop line of the second signalized intersection and the ending point of the analyzed facility. The length of Segment 12 can be calculated using Equation 6-3. 2_12downeffDSSLenLL (6-3) Where: DSSL : the downstream length of the second signalized intersection from the stop line of

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152 the second signalized to the ending point of the facility, mi The length of Segment 12, L 12, is: mi 85.215.10.4 2_12downeffDSSLenLL Step 3: Calculate the free-flow speed mi/h 7.58 3.1060 ALSffBFFSFFS The above equation is Equation 20-2 in the HCM 2000. The f LS and f A values are from Exhibits 20-5 and 20-6, respectively, in Chapter 20 of the HCM 2000. Step 4: Determine the average travel speed on the unaffected two-lane segments (Segment 1, Segment 4, Segment 7, Segment 9, and Segment 12) Use the HCM 2000 methodology to calculate the average travel speeds on the unaffected two-lane segments. The average travel speeds of these basic two-lane segments are summarized in the Table 6-2. Table 6-2. Average travel speed for the unaffected two-lane segments Average Travel Speed (mi/h) Segment 1 ATS 1 = 47.0 mi/h Segment 4 ATS 4 = 46.9 mi/h Segment 7 ATS 7 = 46.9 mi/h Segment 9 ATS 9 = 46.8 mi/h Segment 12 ATS 12 = 46.1 mi/h Step 5: Determine the average travel speed of the affected downstream segments of the signalized intersection (Segment 3 and Segment 11) For the affected downstream segment of the signalized intersection, an adjustment factor for the effect of a signalized intersection on average travel speed will be applied to the average travel speed without a signalized intersection to compute the average travel

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153 speed on the affected downstream segment of the signalized intersection. The adjustment factors can be obtained from Table 5-3 based on the traffic flow rate. The adjustment factor for Segment 3 can be interpolated as mi/h 215.2660880800.1281.2)660850(8.1 ATSf So the average travel speed of Segment 3 is mi/h7.44215.29.46 43ATSfATSATS The adjustment factor for Segment 11 can be interpolated as mi/h 259.2660880800.1281.2)660870(8.1 ATSf So the average travel speed of Segment 11 is mi/h8.43259.21.46 1211ATSfATSATS The average travel speeds of these affected downstream segments of the signalized intersection are summarized in Table 6-3. Table 6-3. Average travel speed for the affected downstream two-lane segments Segment No. Average Travel Speed (mi/h) Segment 3 ATS 3 = 44.7 mi/h Segment 11 ATS 11 = 43.8 mi/h Step 6: Determine the average travel speed within the passing lane and its affected downstream segment (Segment 5 and Segment 6) Equation 20-21 in the HCM 2000 is used to compute the average travel speed with the passing lane and its affected downstream two-lane highway. The average travel speeds of Segment 5 and Segment 6 are summarized in Table 6-4.

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154 Table 6-4. Average travel speed for the affected passing lane segments Segment No. Average Travel Speed (mi/h) Segment 5 ATS 5 = 46.1 mi/h Segment 6 ATS 6 = 46.1 mi/h Step 7: Determine the control delay of the signal influence areas (Segment 2 and Segment 10) Use the HCM 2000 analysis methodology to calculate the control delay (Chapter 16). The control delays of the signalized intersection influence areas are summarized in Table 6-5. Table 6-5. Control delays at signalized intersections Segment No. Control Delay (sec/veh) Segment 2 D 2 = 17.8 sec/veh Segment 10 D 10 = 16.4 sec/veh Step 8: Determine the main approach delay at the Two-Way Stop-Controlled Intersection (Segment 8) 1. Calculate the critical gap for left-turn movement from the major street, t c,1 s 15.4000)05.0(0.11.41,,3,,,,, cLTTcGcHVHVcbasecxctttGtPttt 2. Calculate the follow-up time for the left-turn movement from the major street, t f,1 s 25.2)05.0(0.12.21,,,,cHVHVfbasefxctPttt 3. Calculate the potential capacity of the left-turn movement from the major street, c p,1 veh/h12471295 veh2954525013600/25.22953600/15.42951,16651,3600/3600/,,,,,,eecvvvveevcpctvtvxcxpxfxcxcxc 4. Calculate the delay to major left-turn vehicle, d M,LT

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155 54503600119003600,,2,,,TcvccvcvTcdxmxxmxmxxmxxmMLT s 19.8 525.0450124712012473600112471201124712025.0900124736002,LTMd 5. Calculate the probability of queue-free state for left-turning movement from the major approach assuming an exclusive left-turn lane on the major street, 1,op 904.012471201111,11,,,mojmjjocvpcvp 6. Calculate the proportion of through vehicles and right-turn vehicles on the major approach not blocked, 839.018003018007001904.011111*1,2211,*,ojjjjjojopsvsvpp 7. Calculate the delay to through vehicles and right-turn vehicles on the major approach, d T,RT s 32.1194.8)839.01()1(,,,0,RTTLTMjRTTddpd 8. Calculate control delay on the major approach, d A

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156 s 30.2730120730319.1194.8120AltrllttrrAdvvvvdvdvdd Step 9: Determine the performance measure of the entire facility. The delay at Segment 1, D 1 is: sec/veh 43.97)3600)(7.5888.20.4788.2(mi/h 7.58mi/h 0.47mi 88.211111111FFSLSLDFFSSL The delay at Segment 2, D 2 is: sec/veh 8.17mi 23.022DL The delay at Segment 3, D 3 is: sec/veh 36.20)3600)(7.5806.17.4406.1(mi/h 7.58mi/h 7.44mi 06.133333333FFSLSLDFFSSL The delay at Segment 4, D 4 is: sec/veh 68.43)3600)(7.5883.29.4683.2(mi/h 7.58mi/h 9.46mi 83.244444444FFSLSLDFFSSL The delay at Segment 5 and Segment 6 is:

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157 sec/veh 64.53)3600)(7.587.15.11.467.15.1(mi/h 7.58mi/h 7.58mi/h 1.46mi/h 1.46mi 70.1mi 50.16,5656,5656,5656565FFSLLSLLDFFSFFSSSLL The delay at Segment 7 is: sec/veh 43.42)3600)(7.5875.29.4675.2(mi/h 7.58mi/h 9.46mi 75.277777777FFSLSLDFFSSL The delay at segment 8 is sec/veh 2.3 mi 1.088DL The delay at Segment 9 is sec/veh 32.46)3600)(7.5897.28.4697.2(mi/h 58.7 mi/h 46.8 mi 2.97 99999999FFSLSLDFFSSL The delay at segment 10 is: sec/veh 4.16mi 19.088DL The delay at Segment 11 is:

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158 sec/veh 70.21)3600)(7.5804.18.4304.1(mi/h 7.58mi/h 8.43mi 04.199999999FFSLSLDFFSSL The delay at segment 12 is: sec/veh 47.77)3600)(7.5885.21.4685.2(mi/h 7.58mi/h 1.46mi 85.21010101010101010FFSLSLDFFSSL Step 10: Determine the performance measure and LOS of the entire facility. 1. The total length of the facility Length of Segment 1, L 1 2.88 miles Length of Segment 2, L 2 0.23 miles Length of Segment 3, L 3 1.06 miles Length of Segment 4, L 4 2.83 miles Length of Segment 5, L 5 1.50 miles Length of Segment 6, L 6 1.70 miles Length of Segment 7, L 7 2.75 miles Length of Segment 8, L 8 0.10 miles Length of Segment 9, L 9 2.97 miles Length of Segment 10, L 10 0.19 miles Length of Segment 11, L 11 1.04 miles Length of Segment 12, L 12 2.85 miles Total Length miles 2085.204.119.02.97 10.075.270.150.183.206.123.088.2121110987654321 ttLLLLLLLLLLLLLL 2. The total delay of the facility Delay of Segment 1, D 1 43.97 sec Delay of Segment 2, D 2 17.80 sec Delay of Segment 3, D 3 20.36 sec Delay of Segment 4, D 4 43.68 sec Delay of Segment 5, D 5 53.64 sec

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159 Delay of Segment 6, D 6 Delay of Segment 7, D 7 42.43 sec Delay of Segment 8, D 8 2.30 sec Delay of Segment 9, D 9 46.32 sec Delay of Segment 10, D 10 16.40 sec Delay of Segment 11, 11D 21.70 sec Delay of Segment 12, 12D 47.77 sec Total Delay sec/veh35677.4770.2140.1632.4630.243.4264.5368.4336.2080.1797.43 121110987654321ttDDDDDDDDDDDDDD 3. Calculate the total travel time of the facility based on the free flow speed sec/veh 1227)3600(7.5820FF S LTtFFS 4. Calculate the percent time-delayed of the facility %02.291227356 )()(,,FFSLDFFSLFFSLDDPTDtTSHSSHHSHSH From Table 5-8, this value of percent time-delayed gives an LOS value of D. By comparison, if the two signalized intersections and one Unsignalized intersection were removed, an average travel speed of 46.9 mph would be estimated with the HCM 2000 Chapter 20 methodology, which would result in an LOS of C, again using the criteria in Exhibit 20-2 of the HCM 2000 (for ATS only). So in this case, the LOS is one grade worse due to the presence of the signals. Even though the operations of the signals are still relatively good, with borderline LOS B/C (from LOS criteria in HCM 2000 Exhibit

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160 16-2), they are adding just enough of a penalizing effect to reduce the LOS over the length of the facility.

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CHAPTER 7 SUMMARY AND RECOMMENDATIONS This chapter summarizes the dissertation, discusses the findings, and outlines future research directions. Developing a method for the assessment of traffic operations on two-lane highway facilities has proven to be a challenging and complex issue. Despite the progress of this dissertation, many potential research extensions deserve consideration. 7.1 Summary This dissertation makes some contributions in the area of traffic operations assessment for the highway system. In this dissertation, the focus is on the development of a method for the assessment of traffic operations on two-lane highways that include occasional traffic signals and TWSC intersections. This particular type of facility is not currently addressed by any of the methodology chapters within the HCM 2000. The features of the methodology developed in this dissertation are summarized as follows: The method maintains some fidelity to the HCM 2000 by using the existing methodologies for the two-lane highway segments and signalized intersections. For the two-lane highway methodology (HCM Chapter 20), the method for calculation of average travel speed (ATS) is utilized. The average travel speed of two-lane highway segments with a passing lane is also calculated using the methodology of the HCM Chapter 20. For signalized intersections (HCM Chapter 16), the current method for the calculation of control delay is utilized. For unsignalized intersections, the method for the calculation of delay to the vehicles with highest priority is utilized (HCM Chapter 17). In this method, a common time/delay based service measure is used for each segment and point of the entire facility. The service measure values for each segment are 161

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162 aggregated to obtain an estimate of the service measure value for the entire facility. The LOS of the entire facility is determined by the aggregated service measure. The unified facility-wide service measure not only avoids the anomalies caused by the application of multiple service measures, but also provides a MOE describing traffic operations in terms discernible by motorists from the viewpoint of the entire facility. By using a time/delay based service measure, this method is similar to the current HCM methodology for urban streets with signalized intersection. For transportation agencies looking to analyze the impacts of adding a lane (or lanes) to a two-lane highway, along with adding some signalized intersections, thus possibly changing the classification to an urban arterial in some segments, this will provide for consistency in the LOS analyses. The primary contribution of the work in this dissertation is the development of equation and analytical relationships to determine the upstream and downstream boundary points that define the transition between the basic two-lane highway segment and the effective influence area of the signalized intersection and the TWSC intersection as well as the corresponding method for calculating an overall facility service measure based on percent time-delayed and then translating to a level of service grade. In the proposed segmentation method, a signalized intersection is not regarded as an isolated point. The interaction between a signalized intersection and upstream and downstream highway segments are taken into account by considering the signalized intersection as a segment and determining its effective length. The components of the signal influence area include deceleration distance, stopping distance, and acceleration distance, which are consistent with those of control delay defined in the HCM 2000deceleration delay, stop delay, and acceleration delay. The segment delay time for the signalized intersection influence area is determined by the intersection control delay. Two regression models are developed to determine the relationship between the length of signal influence area and corresponding traffic, roadway, and signal characteristics. One is for the signalized intersection with an exclusive left-turn lane; the other is for without a left-turn lane. In determining the length of the affected downstream segment, the parameter, EPF was used to represent the effects of a signalized intersection on the downstream two-lane highway segment. Shifted negative exponential and composite distributions were used to calculate the parameter of EPF. Under very low volume conditions, the shifted negative exponential distribution was used to define the time headway distribution for the EPF calculation; under higher volume conditions, the composite distribution was used. The calculated values of EPF were input into the TWOPAS simulation model to determine the length of the affected downstream segment. Traffic volume is the most significant factor for the affected downstream length of a signalized intersection and this relationship was determined to be inversely proportional. This structure easily allows for including other two-lane highway segment types (e.g., passing lanes, which already has a method for calculating ATS in the HCM) and

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163 other intersection types (e.g., unsignalized, which also uses a control delay service measure). Meanwhile, this methodological approach provides a balance between one that is intuitive and logical from both an analytical and travelers perspective and complexity. The method of analysis for multilane highways could be modified to fit into the proposed framework such that combinations of two-lane highway segments, multilane highway segments, and occasional traffic signals can be analyzed as an overall facility. Personnel with the FDOT System Planning Office have indicated that a facility-based evaluation methodology for two-lane highways would be much more useful to them than just the individual segment and point analysis methodologies. With the continual increase in growth and development, combinations of various types of two-lane highway segments, multilane highway segments, signalized intersections, and unsignalized intersections are also increasing; as such, transportation planners and engineers need tools to perform more comprehensive roadway facility evaluations. This is consistent with the fact that drivers typically evaluate the quality of their trip over its entire length, not just in separate pieces. This type of methodology will be particularly useful to those managing the transportation system in more rural areas. These areas are often faced with decisions on whether to add a signal along a two-lane highway through a small town, or go to a multilane configuration. Finally, the methodology has been incorporated into the existing HIGHPLAN software program. Currently, HIGHPLAN only allows for the input of data specific to one segment. The updated version incorporating the results from this research includes a segment and intersection data input screen to allow for the calculation of a facility LOS value.

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164 7.2 Further Research In this research, the regression models for determining the upstream effective length of a signalized intersection were developed using the data obtained from the CORSIM simulation program. Although the coefficients of the regression models show logical relationships among all the variables considered, the model validation was somewhat limited. On analyzing the potential effect of a signalized intersection on the downstream two-lane highway operation, the EPF parameter was used to represent the effects of a signalized intersection. Although the EPF calculation takes into account many factors such as the signal timing plan, travel speed, and the time headway distribution, the single EPF value seems overstressed to some degree. A simulation program capable of simulating the combination of two-lane highway segments and signalized intersections (one was still not available at the time of publication of this dissertation) would provide the capability to perform some validation of the model proposed in this research. Obviously, validation with field data is the most desirable option, and it is hoped that this could be done in a future study. With regard to the two-way stop-controlled intersection incorporated in this methodology, additional study on the full effects of these types of intersections on two-lane highways should be investigated, particularly as it relates to driver behavior in reacting to left-turning vehicles from the major highway. Additionally, all-way stop controlled intersections are sometimes used in small towns instead of a signal, and even roundabouts to a lesser extent. These intersection types should be considered for inclusion into the methodology as part of a future project. With regard to the application of this methodology to multilane highways, multilane highway segments and freeway segments currently share the same service

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165 measure, density. Given the similarity in operational features of these segments, this makes some sense. However, in some respects, multilane highways that include the presence of signalized intersections have more in common with signalized arterials or two-lane highways (with occasional signals) than freeways. Since freeways, by definition, are always uninterrupted, it becomes more difficult to make comparisons between an interrupted facility and one that includes occasional interruptions. Combining multilane highway segments, that use density for the service measure, with signalized intersections, that use delay as the service measure, poses the same challenge as that for two-lane highways and signalized intersections. That is, the service measures for each facility type are somewhat disparate, but even more so in the case of multilane highways and signals, as the density measure has no time component to it, whereas the signal delay measure is strictly time-based. As was done for this two-lane facility analysis methodology, a speed/delay measure can be implemented for multilane highways. However, as indicated by current empirical evidence, average speeds on multilane highways (as well as freeways) are relatively constant up to fairly high flow rates, and thus LOS based upon speed does not reflect the likely discomfort experienced by travelers for increasing flow rates. Density, on the other hand, always increases with increasing flow rate (for under-saturated conditions) and thus reflects traveler discomfort more adequately. To some extent, the use of speed for two-lane highways has the same limitations (compared to percent time-spent-following); however, speed is more readily impacted by flow rate on two-lane highways due to the need to use the oncoming lane for passing maneuvers.

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166 Percent time-spent-following may be more applicable than speed on multilane highways, as it correlates better with increasing density (decreasing headways) at lower volumes. Although this measure has a time component to it, it would still require some manipulation to be compatible with the delay measure of signalized intersections. Alternatively, the signal delay measure might be manipulated to yield a comparable PTSF value. While these manipulations may also have been possible for the two-lane highway facility methodology, it should be noted again that one of the recognized drawbacks of the PTSF measure was its potential lack of applicability to certain types of two-lane highways. Furthermore, these manipulations of either the PTSF measure or the signal delay measure would potentially lead to a less intuitive level of service methodology. Further research needs to be done on the application of the methodological approach described in this dissertation to multilane highways facilities. In this dissertation, a LOS threshold table for the two-lane facility is presented based on the service measure, percent time-delayed. The threshold value selection is guided by the concept that adding a signalized intersection along a two-lane highway should not result in an improvement to the LOS that would be estimated for an equivalent two-lane highway with no signalized intersection(s) present. Nonetheless, the selection of the threshold values was still somewhat arbitrary. Ideally, the selected thresholds should be chosen such that they correspond to actual drivers level of satisfaction with the operating conditions for the given level of service value. Future research that directly investigates driver satisfaction on these facilities under operating conditions should be conducted to ensure threshold values are truly appropriate.

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APPENDIX A PASSING PERCENTAGE AND AVERAGE TRAVEL SPEED ON TWO-LANE HIGHWAYS

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Figure A.1. Passing percentage for various levels of advancing and opposing traffic volume on two-lane highways 168

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Figure A-2. Average travel speed for various levels of advancing and opposing traffic volume on two-lane highways 169

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Figure A-3. Percent time-spent-following for various levels of advancing and opposing traffic volume on two-lane highways 170

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APPENDIX B HEADWAY DISTRIBUTION Table B-1. Time headway distribution (traffic flow rate = 900 veh/h ~ 1140 veh/h) 5414.0sec,1sec,0.2,4686.0sec,0.4sec,5.1sec,5.5 ppPNPNPNPPsEPst 171

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Composite Distribution (Mean Headway = 3.5 sec)-0.050.000.050.100.150.200.01.02.03.04.05.06.07.08.09.010.0Headway (sec)Probability Shifted Negative Exponential Distribution Normal Distribution Composite Distribution Measured Distribution Figure B-1. Composite time headway distribution (based on Table B-1) 172

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173 Table B-2. Chi-Square test calculation (based on Table B-1) Time Headway Group f 0 f t f 0 f t 20)(tff ttfff20)( 0.0 0.5 16 33 -17 301 9.0686 0.5 1.0 84 69 15 230 3.3160 1.0 1.5 150 113 37 1394 12.3213 1.5 2.0 210 211 -1 1 0.0037 2.0 2.5 207 203 4 18 0.0904 2.5 3.0 172 165 7 45 0.2712 3.0 3.5 116 115 1 1 0.0116 3.5 4.0 86 74 12 151 2.0560 4.0 4.5 57 48 9 75 1.5585 4.5 5.0 44 35 8 72 2.0414 5.0 5.5 29 29 0 0 0.0043 5.5 6.0 25 24 1 0 0.0160 6.0 6.5 18 22 -3 10 0.4455 6.5 7.0 13 19 -6 34 1.7938 7.0 7.5 16 17 -1 1 0.0556 7.5 8.0 11 15 -4 18 1.2305 8.0 8.5 7 13 -6 42 3.2172 8.5 9.0 9 12 -2 5 0.4625 9.0 9.5 7 10 -4 13 1.2671 > 9.5 44 77 -33 1089 14.2249 1320 1320 0 4561.532CALC n = (I 1 p) = ( 20 1 ) 4 = 15. Significant Level = 0.05, 0.252TABLE 0.254561.53,22TABLECALC ; Therefore, reject hypothesi

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Table B-3. Time headway distribution (traffic flow rate = 1200 veh/h ~ 1440 veh/h) 5926.0sec,6.0sec,6.1,4074.0sec,0.2sec,3.2sec,3.4 ppPNPNPNPPsEPst 174

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Composite Distribution (Mean Headway = 2.7 sec)-0.050.000.050.100.150.200.01.02.03.04.05.06.07.08.09.010.0Headway (sec)Probability Shifted Negative Exponential Distribution Normal Distribution Composite Distribution Measured Distribution Figure B-2. Composite time headway distribution (based on Table B-3) 175

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176 Table B-4. Chi-Square test calculation (based on Table B-3) Time Headway Group f 0 f t f 0 f t 20)(tff ttfff20)( 0.0 0.5 20 23 -3 12 0.5070 0.5 1.0 102 98 4 14 0.1463 1.0 1.5 227 215 12 137 0.6350 1.5 2.0 256 245 11 113 0.4594 2.0 2.5 216 196 20 411 2.0962 2.5 3.0 148 152 -4 19 0.1218 3.0 3.5 107 91 16 240 2.6300 3.5 4.0 73 65 7 51 0.7832 4.0 4.5 49 51 -2 4 0.0790 4.5 5.0 33 40 -7 44 1.0991 5.0 5.5 18 31 -12 153 4.9525 5.5 6.0 16 24 -8 67 2.7839 6.0 6.5 12 19 -7 47 2.4899 6.5 7.0 9 15 -5 28 1.9480 7.0 7.5 8 11 -3 12 1.0339 7.5 8.0 5 9 -4 13 1.4306 8.0 8.5 4 7 -3 9 8.5 9.0 4 5 -1 2 9.0 9.5 3 4 -2 2 0.7823 > 9.5 11 15 -4 17 1.1631 1320 1320 0 141.252CALC n = (I 1 p) = ( 18 1 ) 4 = 13. Significant Level = 0.05, 4.222TABLE 4.22141.25,22TABLECALC ; Therefore, reject hypothesi

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Table B-5. Time headway distribution (traffic flow rate = 1500 veh/h ~ 1740 veh/h) 6818.0sec,5.0sec,5.1,3182.0sec,5.1sec,2.2sec,7.3 ppPNPNPNPPsEPst 177

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Composite Distribution (Mean Headway = 2.2 sec)-0.050.000.050.100.150.200.250.01.02.03.04.05.06.07.08.09.010.0Headway (sec)Probability Shifted Negative Exponential Distribution Normal Distribution Composite Distribution Measured Distribution Figure B-3. Composite time headway distribution (based on Table B-5) 178

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179 Table B-6. Chi-Square test calculation (based on Table B-5) Time Headway Group f 0 f t f 0 f t 20)(tff ttfff20)( 0.0 0.5 22 19 3 10 0.4934 0.5 1.0 140 122 18 310 2.5355 1.0 1.5 312 307 4 19 0.0616 1.5 2.0 294 307 -13 164 0.5342 2.0 2.5 209 198 10 102 0.5158 2.5 3.0 125 117 9 74 0.6293 3.0 3.5 78 71 7 47 0.6638 3.5 4.0 46 50 -4 15 0.2955 4.0 4.5 30 36 -5 30 0.8433 4.5 5.0 21 26 -5 21 0.8143 5.0 5.5 13 18 -5 27 1.4748 5.5 6.0 7 13 -7 43 3.2939 6.0 6.5 7 9 -3 8 0.8607 6.5 7.0 7 7 0 0 0.0044 7.0 7.5 3 5 -2 5 7.5 8.0 3 3 -1 1 8.0 8.5 0 2 -2 6 1.9678 8.5 9.0 2 2 0 0 9.0 9.5 1 1 0 0 > 9.5 3 1 -2 4 0.4183 1320 1320 0 4068.152CALC 70.192TABLE n = (I 1 p) = ( 16 1 ) 4 = 11. Significant Level = 0.05, 70.1941.15,22TABLECALC ; Therefore, not reject hypothesis.

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APPENDIX C ENTERING PERCENT FOLLOWING (EPF) CALCULATION C.1 Methods to Calculate EPF Downstream of Signal On calculating EPF downstream of signal, shifted negative exponential distribution and composite distribution are introduced into Dixon et al.s methodology [3]. Estimation of the percentage of entering traffic following is based on a flow profile immediately downstream of the signalized intersection. A flow profile immediately downstream of the signalized intersection at location A is shown in the Figure C-1. The A denotes a location immediately downstream of the signalized intersection. As shown in the Figure C-1, there are three movements that contribute to the flow profile: Movement 1: Primary contributing movement. They are through movements from the upstream major street, Movement 2: Secondary contributing movement. They are right-turn movements from the minor street, and Movement 3: Secondary contributing movement. They are left-turn movements from the minor street. As shown in the Figure C-1, the total cycle-length is divided into three states. The above three movements are discharged through the three states. They are: First state: Discharge from the through movement queue during the first phase Second state: Discharge from the through movement without a queue plus any right-turn on red executed during the first phase Third state: Discharge from the right and left turn movements during the second phase 180

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181 Figure C-1. Two-lane highway traffic flow downstream of a signalized intersection Source: Dixon, Michael P., Michael Kyte, and Satya Sai Kumar Sarepali. Effects of Upstream Signalized Intersections on Two-Lane Highway Operations, Transportation Research Board, Washington D.C., 2004 Entering percent following at location A can be estimated using equation C-1: (C-1) aaaVVFEPF (C-2) iiaVFVF Where: EPF: percent of vehicles following at Point A, immediately downstream of a a signalized intersection, VF: total number of vehicles following per cycle at location A, veh a

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182 VF: total number of vehicles following per cycle from movement i, veh and i V a : total number of vehicles per cycle at location A, veh To determine the EPF a the key point is to decide the denominator, Va, and nominator, VFa. Because Va is the summation of the cycle-by-cycle volumes from movements 1, 2, and 3, it can be determined if volumes for movements 1, 2 and 3 and the cycle length are known. This leaves the estimation of VFa, the number of vehicles following at location A, which can be estimated by movement. Vehicles following in movement 1 Movement 1 is discharged during phase one, which is divided into flow state 1 and flow state 2. During state 1, since vehicles discharged are in a platoon, it can be assumed that all of the queued vehicles are in a platoon at location A, and are following, except the platoon leader, as represented in Equation C-4. Note that Equation C-4 is based on a deterministic queue length model, consistent with queue length equations used in the HCM 2000 signalized intersection analysis procedure. Equation C-3 is used to calculate t Q1 in Equation C-4 based on traffic flow rates and the timing plan of the signal. Here, uniform arrivals are assumed. Stochastic queue length models could be used instead to provide more realistic representations of the effects of random vehicle arrivals on queue length. )(11111gCvsvtQ (C-3) Where: t Q1 : time for queue at movement 1 to dissipate, sec v 1 : movement 1 demand flow rate, veh/h s 1 : saturation flow rate for movement 1, veh/h

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183 C: cycle length, sec and g 1 : phase one effective green time, sec 1)3600(s 111QQtVF (C-4) Where: VF Q1 : number of vehicles following in movement 1 that are discharging from a queue, veh/h During State 2, vehicles discharging from movement 1 when no queue is present may or may not be following at location A. If it is assumed that they are following if their headway is less than or equal to 3.0 seconds, the number of vehicles following at location A can be estimated using the shifted negative exponential distribution or composite distribution. When traffic flow rate is low, the shifted negative exponential distribution is used through Equation C-5; when traffic flow rate is high, the composite distribution is used through Equation C-6. )3600/()(11112,1.3600 v anqvtQNQetgVF (C-5) Where: VF NQ1 : number of vehicles following in movement 1 that are discharging when no queue is present, veh 2,anqv : flow rate at location A during flow rate 2, when no queue is present, veh/h : user-selected parameter, which affects the shift of the distribution, sec Or tsttPttNPQNQdtesPePtgVFPNP)21(1)3600( v 2)(21)/()(1111 (C-6)

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184 Where: P p : proportion of vehicle in platoon, % P NP : proportion of vehicles not in platoon, % pt : mean headway of the vehicles in platoon, sec Npt : mean headway of the vehicles not in platoon, sec : the minimum time headway for vehicles not in platoon, sec s: standard deviation of normal distribution, t: time headway being investigated, sec t : mean headway, sec/v 11212,QRTORaNQtgCPvvV (C-7) Where: v 2 : movement two demand flow rate, veh/h P RTOR : proportion of vehicles turning right on red When using Equation C-5 or Equation C-6, the following items should be noted: The through movement volume, v1, is used in Equation C-5 or Equation C-6 because it is estimating the number of vehicles following in movement 1. The time during the green time when no queue is present for movement 1 is g 1 tQ1. The proportion of these non-queued vehicles that are following, given a headway criterion of t, is estimated by the value in the brackets containing the shifted negative exponential distribution in Equation C-5 or the composite distribution Equation C-6. The volume, Vshown in Equation C-7, is used to calculate the mean headway because it is the volume occurring during flow state 2 at location A. Also note that Equation C-7 is comprised of the movement 1 flow rate (the first element) and the right-turn-on-red flow rate (the second element), which are the movements arriving at location A during flow state 2. 2,aNQ

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185 Proportion of right turn vehicles turning on red can be determined from the field measurement or by estimation Finally, the total number of through vehicles that are following at location A can be estimated as shown in Equation C-8. Note that an alternative to the estimation of as given by Equation C-4, is available as part of the signalized intersections procedure in the HCM 2000 and should be considered as part of a formal procedure implementing the methodology. 1Qt NQ1Q11VFVF VF (C-8) Where: VF 1 : total number of vehicles following per cycle from movement 1, veh Vehicles following in Movement 2 In the cross street, one lane is shared by through vehicles, left-turn vehicles, and right-turn vehicles. During the phase two, the left-turn vehicles need to yield to the through vehicles and right-turn vehicles in the opposite direction to drive into the main street. Here it is assumed that the secondary nature of left-turn movement and right-turn movement do not justify determining how these movements interact with other movements during the second phase. Vehicles in movement 2 are dissipated in State 2 and State 3. In the flow state 2, the right-turn vehicles are turning on red. When traffic flow rate in the flow state 2 is low, the number of vehicles following from movement two is estimated using Equation C-9, assuming a shifted negative exponential distribution of headways in the flow state 2. When the traffic flow rate in the flow state 2 is high, Equation C-10 is used for calculation, assuming a composite distribution of headway in the flow state 2.

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186 )1(3600v)3600/()(222,anqvtPRORePCVF (C-9) Where: : number of vehicles following in movement 2 that are discharging on red, 2VF veh Or ))21(1(3600v2)(21)/()(22tsttPttNPPTORdtesPePPCVFPNP (C-10) In the flow state 3, the number of vehicles following from movement two is estimated using Equation C-11 or Equation C-12, respectively, assuming a negative exponential distribution of headways or composite distribution. When traffic flow rate is low, the shifted negative exponential distribution is used through Equation C-11; when traffic flow rate is high, the composite distribution is used through Equation C-12. )1)(1(3600v)3600/()(223,avtPTORePCVF (C-11) Where: : number of vehicles following in movement 2 that are discharging not on 2VF red, veh : flow rate at location A during flow state 3, veh/h and 3,av Or ))21(1)(1(3600v2)(21)/()(22tsttPttNPPTORdtesPePPCVFPNP (C-12) )1(2313,RTORaPvvgCCv (C-13)

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187 Where: : movement 3 demand flow rate, veh/h 3v When using Equation C-9, C-10, C-11 or C-12, the following items should be noted: The right-turn movement volume, v 2 is used in Equation C-9, C-10, C-11 or C-12, because it is estimating the number of vehicles following in movement 2. The volume, shown in Equation C-9, is used to calculate the mean headway because it is the volume occurring during flow state 3 at location A. Also note that Equation C-11 is comprised of the movement 3 flow rate (the first element) and the right-turn-on-green flow rate (the second element), which are the movements arriving at location A during flow state 3. 3,av The variable, (, is the portion of right-turn vehicle dissipated on green in the flow state 3. )1RTORP Finally, the total number of right-turn vehicles that are following at location A can be estimated as shown in Equation C-13. 222 VFVFVF (C-13) Where: : total number of vehicle following per cycle from movement 2, veh 2VF Vehicles following in movement 3 Vehicles following from the left-turn movement are determined for flow state 3 only. When traffic flow rate in the flow state 3 is low, the number of vehicles following from movement 3 is estimated using Equation C-14, assuming a shifted negative exponential distribution of headways in the flow state 3. When traffic flow rate in the flow state 3 is high, Equation C-15 is used for calculation, assuming a composite distribution of headway in the flow state 3.

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188 )3600/()(333,13600vavteCVF (C-14) Where: 3VF : total number of vehicle following per cycle from movement 3, veh Or ))21(1)(1(3600v2)(21)/()(33tsttPttNPPTORdtesPePPCVFPNP (C-15) When using Equation C-14 or C-15, the following items should be noted: The right-turn movement volume, v 3 is used in Equation C-14 and C-15, because it is estimating the number of vehicles following in movement 3. The volume, shown in Equation C-14, is used to calculate the mean headway because it is the volume occurring during flow state 3 at location A. Also note that Equation C-14 is comprised of the movement 3 flow rate (the first element) and the right-turn-on-green flow rate (the second element), which are the movements arriving at location A during flow state 3. 3,av When determining the number of vehicles following at a location immediately downstream of the signalized intersection, either the shifted negative exponential distribution or composite distribution of headway is used. In Equation C-5, Equation C-9, Equation C-11, and Equation C-14, the shifted negative exponential distribution of headways is assumed. The traffic flow rates used to calculate mean headway are different under different flow states for different movements. In Equation C-6, Equation C-10, Equation C-12, and Equation C-15, the composite distribution of headways is assumed. Note that the variables sttPnppNP,,,,,P P in these equations are expressed in the same ways, but their values are different. All these values are decided by the vehicle volumes under the different conditions. It is summarized as follows:

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189 In Equation C-6, vehicles following from the through movement that are discharging when no queue is present are determined. The flow rate at location A during flow state 2, v is used to determine these parameters of 2,aNQ sttPnppNP,,,,,P P in the composite distribution. Note that v is composed of the movement 1 flow rate and the right-turn-on red flow rate. 2,aNQ In Equation C-10, vehicles following from the right-turn movement that are discharging on red during flow state 2 are determined. The flow rate at location A during flow state 2, v is still used to determine these parameters of 2,aNQ sttPnppNP,,,,,P P in the composite distribution. In Equation C-12, vehicles following from the right-turn movement that are discharging on green during flow state 3 are determined, and the flow rate at location A during flow state 3, is used to determine these parameters of 3,av sttPnppNP,,,,,P P in the composite distribution. Note that the flow rate 3 volume used is comprised of left-turn vehicles and right-turn-on-green vehicles. In Equation C-15, vehicles following from the left-turn movement during flow state 3 are determined, and the flow at location A during flow state 3, v is still used to determine these parameters of 3,a ,s,t,t,,PPnppNPP in the composite distribution. After are decided, the EPF at location A, can be calculated using the following equation: 321 and ,VFVFVF aaVVFVFVFEPF321 (C-16) Table C-1 summarized the values of EPF under the different traffic conditions and signal timing plans. Due to plenty of calculation, a program was developed to calculate the Entering Percent Following using the Visual Basic Language. The Visual Basic code is presented in Appendix D. C.2 Method to Calculate EPF Without Signal Dixon et al. concluded that it was appropriate to represent the effects of a signalized intersection on the downstream two-lane highway operations through the EPF parameters, as long as the percent following immediately downstream of a signalized intersection can be determined. In this study, the methodology for determining Entering

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190 Percent Following referred to Dixon et al.s methodology [3]. The main difference from their methodology reflects on the application of distributions for time headway. As discussed in Chapter 4, the shifted negative exponential distribution and composite distribution are introduced into this methodology. The detailed procedure determining Entering Percent Following downstream of a signalized intersection are presented as follows. The entering percent following at the location A, without experiencing the effects of a signalized intersection can be calculated using Equation C-17 or C-18. When the traffic flow rate is low, the headway distribution of entering traffic can be assumed to be shifted negative exponential and Equation C-17can be used to estimate EPF; when the traffic flow is high, the headways of entering traffic can be assumed to following composite distribution ad Equation C-18 can be used to estimate EPF. )3600/()(1100aqtaeEPF (C-17) Where: EPF a : entering percent following at the location a : flow rate at location a, vph aq Or ))21(1)(1(1002)(21)/()(tsttPttNPPTORadtesPePPEPFPNP (C-18) aqt3600 (C-19) Where: t : average time headway, sec

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191 In Equation C-18, the average time headway is calculated using Equation C-19, and other parameters ( ,t,t,,P PnppNPP ) in the composite distribution can be determined referring to the detailed procedure presented in Chapter 4.

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192 Table C-1. Entering Percent Following with a signalized intersection Through Vehicles (veh/h) Right/Left Turn Vehicles (veh/h) Cycle Length (sec) g/C EPF Through Vehicles (veh/h) Right/Left Turn Vehicles (veh/h) Cycle Length (sec) g/C EPF 200 20 60 0.6 0.2069 200 20 60 0.7 0.1192 200 20 60 0.8 0.0324 200 20 75 0.6 0.2615 200 20 75 0.7 0.1737 200 20 75 0.8 0.0869 200 20 90 0.6 0.2978 200 20 90 0.7 0.2101 200 20 90 0.8 0.1233 200 20 105 0.6 0.3238 200 20 105 0.7 0.2361 200 20 105 0.8 0.1493 200 20 120 0.6 0.3433 200 20 120 0.7 0.2556 200 20 120 0.8 0.1687 200 40 60 0.6 0.1984 200 40 60 0.7 0.1205 200 40 60 0.8 0.0457 200 40 75 0.6 0.2484 200 40 75 0.7 0.1705 200 40 75 0.8 0.0957 200 40 90 0.6 0.2818 200 40 90 0.7 0.2038 200 40 90 0.8 0.1291 200 40 105 0.6 0.3056 200 40 105 0.7 0.2276 200 40 105 0.8 0.1529 200 40 120 0.6 0.3234 200 40 120 0.7 0.2455 200 40 120 0.8 0.1707 200 60 60 0.6 0.1958 200 60 60 0.7 0.1275 200 60 60 0.8 0.0655 200 60 75 0.6 0.242 200 60 75 0.7 0.1737 200 60 75 0.8 0.1117 200 60 90 0.6 0.2727 200 60 90 0.7 0.2044 200 60 90 0.8 0.1425 200 60 105 0.6 0.2947 200 60 105 0.7 0.2264 200 60 105 0.8 0.1644 200 60 120 0.6 0.3112 200 60 120 0.7 0.2429 200 60 120 0.8 0.1809 400 40 60 0.6 0.4515 400 40 60 0.7 0.3662 400 40 60 0.8 0.2826 400 40 75 0.6 0.4788 400 40 75 0.7 0.3935 400 40 75 0.8 0.3099 400 40 90 0.6 0.4969 400 40 90 0.7 0.4117 400 40 90 0.8 0.3281 400 40 105 0.6 0.5099 400 40 105 0.7 0.4246 400 40 105 0.8 0.3411 400 40 120 0.6 0.5197 400 40 120 0.7 0.4344 400 40 120 0.8 0.3508 400 80 60 0.6 0.4309 400 80 60 0.7 0.3573 400 80 60 0.8 0.2896 400 80 75 0.6 0.4559 400 80 75 0.7 0.3823 400 80 75 0.8 0.3146 400 80 90 0.6 0.4725 400 80 90 0.7 0.399 400 80 90 0.8 0.3313 400 80 105 0.6 0.4844 400 80 105 0.7 0.4109 400 80 105 0.8 0.3432 400 80 120 0.6 0.4934 400 80 120 0.7 0.4198 400 80 120 0.8 0.3521 400 120 60 0.6 0.4219 400 120 60 0.7 0.3607 400 120 60 0.8 0.3103 400 120 75 0.6 0.445 400 120 75 0.7 0.3838 400 120 75 0.8 0.3334 400 120 90 0.6 0.4604 400 120 90 0.7 0.3992 400 120 90 0.8 0.3488 400 120 105 0.6 0.4714 400 120 105 0.7 0.4102 400 120 105 0.8 0.3597 400 120 120 0.6 0.4796 400 120 120 0.7 0.4184 400 120 120 0.8 0.368

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193 600 60 60 0.6 0.7 0.5988 600 60 60 0.5149 600 60 60 0.8 0.4334 600 60 75 0.6 0.6169 600 60 75 0.7 0.533 600 60 75 0.8 0.4516 600 60 90 0.6 0.6291 600 60 90 0.7 0.5452 600 60 90 0.8 0.4637 600 60 105 0.6 0.6377 600 60 105 0.7 0.5538 600 60 105 0.8 0.4724 600 60 120 0.6 0.6442 600 60 120 0.7 0.5603 600 60 120 0.8 0.4789 600 120 60 0.6 0.5736 600 120 60 0.7 0.5033 600 120 60 0.8 0.4408 600 120 75 0.6 0.5903 600 120 75 0.7 0.52 600 120 75 0.8 0.4574 600 120 90 0.6 0.6014 600 120 90 0.7 0.5311 600 120 90 0.8 0.4685 600 120 105 0.6 0.6093 600 120 105 0.7 0.539 600 120 105 0.8 0.4765 600 120 120 0.6 0.6153 600 120 120 0.7 0.545 600 120 120 0.8 0.4824 600 180 60 0.6 0.5643 600 180 60 0.7 0.5083 600 180 60 0.8 0.4722 600 180 75 0.6 0.5797 600 180 75 0.7 0.5237 600 180 75 0.8 0.4876 600 180 90 0.6 0.5899 600 180 90 0.7 0.5339 600 180 90 0.8 0.4978 600 180 105 0.6 0.5973 600 180 105 0.7 0.5413 600 180 105 0.8 0.5051 600 180 120 0.6 0.6028 600 180 120 0.7 0.5468 600 180 120 0.8 0.5106 800 80 60 0.6 0.7213 800 80 60 0.7 0.6372 800 80 60 0.8 0.5562 800 80 75 0.6 0.735 800 80 75 0.7 0.6508 800 80 75 0.8 0.5698 800 80 90 0.6 0.7441 800 80 90 0.7 0.6599 800 80 90 0.8 0.5789 800 80 105 105 0.6 0.7506 800 80 0.7 0.6664 800 80 105 0.8 0.5854 800 80 120 0.6 0.7554 800 80 120 0.7 0.6713 800 80 120 0.8 0.5903 800 160 60 0.6 0.7 0.6951 800 160 60 0.6261 800 160 60 0.8 0.5664 800 160 75 0.6 0.7076 800 160 75 0.7 0.6386 800 160 75 0.8 0.5789 800 160 90 0.6 0.7159 800 160 90 0.7 0.6469 800 160 90 0.8 0.5873 800 160 105 0.6 0.7219 800 160 105 0.7 0.6529 800 160 105 0.8 0.5932 800 160 120 0.6 0.7263 800 160 120 0.7 0.6573 800 160 120 0.8 0.5977 800 240 60 0.6 0.6878 800 240 60 0.7 0.6346 800 240 60 0.8 0.6205 800 240 75 0.6 0.6993 800 240 75 0.7 0.6461 800 240 75 0.8 0.6321 800 240 90 0.6 0.707 800 240 90 0.7 0.6538 800 240 90 0.8 0.6398 800 240 105 0.6 0.7125 800 240 105 0.7 0.6593 800 240 105 0.8 0.6453 800 240 120 0.6 0.7166 800 240 120 0.7 0.6634 800 240 120 0.8 0.6494 1000 100 60 0.6 0.8435 1000 100 60 0.7 0.7798 1000 100 60 0.8 0.7184 1000 100 75 0.6 0.8544 1000 100 75 0.7 0.7907 1000 100 75 0.8 0.7294 1000 100 90 0.6 0.8617 1000 100 90 0.7 0.798 1000 100 90 0.8 0.7366 1000 100 105 0.6 0.8669

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194 1000 100 105 0.7 0.8032 1000 100 105 0.8 0.7418 1000 100 120 0.6 0.8708 1000 100 120 0.7 0.8071 1000 100 120 0.8 0.7457 1000 200 60 0.6 0.8121 1000 200 60 0.7 0.7656 1000 200 60 0.8 0.7389 1000 200 75 0.6 0.8221 1000 200 75 0.7 0.7756 1000 200 75 0.8 0.7489 1000 200 90 0.6 0.8288 1000 200 90 0.7 0.7823 1000 200 90 0.8 0.7556 1000 200 105 0.6 0.8335 1000 200 105 0.7 0.787 1000 200 105 0.8 0.7603 1000 200 120 0.6 0.8371 1000 200 120 0.7 0.7906 1000 200 120 0.8 0.7639 1000 300 60 0.6 0.8027 1000 300 60 0.7 0.7888 1000 300 60 0.8 0.7749 1000 300 75 0.6 0.812 1000 300 75 0.7 0.798 1000 300 75 0.8 0.7841 90 0.6 0.8181 1000 300 0.7 0.8042 1000 300 90 0.8 0.7903 1000 300 105 0.6 0.8225 1000 300 105 0.7 0.8086 1000 300 105 0.8 0.7947 1000 300 120 0.6 0.8258 1000 300 120 0.7 0.8119 1000 300 120 0.8 0.798 1200 120 60 0.7 0.8657 1200 120 60 0.8 0.803 1200 120 75 0.7 0.8748 75 0.8 0.8121 1200 120 90 0.7 0.8808 1200 120 105 90 0.8 0.8182 1200 120 0.7 0.8852 1200 120 105 0.8 0.8225 1200 120 120 0.7 0.8884 1200 120 120 0.8 0.8258 1200 240 60 0.7 0.8495 1200 240 60 0.8 0.827 1200 240 75 0.7 0.8579 1200 240 75 0.8 0.8353 1200 240 90 0.7 0.8634 1200 240 90 0.8 0.8409 1200 240 105 0.7 0.8674 1200 240 105 0.8 0.8449 1200 240 120 0.7 0.8704 1200 240 120 0.8 0.8478 1200 360 60 0.7 0.8815 1200 360 60 0.8 0.8521 1200 360 75 0.7 0.8892 1200 360 75 0.8 0.8598 1200 360 90 0.7 0.8943 1200 360 90 0.8 0.8649 1200 360 105 0.7 0.8979 1200 360 105 0.8 0.8686 1200 360 120 0.7 0.9007 1200 360 120 0.8 0.8713 1400 140 60 0.8 0.8915 1400 140 75 0.8 0.8993 1400 140 90 0.8 0.9045 1400 140 105 0.8 0.9082 1400 140 120 0.8 0.911 1400 280 60 0.8 0.9134 1400 280 75 0.8 0.9205 1400 280 90 0.8 0.9253 1400 280 105 0.8 0.9287 1400 280 120 0.8 0.9313 1400 420 60 0.8 0.9249 1400 420 75 0.8 0.9315 1400 420 90 0.8 0.9359 1400 420 105 0.8 0.9391 1400 420 120 0.8 0.9414 1000 300 90 1200 120

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195 Table C-2. Entering Percent Following with no signalized intersection Volume (veh/h) EPF Volume (veh/h) EPF Volume (veh/h) EPF 220 0.1458 240 0.1584 260 0.1708 440 0.2778 480 0.3003 520 0.3224 660 0.3962 720 0.4262 780 0.4553 880 0.5015 960 0.5366 1040 0.5701 1100 0.5941 1200 0.6321 1300 0.6677 1320 0.6745 1440 0.7135 1560 0.7492 1540 0.7434 1680 0.7817 1820 0.8157

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APPENDIX D VISUAL BASIC CODE D.1 Calculate Entering Percent Following Sub Calculate_EPF() Dim EPF As Double 196 Dim VFA_Total, VA, VF1, VF2, VF3, V1, V2, V3 As Double Dim VFQ1, VFNQ1, VNQ_a_2, V_a_3, Prtor As Double Dim Tq1, S1, C, g1, t As Double Dim Percent_Following_1, Percent_Following_2 As Double set values for some parameters S1 = 1800 V1 = G_Volume V2 = G_R_L V3 = G_R_L C = G_Cycle g1 = G_Cycle G_g_C g_c = g1 / C Prtor = 0.1 t = 3 set the propability of headway greater than 3 at the different flow rates PF_800 = 0.4647 PF_1028 = 0.6889 PF_1333 = 0.7741

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PF_1636 = 0.8654 tell if the demand is above capacity If ((V1) / (S1 g_c)) > 1 Then 197 G_Comment = "Over Capacity!" G_EPF = 0.99999 GoTo LAB1 End If vehicle following in movement one Tq1 = V1 / (S1 V1) (C C g_c) VFQ1 = S1 (Tq1 / 3600) 1 If ((V1) / (S1 g_c)) = 1 Then VNQ_a_2 = V1 Else VNQ_a_2 = V1 + V2 Prtor (C / (C g_c Tq1)) End If If VNQ_a_2 < 800 Then Percent_Following_1 = 1 Exp(-(t 0.5) / (3600 / VNQ_a_2 0.5)) ElseIf VNQ_a_2 < 1028 Then Percent_Following_1 = PF_800 + (VNQ_a_2 800) / (1028 800) (PF_1028 PF_800) ElseIf VNQ_a_2 < 1333 Then Percent_Following_1 = PF_1028 + (VNQ_a_2 1028) / (1333 1028) (PF_1333 PF_1028) ElseIf VNQ_a_2 < 1636 Then Percent_Following_1 = PF_1333 + (VNQ_a_2 1333) / (1636 1333) (PF_1636 PF_1333) Else

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Percent_Following_1 = PF_1636 End If VFNQ1 = V1 ((C g_c Tq1) / 3600) Percent_Following_1 VF1 = VFQ1 + VFNQ1 vehicle following in movement Two and Three V_a_3 = (C / (C C g_c)) (V3 + V2 (1 Prtor)) If V_a_3 < 800 Then Percent_Following_2 = 1 Exp(-(t 0.5) / (3600 / V_a_3 0.5)) ElseIf V_a_3 < 1028 Then Percent_Following_2 = PF_800 + (V_a_3 800) / (1028 800) (PF_1028 PF_800) ElseIf V_a_3 < 1333 Then Percent_Following_2 = PF_1028 + (V_a_3 1028) / (1333 1028) (PF_1333 PF_1028) ElseIf V_a_3 < 1636 Then Percent_Following_2 = PF_1333 + (V_a_3 1333) / (1636 1333) (PF_1636 PF_1333) Else Percent_Following_2 = PF_1636 End If VF2 = V2 (C / 3600) ((1 Prtor) Percent_Following_2 + Prtor Percent_Following_1) VF3 = V3 C / 3600 Percent_Following_2 The Entering Percent Following EPF = (VF1 + VF2 + VF3) / ((V1 + V2 + V3) / 3600 C) 198

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LAB1: End Sub D.2 Extract Average Travel Speed From CORSIM Output Sub Processing_CORSIM_Output(Common_directory) Dim OutputFile_1, OutputFile_2, OutputFile_3, OriginalFile As String Dim A, B, C, D, E, file_number As Integer Dim Switch, key_word, lineoftext As String Dim i, j, k, point, length_string As Integer Dim k1 As Double Dim Array_speed(1 To 1200, 1 To 2), Array_1(1 To 120, 1 To 2) As String Dim speed, link_info, link_1, link_2, Print_String, Sum_Speed, As String For A = 400 To 1000 Step 300 For B = 0.5 To 0.6 Step 0.05 For C = 60 To 90 Step 15 For D = 55 To 75 Step 10 For E = 8 To 11 Step 3 FileHeader_1 = CStr(A) + "_" + CSt r(B) + "_" + CStr(C) + "_0" + CStr(D) + "_" + CStr(E) + "%" 199 For file_number = 1 To 10 OriginalFile = Common_directory + FileHeader_1 + "_" + CStr(file_number) + ".out" OutputFile_1 = Common_directory + FileHeader_1 + ".txt" OutputFile_2 = Common_directory + FileHeader_1 + "_2.txt" OutputFile_3 = Common_directory + FileHeader_1 + ".csv" Open OriginalFile For Input As #1

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Open OutputFile_1 For Output As #2 Switch = "Close" Do Until EOF(1) Line Input #1, lineoftext lineoftext = Trim(lineoftext) key_word = Left(lineoftext, 12) If key_word = "VEHICLE MINU" Then Switch = "Open" i = 1 GoTo Lab1 200 End If If key_word = "0SUBNETWORK=" Then Switch = "Close" GoTo Lab2 End If If Switch = "Open" And i > 5 And i < 51 Then Print #2, lineoftext End If Lab1: i = i + 1 Loop Lab2: Close #1 Close #2 Open OutputFile_1 For Input As #3 Open OutputFile_2 For Append As #4 i = 1 Do Until EOF(3)

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Line Input #3, lineoftext lineoftext = Trim(lineoftext) point = InStr(lineoftext, ")") link_info = Left(lineoftext, point 1) point = InStr(lineoftext, ",") length_string = Len(link_info) link_1 = Trim(Mid(link_info, 2, length_string point)) link_2 = Trim(Right(link_info, length_string point)) point = InStrRev(lineoftext, ") length_string = Len(lineoftext) speed = Right(lineoftext, length_string point) If CLng(link_1) >= 1184 And CLng(link_2) <= 1304 And CLng(link_1) < CLng(link_2) Then Array_1(i, 1) = link_1 Array_1(i, 2) = speed i = i + 1 End If Loop For j = 1184 To 1304 For i = 1 To 120 If Array_1(i, 1) = CStr(j) Then Print #4, CStr((j 1184) (132 / 5280)) + "," + string_1(i, 2) GoTo Lab3 End If Next i Lab3: Next j Close #3 Close #4 Next file_number 201

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Open OutputFile_2 For Input As #5 Open OutputFile_3 For Output As #6 i = 1 Do Until EOF(5) Line Input #5, lineoftext lineoftext = Trim(lineoftext) point = InStr(lineoftext, ",") Array_speed(i, 1) = Left(lineoftext, point 1) Array_speed(i, 2) = Right(lineoftext, Len(lineoftext) point) i = i + 1 Loop For k = 0 To 3000 Step 25 Print_String = "" Sum_Speed = 0 k1 = CDbl(k) / 1000 For i = 1 To 1200 If Array_speed(i, 1) = CStr(k1) Then Print_String = Print_String + "," + CStr(Array_speed(i, 2)) Sum_Speed = Sum_Speed + CDbl(Array_speed(i, 2)) End If Next i Print #6, Trim(CStr(k1)) + "," + Trim(Print_String) + "," + CStr((Sum_Speed / 10)) Next k Close #5 Close #6 Next E Next D Next C 202

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Next B Next A End Sub OriginalFile_1 = Common_Directory + Header_OriginalFile_1 OriginalFile_2 = Common_Directory + Header_OriginalFile_2 203 D.3 Determine Upstream Effective Length Sub Getting_Expective_Length(Common_Directory) Dim OriginalFile_1, OriginalFile_2, OutputFile, Print_Head As String Dim Header_OriginalFile_1, Header_OriginalFile_2 As String Dim A, B, C, D, E, F, file_number As Integer Dim lineoftext As String Dim i, j, k, point, length_string As Integer Dim String_WithoutSignal(1 To 120, 1 To 2), String_WithSignal(1 To 120, 1 To 13) As String Dim Diff_1, Diff_2 As Double For A = 400 To 1000 Step 300 For B = 50 To 60 Step 5 For C = 60 To 90 Step 15 For D = 55 To 75 Step 10 For E = 5 To 11 Step 3 Header_OriginalFile_1 = CStr(A) + "_0" + CStr(B) + "_" + CStr(C) + "_0" + CStr(D) + "_" + CStr(E) + "%.csv" F = A / B 100 A Header_OriginalFile_2 = "WithoutSignal_" + CStr(A) + "_" + CStr(F) + ".csv" OutputFile = Common_Directory + Header_OriginalFile_1+".csv" Open OriginalFile_1 For Input As #1

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Open OriginalFile_2 For Input As #2 Open OutputFile For Append As #3 j = 1 End If text 204 Do Until EOF(1) Line Input #1, lineoftext lineoftext = Trim(lineoftext) If Len(lineoftext) < 20 Then GoTo LabA1 point = InStr(lineoftext, ",") k = 1 Do Until point = 0 String_WithSignal(j, k) = Left(lineoftext, point 1) k = k + 1 length_string = Len(lineoftext) lineoftext = Right(lineoftext, length_string point) point = InStr(lineoftext, ",") Loop j = j + 1 Loop LabA1: j = 1 Do Until EOF(2) Line Input #2, lineof lineoftext = Trim(lineoftext) If Len(lineoftext) < 20 Then GoTo LabA2

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End If point = InStr(lineoftext, ",") k = 1 Do Until point = 0 String_WithoutSignal(j, k) = Left(lineoftext, point 1) k = k + 1 length_string = Len(lineoftext) lineoftext = Right(lineoftext, length_string point) point = InStr(lineoftext, ",") Loop j = j + 1 Loop LabA2: Print_Head = CStr(A) + "," + "0." + CStr(B) + "," + CStr(C) + "," + "0." + CStr(D) + "," + CStr(E) + "%" + "," For j = 3 To 12 For i = 40 To 1 Step -1 Diff_1 = CDbl(String_WithoutSignal(i + 1, 2)) CDbl(String_WithSignal(i + 1, j)) Diff_2 = CDbl(String_WithoutSignal(i, 2) CDbl(String_WithSignal(i, j))) If Diff_2 = 0 Then Print_Head = Print_Head + CStr(1 CDbl(String_WithoutSignal(i + 1, 1))) + "," GoTo LabA3 End If If Diff_1 > 0 And Diff_2 < 0 Then Print_Head = Print_Head + CStr(1 CDbl(String_WithoutSignal(i + 1, 1))) + "," GoTo Lab1A3 End If If Diff_1 > 0 And Diff_2 > 0 And Diff_1 < 5 And Diff_2 < 5 And 205

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Abs(Diff_1 Diff_2) < 0.5 Then Print_Head = Print_Head + CStr(1 CDbl(String_WithoutSignal(i, 1))) + "," GoTo LabA3 End If Next i 206 LabA3: Next j Print #3, Print_Head Close #1 Close #2 Close #3 Next E Next D Next C Next B Next A End Sub

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APPENDIX E PLOTS OF DIFFERENCE IN AVERAGE TRAVEL SPEED FROM TWOPAS Traffic Flow Rate = 440 vph-1-0.500.511.52050100150200250300Position (100ft)Speed Difference (mph) 60Sec_0.6 60Sec_0.7 60Sec_0.8 90Sec_0.6 90Sec_0.7 90Sec_0.8 120Sec_0.6 120Sec_0.7 120Sec_0.8 Downstream Effective Length Figure E-1. Difference in the average travel speed with traffic volume = 440 veh 207

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Traffic Flow Rate = 660 vph-0.500.511.522.5050100150200250300Position (100ft)Speed Difference (mph) 60Sec_0.6 60Sec_0.7 60Sec_0.8 90Sec_0.6 90Sec_0.7 90Sec_0.8 120Sec_0.6 120Sec_0.7 120Sec_0.8 Downstream Effective Length Figure E-2. Difference in the average travel speed with traffic volume = 660 veh/h 208

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Traffic Flow Rate = 880 vph-0.500.511.522.5050100150200250300Position (100ft)Speed Difference (mph) 60Sec_0.6 60Sec_0.7 60Sec_0.8 90Sec_0.6 90Sec_0.7 90Sec_0.8 120Sec_0.6 120Sec_0.7 120Sec_0.8 Downstream Effective Length Figure E-3. Difference in the average travel speed with traffic volume = 880 veh/h 209

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Traffic Flow Rate = 1100 vph-1-0.500.511.522.533.54050100150200250300Position (100ft)Speed Difference (mph) 60Sec_0.6 60Sec_0.7 60Sec_0.8 90Sec_0.6 90Sec_0.7 90Sec_0.8 120Sec_0.6 120Sec_0.7 120Sec_0.8 Downstream Effective Length Figure E-4: Difference in the average travel speed with traffic volume = 1110 veh/h 210

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Traffic Flow Rate = 1320 vph-1-0.500.511.522.53050100150200250300Position (100ft)Speed Difference (mph) 60Sec_0.7 60Sec_0.8 90Sec_0.7 90Sec_0.8 120Sec_0.7 120Sec_0.8 Downstream Effective Length Figure E-5. Difference in the average travel speed with traffic volume = 1320 veh/h 211

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APPENDIX F PLOTS OF DIFFERENCE IN AVERAGE TRAVEL SPEED FROM CORSIM Traffic Flow Rate = 220 veh/h01020304050607000.511.522.533.544.5Position Along the Downstream Segment (mi)Average Travel Speed (mi/h) C=120 sec; g/C=0.6 C=120 sec; g/C=0.7 C=120 sec; g/C=0.8 C=90 sec; g/C=0.6 C=90 sec; g/C=0.7 C=90 sec; g/C=0.8 C=60 sec; g/C=0.6 C=90 sec; g/C=0.7 With No Signal Downstream Effective LengthSignalized Intersection Figure F-1. Difference in the average travel speed with traffic volume = 220 veh/h 212

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Traffic Flow Rate = 440 veh/h010203040506000.511.522.533.544.5Position Along the Downstream Segment (mi)Average Travel Speed (mi/h) C=120 sec; g/C=0.6 C=120 sec; g/C=0.7 C=120 sec; g/C=0.8 C=90 sec; g/C=0.6 C=90 sec; g/C=0.7 C=90 sec; g/C=0.8 C=60 sec; g/C=0.6 C=90 sec; g/C=0.7 With No Signal Downstream Effective Len g th OASignalized Intersection Figure F-2. Difference in the average travel speed with traffic volume = 440 veh/h 213

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Traffic Flow Rate = 660 veh/h010203040506000.511.522.533.544.5Position Along the Downstream Segment (mi)Average Travel Speed (mi/h) C=120 sec; g/C=0.6 C=120 sec; g/C=0.7 C=120 sec; g/C=0.8 C=90 sec; g/C=0.6 C=90 sec; g/C=0.7 C=90 sec; g/C=0.8 C=60 sec; g/C=0.6 C=90 sec; g/C=0.7 With No Signal Downstream Effective LengthSignalized Intersection Figure F-3. Difference in the average travel speed with traffic volume = 660 veh/h 214

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Traffic Flow Rate = 880 veh/h01020304050607000.511.522.533.544.5Position Along the Downstream Segment (mi)Average Travel Speed (mi/h) C=120 sec; g/C=0.6 C=120 sec; g/C=0.7 C=120 sec; g/C=0.8 C=90 sec; g/C=0.6 C=90 sec; g/C=0.7 C=90 sec; g/C=0.8 C=60 sec; g/C=0.6 C=90 sec; g/C=0.7 With No Signal Downstream Effective LengthSignalized Intersection Figure F-4. Difference in the average travel speed with traffic volume = 880 veh/h 215

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Traffic Flow Rate = 1100 veh/h01020304050607000.511.522.533.544.5Position Along the Downstream Segment (mi)Average Travel Speed (mi/h) C=120 sec; g/C=0.6 C=120 sec; g/C=0.7 C=120 sec; g/C=0.8 C=90 sec; g/C=0.6 C=90 sec; g/C=0.7 C=90 sec; g/C=0.8 C=60 sec; g/C=0.6 C=90 sec; g/C=0.7 With No Signal Downsteam Effective LengthSignalized Intersection Figure F-5. Difference in the average travel speed with traffic volume = 1100 veh/h 216

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APPENDIX G NOMENCLATURE TABLE a : deceleration rate ATS 1 : average travel speed without the effect of a signalized intersection, mi/h ATS 2 : average travel speed within the downstream effective length of the upstream signalized intersection ATS d : average traffic speed in the analysis direction ATS pl : average travel speed for the entire segment including the passing lane (mi/h) BFFS: Base flow-flow speed for both directions of travel combined BPTSF: Base percent time-spent-following for both directions of travel combined c: capacity of lane group c L : lane group capacity per lane, veh/lane c m,x : capacity of movement x, veh/h C: cycle length d: control delay per vehicle d 1 : uniform control delay assuming uniform arrivals d 2 : incremental delay to account for effects of random arrivals d 3 : initial queue delay d A : delay for approach A d I : delay per vehicle for the intersection d l : computed control delay for the left-turn movements, s/veh d M, LT : delay to major street left-turning vehicles, s/veh d r : computed control delay for the right-turn movements, s/veh d Rank1 : delay to Rank 1 vehicles, s/veh dputed control delay for the through movements, s/veh D t: com D delay at the two-lane highway downstream of the signalized intersection f adjustment factor for access-point density f adjustment factor for approach grade : DH: delay time per vehicle for the two-lane highway segment, s/veh D S : delay time per vehicle for the signalized intersection influence area, s/veh D U : delay at the two-lane highway upstream of the signalized intersection E T : passenger-car equivalent for trucks E R : passenger-car equivalent for RVs EPP a : entering percent platooned at location a A: f ATS : adjustment factor for the effect of a signalized intersection on the average travel speed within the downstream effective length, mi/h. G: f HV : adjustment factor for heavy vehicles fLpb: pedestrian adjustment factor for left-turn movements f LS : adjustment factor for lane width and shoulder width f LT : adjustment factor for left turns in lane group f LU : adjustment factor for lane utilization f np : adjustment factor for percentage of no-passing zones 217

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218 f p : adjustment factor for existence of parking activity adjacent to the lane group f PA : supplemental adjustment factor for platoon arrival during the green fpl: factor for the effect of a passing lane on average travel speed PTD: percent time-delayed per vehicle f PTSF : adjustment factor for percent time-spent-following fRpb: pedestrian-bicycle adjustment factor for right-turn movements f RT : adjustment factor for right runs in lane group f W : adjustment factor for lane width F: a smoothing factor FFS: free flow speed for two-lane highways FFS H : free flow speed for the two-lane highway segment, ft/s FFS S : free flow speed for the signalized intersection influence area, ft/s g: effective green time for lane group g/C: effective green to cycle length ratio G: roadway grade I: upstream filtering factor for platoon arrivals L: length of the entire facility, ft L i : length of segment i L A : acceleration length Len eff_down : downstream effective length of a signalized intersection, mi Len eff_up : upstream effective length of a signalized intersection, ft L H : length of the two-lane highway segment, ft and L S : length of a signalized intersection influence area, ft L t : total length of analysis facility L U : length of two-lane highway upstream of the signalized intersection L V : average vehicle length LOS: level of service of the facility LOS i : the level of service of segment i k B : second-term adjustment factor related to early arrivals N: number of lanes in lane group jp,0 : proportion of Rank 1 vehicles not blocked P: proportion of all vehicles arriving during green P NP : proportion of vehicles not in platoon P P : proportion of vehicles in platoon P R : proportion of RVs in the traffic stream P RTOR : proportion of right turn vehicles turning on red P T : proportion of trucks in the traffic stream PHF: peak-hour factor PF: progression adjustment factor PF2: adjustment factor for effects of progression, veh q: hourly flow rate of traffic entering the two-lane highway, veh/h Q : maximum distance in vehicles over which queue extends from stop line, veh Q : average queue length, ft 1Q : first-term queued vehicles, veh, 2Q : second-term queued vehicles, veh

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219 Q QS average travel speed for two-lane highway downstream of the signalized intersection : average queue length bLQ : initial queue at start of analysis period, veh r: effective red time R p : platoon ratio s: saturation flow rate for subject lane group s L : lane group saturation flow rate per lane, veh/h S: standard deviation of normal distribution D: HS : average travel speed for two-lane highway segment, ft/s S m : mean speed of the measure sample S U : average travel speed for two-lane highway upstream of the signalized intersection SSD: stopping sight distance t: headway criteria used to define when vehicles are following, sec Pt : mean highway of the vehicles in platoon NPt : mean highway of the vehicles not in platoon t r: perception-reaction time T: analysis time period, h (T=0.25 for a 15-min period) T t : total travel time T tffs : total travel time based on FFS t Q1 : time for queue at movement one to dissipate V: demand volume for the full peak hour in the analysis direction v: speed at the end of the acceleration cycle, ft/s v 0 : speed at the beginning of the acceleration cycle, ft/s v 1 : movement 1 demand flow rate v 2 : movement 2 demand flow rate v 3 : movement 3 demand flow rate v d : passenger-car equivalent flow rate for the peak 15-min period in the analysis direction v i,1 : major-street through vehicles in shared lane, veh/h v i,2 : major-street right-turning vehicles in shared lane, veh/h v l : flow rate of left-turn traffic on the approach, veh/h v o : passenger-car equivalent flow rate for the peak 15-min period in the opposing direction v r : flow rate of right-turn traffic on the approach, veh/h v t : flow rate of through traffic on the approach, veh/h v x : flow rate for movement x, veh/h 3,av : flow rate at location A during flow state 3 V a : total number of vehicle per cycle at location a VF 1 : total number of vehicle following per cycle from movement 1 VF 2 : total number of vehicle following per cycle from movement 2 2VF : number of vehicle following per cycle from movement 2 during state 3 2VF : number of vehicle following per cycle from movement 2 during state 2 VF 3 : total number of vehicle following per cycle from movement 3 VF Q1 : number of vehicles following in movement 1 discharging from a queue VF NQ1 : number of vehicles following in movement 1 discharging when no queue is present

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220 X: v/c ratio X L : ratio of flow rate to capacity Y c : sum of critical lane group v/s ratios : acceleration model parameters, based on the design vehicle type u : average service rate : the minimum time headway for vehicles not in platoon : average arrival rate

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LIST OF REFERENCES 1. Transportation Research Board. Highway Capacity Manual. National Research Council, Washington D.C., USA. 2000. 2. AASHTO (American Association of State Highway and Transportation Officials). A Policy on Geometric Design of Highways and Streets, Fourth Edition, Washington, DC, 2001. 3. Dixon, Michael P., Michael Kyte, and Satya Sai Kumar Sarepali. Effects of Upstream Signalized Intersections on Two-Lane Highway Operations, Presentation at Transportation Research Board, Washington D.C., 2004. 4. Florida Department of Transportation. 2002 Quality/Level of Service Handbook, Tallahassee FL, 2002. 5. Washburn, Scott S., Douglas S. Mcleod, and Kenneth G. Courage. Adaptation of the HCM2000 for Planning Level Analysis of Two-lane and Multilane Highways in Florida, Transportation Research Board, Washington D.C., 2002, TRB 1802, pp. 62-68. 6. Interactive Highway Safety Design Model (IHSDM), Traffic Analysis Module (TAM) Engineerings Manual. Federal Highway Administration, Turner-Fairbank Highway Research Center, VA, 2003. 7. Glen, Koorey. Assessment of Rural Road Simulation Modeling Tools, IPENZ Transportation Group Technical Conference, New Zealand 2002. 8. ITT Industries for FHWA Office of Operations Research, Development and Technology, CORSIM Users Guide, Colorada Springs, CL, 2000. 9. University of Florida, Transportation Research Center, TRANSYT-7F Users Guide. Methodology for Optimizing Signal Timing, Gainesville, FL, 2003. 10. Hillier, J.A. and R. Rothery. The Synchronization of Traffic Signals for Minimum Delay, Transportation Science 1967, Vol. 2. May pp. 81-94. 11. Harwood, Douglas W., Adolf D. May, Ingrid B. Anderson, Lannon Leiman, and A. Ricardo Archilla. Capacity and Quality of Service of Two-lane Highways, Final Report of NCHRP Project 3-55(3). TRB, National Research Council, Washington, D.C. 1999. 12. Long, Gary. Acceleration Characteristics of Starting Vehicles, Transportation Research Board, Washington D.C., 2000. TRR 1737, pp. 58. 221

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222 Drew, Donald R. Traffic Flow Theory and Control. McGraw-Hill, Inc., New York, 1996. 13. 14. Institute of Transportation Engineers. Transportation and Traffic Engineering Handbook, 2 nd Edition, Prentice-Hall, Inc., Englewood Cliffs, NJ., 1982, 883 pages. 15. May, Adolf D. Traffic Flow Fundamentals, Prentice Hall, Inc. Englewood Cliffs, NJ, 1990. 16. Daniel, Frank C. Barnes, and Andre Schuhl. Poisson and Other Distributions in Traffic, Eno Foundaion, Saugatuck, CN, 1971. 17. Trafficware Training Services, Synchro and SimTraffic Guide, Sugar Land, TX, 2005. 18. Bonneson, A. James, and Fontaine, D. Michael, NCHRP REPORT 457 Engineering Study Guide for Evaluating Intersection Improvements, Texas Transportation Institute, Texas A&M University, College Station, TX, 2001.

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BIOGRAPHICAL SKETCH Qingyong Yu was born on August 12, 1975, in the Liaoning Province of China. He graduated with a Bachelor of Science Degree from the Department of Mining Engineering of the China University of Mining and Technology in 1997. Upon the completion of the undergraduate studies, he enrolled the College of Traffic and Transportation of Southwest Jiaotong University. In 1998, he was chosen as the representative of the graduate school to participate in developing Chinese Railway Passenger Tickets Distribution and Booking System, which is the largest and most complicated tickets distribution system in the world up to date. This project received first place in the 2000 National Science and Technology Progress Award, the most prestigious award in China; also it is part of the Smithsonians Archive in the United States. He obtained a Masters Degree in Engineering from the College of Traffic and Transportation of the Southwest Jiaotong University in May 2000. After graduation, he worked for Asiainfo Technologies (China) Inc. as a system engineer and provided technical consulting services for 12 projects, which covered more than five major areas in China (a potential market of 300 million users). In 2000 he was the only new employee in this company to achieve the Excellent Employee Award. In August 2001, he earned a graduate research assistantship from Mississippi State University and begun his graduate study in the Department of Civil Engineering. In January 2003, he transferred to the Department of Civil and Coastal Engineering of the 223

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224 University of Florida and obtained a Master of Engineering Degree in Civil Engineering in December 2003. After that, he continued his PhD program in traffic engineering. He was awarded Civil and Coastal Engineering (CCE) Alumni Fellowship to complete his studies at University of Florida. Meanwhile, he obtained the Outstanding Academic Achievement Award from University of Florida in 2003, 2004 and 2005.


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Title: Methodology for Operational Performance Assessment of Two-Lane Highway Facilities
Physical Description: Mixed Material
Copyright Date: 2008

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Holding Location: University of Florida
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METHODOLOGY FOR THE OPERATIONAL
PERFORMANCE ASSESSMENT OF TWO-LANE HIGHWAY FACILITIES

















By

QINGYONG YU


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2006


































Copyright 2006

by

Qingyong Yu















ACKNOWLEDGEMENTS

First I would like to say thank you to the many people who generously supported

me, both directly and indirectly, throughout my graduate studies at University of Florida

and in the process of completing my dissertation.

Secondly, I would like to express my deepest gratitude to Dr. Scott Washburn, my

advisor and dissertation committee chairman. It was with his guidance, his

encouragement and his financial support that helped me to finish my dissertation. I will

never forget the many weekends he gave up with his family to discuss the research with

me; I will always remember his encouragement and praise when I made any little

improvement; and many thanks go to him for his instructive comments to my proposal

and dissertation. Without his help I would not be where I am today.

I would also like to express my appreciation to my committee members, Dr. Lily

Elefteriadou, Mr. William M. Sampson, Dr. Charles R. Glagola, and Dr. Ruth Steiner for

their insight, guidance and patience throughout my studies and in the preparation of the

dissertation.

Finally, I dedicate this dissertation to my loving parents. Every call from them

made me feel that I was surrounded by their love. Here I would like them to share my

success with me.
















TABLE OF CONTENTS

page

ACKNOWLEDGEMENTS .............................................. iii

L IST O F T A B L E S .......... .......... .................. ................................... vii

LIST OF FIGURES .................................................................................. ix

AB STRACT ...................................... .......... ......................... xii

CHAPTER

1 IN TROD U CTION ................................... ............................ .............. 1

1.1 B background ...................... ............... ............. ................................ . 1
1.2 Problem Statement ....... ............... .......... ......... ......... .. ........ 1
1.3 Objectives and Tasks ............................... .................. 4
1.4 O organization of the D ocum ent...................... ................................. .............. 7

2 OVERVIEW OF ANALYSIS METHODS ...................................9

2 .1 A n alytical M eth od s ........ ............ .. .. .................................. ... ....... .... ......... 9
2.1.1 HCM Methodology for Two-Lane Highways ........................................ 9
2.1.2 HCM Methodology for Signalized and Unsignalized Intersections.............. 11
2.1.3 HCM Methodology for Urban Streets ..................................................... 12
2.1.4 Performance M measure Definition.................................................................. 12
2.1.5 FDOT HIGHPLAN Software .................... ..................................... 13
2.2 Sim ulation M methods ................................................ ........ .. ........ .. 14
2.2.1 TW OPA S Softw are....................................................... .......................... 14
2.2.2 TR A RR Softw are.......................................................... .......................... 17
2 .2 .3 C O R SIM Softw are .................. ............. ...................................................... 18
2.3 Effect of Upstream Signal on Two-Lane Highway PTSF ............ ................ 20

3 CONCEPTUAL OVERVIEW OF TWO-LANE HIGHWAY
FACILITY ANALYSIS METHODOLOGY ........................................22

3.1 Conceptual Framework for Facility Evaluation Methodology ............................ 22









3.1.1 The Definition of a Two-Lane Highway with Signalized/Unsignalized
Intersections ................... .............................22.........
3.1.2 Service M measure C consistency .................. .............. ............. ................. 26
3.1.3 Impacts of Signalized Intersection on Adjacent Highway Segments ............ 29
3.1.3.1 Effects of intersections on the upstream two-lane highway operation..... 30
3.1.3.2 Effects of intersections on the downstream two-lane highway operation 33
3.2 M ethodological A approach ............................................... ........................... 37
3.2.1 Service M measure Selection ..................................................... ... ................. 37
3.2.2 Facility Segm entation .................................................. 42
3.2.3 Overview of Computational M ethodology .................................................... 46

4 DEVELOPMENT OF FACILITY SEGMETNATION
C O M PU TA TIO N ........................................... .............................. 53

4.1 Effective Length of the Influence Area Upstream of the Signalized Intersection.. 54
4.1.1 Recommended Length in FDOT's 2002 Level/Quality of Service Handbook 54
4.1.2 Components of the Signal Influence Area....... ........................................ 55
4.1.2.1 D eterm ining stopping sight distance............................... .................... 59
4.1.2.2 Determining average queue length ................................. .............. 61
4.1.2.3 Determining acceleration distance............ ................................ 63
4.1.3 Sim ulation and Regression Analysis .............. .............................. ....... ....... 67
4.1.3.1 C contributing factor selection.............................................. .... .. .............. 68
4.1.3.2 Sim ulation m odel selection......................... ............................ ...... 70
4.1.3.3 Simulation model experimental design........................... .... .......... 72
4.1.3.4 Regression model development..................... ........ .............. 73
4.2 Effective Length of the Influence Area Downstream of Signalized Intersection... 77
4.2.1 Entering Percent Following of TWOPAS ................................................... 77
4 .2 .2 H eadw ay D distribution ...................................................................................... 78
4.2.2.1 Shifted negative exponential distribution ............................................. 79
4.2.2.2 Composite distribution.............. .............................. 80
4.2.3 Determining Entering Percent Following .................... ............................... 85
4.2.4 Effective Length of a Signalized Intersection on the Downstream Segment.. 89
4.2.5 Evaluation Based on CORSIM Simulation.............................. .................... 96

5 ESTIMATION OF SERVICE MEASURE VALUES...................... 100

5.1 F ree-Flow Speed E stim ation ....................................................... .................... 100
5.1.1 Field M easurem ent of Free-Flow Speed...................................................... 101
5.1.2 Estim eating Free-Flow Speeds .......................... ....... ................................. 102
5.2 Performance Measure on the Unaffected Two-Lane Highway Segment ......... 103
5.3 Performance Measure on an Affected Two-Lane Highway Segment ................ 105
5.4 Service Measure on a Two-Lane Highway with a Passing Lane........................ 112
5.5 Service Measure at a Signalized Intersection ............................................... 115
5.6 Service Measure at a TWSC Unsignalized Intersection.................................. 117
5.7 L evel of Service Thresholds ............................................ ........... ........ ...... 125









6 APPLICATION EXAMPLES ........ ............................. ... 127

6.1 Input Parameters .. ............... .............. ........ .. 127
6.2 Example 1 ........................................ .............. 128
6 .2 E x am ple 2 ................................................... 137

7 SUMMARY AND RECOMMENDATIONS .................................. 161
7 .1 S u m m ary ................................................................... 16 1
7.2 Further R research .................. ..................................... .. ........ .. 164

APPENDIX

A PASSING PERCENTAGE AND AVERAGE TRAVEL SPEED ON
TWO-LANE HIGHWAYS ........................................................... 167

B HEADWAY DISTRIBUTION.............. ........................ 171

C ENTERING PERCENT FOLLOWING CALCULATION............. 180

C.1 M ethods to Calculate EPF Downstream of Signal..................... .. ............. 180
C.2 M ethod to Calculate EPF W without Signal ............................ ........................... 189

D VISUAL BASIC CODE............................................. ................ 196

D .1 Calculate Entering Percent Follow ing ............................................................... 196
D.2 Extract Average Travel Speed From CORSIM Output.......................................199
D.3 Determine Upstream Effective Length............................................................ 203

E PLOTS OF DIFFERENCE IN AVERAGE TRAVEL SPEED FROM
T W O P A S ............................................................ ........ .......... .. 207

F PLOTS OF DIFFERENCE IN AVERAGE TRAVEL SPEED FROM
C O R S IM ............................................................. ..... .. .. .. ... .... .. 2 12

G NOMENCLATURE TABLE ........................................ ................. 217

H LIST OF REFERENCES................................................................. 221

I BIOGRAPHICAL SKETCH .............................................................. 223
















LIST OF TABLES

Table p

3-1. Traffic sim ulation conditions............................................... .......................... 30

3-2. Service m measure evaluation ............................................... ............................ 41

3-3. Summary of programs used at each step .......... .............................. .............. 51

3-4. Sim ulation m odel evaluation........................................................ .............. 52

4-1. Normal acceleration rates, distance, and elapsed time ............................................ 65

4-2. Regression m odel sum m ary.................................................... ........................... 66

4-3. Variable input values (w ith a left-turn bay)............................................................. 73

4-4. Variable input values (without a left-turn bay) .............................................. 73

4-5. Regression model (with a left-turn bay)..... ............... ...... .............. 75

4-6. Regression model (without a left-turn bay)............... ......... ........ ........... 76

4-7. Upstream effective length with low traffic volume (ft)........................................... 76

4-8. Composite headway distribution calculation (volume = 1500-1740 veh/h)............ 83

4-9. Chi-Squared test calculation ......................................................... .............. 85

4-10. E entering P percent F ollow ing .......................................................................... .... 88

4-11. Recommended default values for desired speed by vehicle type............................ 90

4-12. Regression model for the downstream effective length ....................................... 95

4-13. Comparison of downstream effective length..................................... ............... 98

5-1. Adjustment (fLs) for lane width and shoulder width .......................................... 103

5-2. Adjustment (f) for access-point density .............................. ... ........... 103










5-3. Adjustment factor,fATs, to ATS for a segment downstream of a signal.................. 111

5-4. Downstream length of roadway affected by passing lane.............. .................... 114

5-5. Factors for estimation of average travel speed within a passing lane ................... 115

5-6. Variable input values (TW SC intersection)................................... .............. 122

5-7. Simulation results on the queue length of the TWSC intersection........................ 123

5-8. LOS criteria for two-lane highway facilities....................................................... 126

6-1. Input data needs for the facility-wide operational analysis ............ ................ 128

6-2. Average travel speed for the unaffected two-lane segments ............ ............... 152

6-3. Average travel speed for the affected downstream two-lane segments................. 153

6-4. Average travel speed for the affected passing lane segments ............................... 154

6-5. Control delays at signalized intersections ...................................... 154

B-1. Time headway distribution (traffic flow rate = 900 veh/h 1140 veh/h) ........... 171

B-2. Chi-Square test calculation (based on Table B-) ............................................... 173

B-3. Time headway distribution (traffic flow rate = 1200 veh/h 1440 veh/h) ......... 174

B-4. Chi-Square test calculation (based on Table B-3) ................................. ........... 176

B-5. Time headway distribution (traffic flow rate = 1500 veh/h ~ 1740 veh/h) ......... 177

B-6. Chi-Square test calculation (based on Table B-5) .............................................. 179

C-1. Entering Percent Following with a signalized intersection................................... 192

C-2. Entering Percent Following with no signalized intersection ................................. 195















LIST OF FIGURES


Figure p

2-1. Screenshot from TW OPAS road editor .................................................................. 15

2-2. Screenshot from Traffic Analysis Module of IHSDM ........................ ........... 16

2-3. Screenshot from TRARR road editor........................... ................ 18

2-4. Screenshot from CORSIM simulation animation (TRAFVU)............................ 19

3-1. Typical basic two-lane, two-way highway segment......................................... 24

3-2. Typical two-lane, two-way highway with a passing lane....................................... 24

3-3. Typical two-lane, two-way highway with an unsignalized intersection ................. 25

3-4. Typical two-lane, two-way highway with a signalized intersection ..................... 26

3-5. Effect of a signalized intersection on average travel speed.................................... 32

3-6. Platoon dispersion, 300 ft from the upstream signalized intersection..................... 35

3-7. Platoon dispersion, 5280 ft from the upstream signalized intersection................. 35

3-8. Platoon dispersion, 10560 ft from the upstream signalized intersection ............... 36

3-9. Segment division of a two-lane highway with multiple isolated signalized
intersections ....... ..................................... ............... 44

3-10. Facility segmentation of a two-lane highway with multiple isolated signalized
intersections ....... ..................................... ............... 45

3-11. Flow diagram of two-lane highway facility operational analysis methodology ..... 50

4-1. L ength of intersection area ............................................................................... 55

4-2. Schematic distance-time diagram at a signalized intersection ................................ 58

4-3 Q u eu e length estim ation ............................................................................ .. .... ...... 59










4-4. Average travel speed along the two-lane highway with signal ............................... 74

4-5. TW OPAS traffic data input interface................................ ................................ 78

4-6. Composite time headway distribution.............................................. .................. 84

4-7. Two-lane highway traffic flow downstream of a signalized intersection ............... 87

4-8. Difference in the average travel speed between with and without signalized
intersection along the downstream two-lane highway............................................. 93

4-9. Difference in the average travel speed with traffic volume = 1100 veh/h .............. 94

4-10. Average travel speed variation with traffic volume = 220 veh ............................ 99

5-1. Downstream operational effects of a signalized intersection on AT..................... 110

5-2. Effect of a passing lane on average travel speed................................................ 114

5-3. Traffic stream s at a TW SC intersection ............................................................ 118

5-4. Guideline for determining the need for a major-road left-turn bay at a two-way stop-
controlled intersection............................... .............. 124

5-5. Length of TW SC intersection area.................................. ....................... .. ........ 125

6-1. A two-lane highway with an isolated signalized intersection ............................... 131

6-2. Segmentation for a two-lane highway facility............................ 143

6-3. Traffic flow rates at three intersections ........................................... .............. 144

6-4. A view of a typical passing lane ..................................................... .......... .. 149

A. 1. Passing percentage for various levels of advancing and opposing traffic volume on
tw o-lane high ays ......... ................................. .......... ........... 168

A-2. Average travel speed for various levels of advancing and opposing traffic volume on
tw o-lane high ays ......... ................................. .......... ........... 169

A-3. Percent time-spent-following for various levels of advancing and opposing traffic
volume e on tw o-lane high ays ........................................ ..................... ..... 170

B-1. Composite time headway distribution (based on Table B-l)................................ 172









B-2. Composite time headway distribution (based on Table B-3)............................... 175

B-3. Composite time headway distribution (based on Table B-5)............................. 178

C-1. Two-lane highway traffic flow downstream of a signalized intersection............... 181


E-1. Difference in the average travel speed with traffic volume

E-2. Difference in the average travel speed with traffic volume

E-3. Difference in the average travel speed with traffic volume

E-4: Difference in the average travel speed with traffic volume

E-5. Difference in the average travel speed with traffic volume

F-1. Difference in the average travel speed with traffic volume

F-2. Difference in the average travel speed with traffic volume

F-3. Difference in the average travel speed with traffic volume

F-4. Difference in the average travel speed with traffic volume

F-5. Difference in the average travel speed with traffic volume


440 veh.................. 207

660 veh/h................ 208

880 veh/h................ 209

1110 veh/h.............. 210

1320 veh/h.............. 211

220 veh/h ................ 212

440 veh/h ................ 213

660 veh/h ................ 214

880 veh/h ................ 215

1100 veh/h.............. 216















Presented to the Graduate School of the University of Florida
in Partial Fulfillment of the Requirements for the
Degree of Doctor of Philosophy

METHODOLOGY FOR THE OPERATIONAL
PERFORMANCE ASSESSMENT OF TWO-LANE HIGHWAY FACILITIES

By

Qingyong Yu

May 2006
Chair: Scott. S. Washburn
Major Department: Civil and Coastal Engineering

Traffic engineers have indicated that a facility-based evaluation methodology for

two-lane highways would be much more useful and practical to them than just the

individual segment and point analysis methodologies. A facility level analysis will allow

the various features (e.g., isolated intersections, continuous grades, passing lanes) that are

typical to an extended length of two-lane highway to be addressed in a combined analysis

with a single performance measure and level of service value resulting.

Currently there is not any operational analysis methodology to address two-lane

highways with different segment types at the facility level. The scope of analysis

provided in the Highway Capacity Manual (HCM) 2000 for two-lane highway is limited

to separated segment within the facility.

In this dissertation, a methodology is developed to assess the operational

performance of an extended length of a two-lane highway facility, which might include

an occasional signalized intersection and other control or roadway segments.









The methodology maintains some fidelity to the HCM 2000 by using the existing

methodologies for the two-lane highway segments and signalized intersections.

Meanwhile, the individual segment in the whole facility is not regarded as an isolated

object, and the impacts between segments are taken into account. A common time/delay

based measure (percent time-delayed) is used for each segment and point of the entire

facility.

The primary contribution of this dissertation is the development of analytical

relationships to determine the upstream and downstream boundary points that define the

transition between basis tow-lane highway segments and the effective influence area of

the signalized intersection and the TWSC intersection, as well as the corresponding

method for calculation of an overall facility service measure based upon percent time-

delayed and then translating it to a Level Of Service (LOS) grade.

The dissertation focuses the efforts on developing the methodology for operational

analysis of a two-lane highway with an isolated signalized intersection at the facility

level. Nonetheless, this research also provides a model for the basic structure of a facility-

level analysis that will be amenable to the incorporation of a variety of segment types.

Finally the methodology has been incorporated into the existing HIGHPLAN software

program.














CHAPTER 1
INTRODUCTION

1.1 Background

Two-lane highways, which account for approximately 80 percent of all paved rural

highways in the United States and carry about 30 percent of all traffic, are important

facilities in our transportation network system [1]. With the increased development in

rural areas, more signals are being installed on two-lane highways typically when these

highways travel through small towns. Additionally, there are a number of other design

and operational treatments developed on extended lengths of two-lane highways, such as

passing lanes, two-way stop-controlled intersections, driveway turnouts, and two-way

left-turn lanes. They can be effective in alleviating some operational problems on two-

lane highways.

Because these design and operational treatments significantly affect traffic

operations on two-lane highways, there is ongoing demand for analysis methodologies

with which to analyze the operating effectiveness of the entire length of two-lane

highway, that is, the facility as a whole. This is consistent with the fact that drivers

typically evaluate the quality of their trip over its entire length, not just in separate

segments.

1.2 Problem Statement

Personnel with the Florida Department of Transportation (FDOT) Systems

Planning Office have indicated that a facility-based evaluation methodology for two-lane

highways would be much more useful to them than just the individual segment and point









analysis methodologies. Segment is a stretch of roadway with homogenous conditions.

Facility is composed of different segments. A facility level analysis will allow the various

features (e.g., isolated intersections, continuous grades, passing lanes) that are typical to

an extended length of two-lane highway to be addressed in a combined analysis with a

single performance measure and level of service value resulting.

Frequently, a traveler is less concerned about the quality of service offered by a

particular segment than the service over a facility that may be served by more than one

segment type. For example, on a two-lane highway with several isolated intersections,

most travelers are concerned about the operation of the whole facility and not just the

operation of a particular intersection, or a particular two-lane highway segment.

From the viewpoint of travelers or transportation engineers, a facility level analysis

on a two-lane highway facility, instead of the segment level, is more practical and

meaningful. Currently, there is not any operational analysis methodology to address two-

lane highways with different segment types at the facility level.

In the Highway Capacity Manual (HCM) 2000 [1], the basic two-lane highways

with or without passing lane can be evaluated with the methodology in Chapter 20,

"Two-Lane Highways". Isolated signalized intersections on two-lane highways can be

evaluated with the methodology in Chapter 16, "Signalized Intersections". The scope of

analysis provided in the HCM 2000 for two-lane highways is mainly limited to separate

segments within the facility, while the methodology to evaluate the facility as a whole is

of much more practical value to transportation engineers.

In the HCM 2000, Chapter 15, "Urban Streets", presents the methodology for

evaluating arterials in urban and suburban areas with multiple signalized intersections at a









spacing of 2.0 miles or fewer. To some degree, the analysis procedure is performed at the

facility level, which combines the segment running time and control delay at the

signalized intersection when determining the performance measure (average travel speed)

for the entire facility. However, this methodology has some obvious drawbacks. They are

the following:

1. The potential impacts between roadway segments and signalized intersections

are not taken into account in this methodology. Continuing research has shown that the

installation of signalized intersections can significantly affect traffic operations on the

two-lane highways, such as decreasing average travel speed, and increasing percent time-

spent-following. The impact between different segment types is a big issue differentiating

the facility-level analysis from the segment-level analysis.

2. In this methodology, the urban street is divided into multiple segments, which is

the full distance from one signalized intersection to the next. The signalized intersection

is regarded as a typical point location within a traffic network, and control delay is

regarded as a typical point performance measure without covering any distance. In the

HCM 2000 [1], by definition, control delay includes movements at slower speeds and

stops on intersection approaches as vehicles move up in queue position or slow down

upstream of an intersection, as well as delay due to re-acceleration downstream of a

signal after stopping or slowing. It implies that control delay happens not at a point, but

actually within a certain distance. Although the time lost due to slow movement before

and after a stop is technically part of the running time, it is also included in control delay.

Segment division in this methodology causes the problem of double-counting the









deceleration-acceleration delay. Segment division introduces error due to the segment

between intersections being longer than they should.

In this dissertation, a methodology for the operational performance assessment of

two-lane highways with isolated signalized intersections (spacing of signalized

intersections is 3 miles or more) will be explored, in addition to a way to combine a

number of different segments (two-way stop-controlled intersection, passing lanes, basic

segment, etc.).

1.3 Objectives and Tasks

The objective of this research is to develop a methodology that can be used to

assess the operational performance of an extended length of a two-lane highway facility,

which might include occasional signalized intersections, unsignalized intersection, and

other control or roadway treatments. This two-lane highway would then be comprised of

multiple segments, with segment delineations occurring with a change in either roadway

or control attribute. The most common types of two-lane highway segments are the

following:

* Basic segment-this is a segment that consists of a simple two-lane cross section,
either level or rolling terrain

* Basic segments with a continuous specific up or down grade

* Three-lane cross section segments, with the additional lane being a passing lane

* Three-lane cross section segments, with the additional lane being a center left-turn
lane

* Three-lane cross section segments, with the additional lane being a right-turn only
lane

* Segments terminating with an isolated signalized intersection

* Segments terminating with an unsignalized intersection









* Segments terminating into a multilane highway

This research focuses on developing the methodology for operational analysis of a

two-lane highway with isolated signalized/un-signalized intersections at the facility level.

Nonetheless, it is intended that this research will also provide a model for the basic

structure of a facility level analysis that will be amenable to the incorporation of a variety

of segment types. The tasks required to accomplish the research study objectives are as

follows.



Task 1: Perform a literature review on current analytical and simulation methods

for evaluating the performance of basic two-lane segments and signalized intersections,

along with previous research on the effects of signalized intersections on a two-lane

highway.

Task 2: Define the basic conceptual framework, from a segmentation and service

measure perspective, for combining two-lane highway segments with intersections into a

facility-wide operational analysis.

Task 3: Investigate traffic operations at the boundary of a two-lane segment and a

signalized intersection (upstream of the signal) and develop a method that can be used to

determine the effective length of the signal's influence area upstream of the signal.

The conceptual approach being taken is that the effective upstream length of the

signal's influence area is a function of average queue length on the approach to the signal

and some portion of perception/reaction time and braking distance before the queue. The

combination of the stopping sight distance (SSD) equation, from the AASHTO "Green

Book" [2], and average queue length formulas from Chapter 16 of the HCM 2000, are

compared to simulation output from CORSIM. A comprehensive experimental design









for simulation is utilized to fully explore the relationship between influence area and the

appropriate traffic and control variables. These results are reconciled against those from

the SSD + Average Queue Length results to arrive at an appropriate relationship.

Task 4: Investigate traffic operations downstream of a signalized intersection and

develop a method that can be used to determine the effective length of the signal's

influence area downstream of the signal.

The conceptual approach being taken is that the effective downstream length of the

signal's influence area is a function of vehicle acceleration and platoon dispersion. Thus,

three types of areas are investigated:

* Simple vehicle dynamics equations related to vehicle acceleration.

* Platoon dispersion downstream of a signal, such as the model currently used in the
TRANSYT-7F program.

* Changes in the vehicle headway distribution downstream of a signal. Previous
work performed by Dixon et al. [3] related to this issue is investigated, with two
main differences being:

o A composite headway distribution model is used for headways instead of a
simple negative exponential model, and

o The EPF (Entering Percent Following) measure as used by Dixon et al. is
related to downstream vehicle speeds as opposed to percent time-spent-
following.

Task 5: Investigate traffic operations at the boundary of a two-lane segment and a

two-way stop-controlled intersection (without sharing left-turn lanes), and develop a

method that can be used to determine the effective length of the two-way stop-controlled

intersection on through traffic on the major street and right-turn traffic from the major

street behind it.

Task 6: Join the components (basic two-lane segment, upstream signal influence

area, signal delay, and downstream signal influence area) into an integrated methodology









for the operational analysis of a two-lane highway facility. This methodology will be

predicated upon the use of an aggregated percent-time-delayed measure as the facility-

wide service measure. As part of this, two example problems are presented.

Task 7: Determine LOS thresholds that maintain a reasonable relationship with

existing LOS thresholds in Chapter 20 (two-lane highways) of the HCM 2000. For

example, with the use of a new service measure for the facility analysis, it should not be

possible to get a better level of service for the two-lane highway when installing a signal

compared to the previous LOS method.

Task 8: Provide a qualitative overview of how the method of analysis for multilane

highways might be modified to fit into this framework such that combinations of two-

lane highway segments, multilane highway segments, and occasional traffic signals can

be analyzed as an overall facility.

Task 9: Modify HIGHPLAN program to include this new methodology for a

facility-level analysis. This will require the addition of a new screen for segment and

intersection data inputs, as well as a new result.

1.4 Organization of the Document

This document is organized into six chapters in addition to the Introduction. Each

of the chapters covers a different aspect of the issue of assessing the operational

performance of a two-lane highway facility consisting of different segment type. In

Chapter 1, the background, objectives, and tasks of this research are introduced and the

stage is set for the organization of the rest of the document. Chapter 2, the literature

review gives a review of the current methodologies for evaluating the operational

performance of basic two-lane segments, and signalized intersections. It also provides a

brief overview of the simulation models and their potential ability to contribute to the









performance evaluation for the two-lane highway facility. Chapter 3 presents the

conceptual framework of the operational analysis procedure for a two-lane highway

facility, and puts forward the methodology of operational analysis for the two-lane

highway facilities. The first two steps of the selection of facility-wide service measure

and facility segmentation are also explored in this chapter. Chapter 4 describes the

procedures for determining component segment lengths of the facility, mainly including

the length of a signalized intersection influence area, and the length of the downstream

segment affected by the upstream signal. Chapter 5 describes the methods for calculating

the service measure value of each segment type. They include the free-flow speed, and

average travel speed on three kinds of two-lane highway segments, and control delay at

the signalized and unsignalized intersections. In Chapter 6, two examples are provided to

illustrate the application of the developed methodology. Finally, Chapter 7 provides

summary and recommendations for future research.















CHAPTER 2
OVERVIEW OF ANALYSIS METHODS

This chapter summarizes current methodologies for evaluating the operational

performance of basic two-lane segments, and signalized intersections. It also provides a

brief overview of the TWOPAS, TRARR, and CORSIM simulation models and their

potential ability to contribute to the performance evaluation for the two-lane highway

facility. Finally previous research on effects of signalized intersections on a two-lane

highway segment is presented.

2.1 Analytical Methods

The following sections give an overview of analytical methodologies presented in

the HCM 2000. They are for two-lane highways, signalized intersections, and urban

streets. Finally the adjustment method used in the FDOT HIGHPLAN software for the

facility level analysis is presented.

2.1.1 HCM Methodology for Two-Lane Highways

The Highway Capacity Manual (HCM) published by the Transportation Research

Board (TRB) presents the widely accepted standards for analysis of two-lane highway

capacity and quality of service.

In the 1950 HCM, the first version of HCM, the procedure for analysis of two-lane

highway capacity developed by O. K. Norman was presented. The capacity of a two-lane

road was determined by comparing the demand for passing with observed actual passing









rates at various flow rates. In the subsequent editions of 1965, 1985, and 2000 [1], the

capacity and quality-of-service analysis procedure of a two-lane highway and their

related service measures were revised. In the 1965 HCM, the capacity of a two-lane

highway was estimated for both directions of travel combined, regardless of the direction

split of traffic, and the two service measures for the operational analysis were the

operating speed of traffic over a roadway section and the volume-to-capacity ratio. A

great improvement in analysis of two-lane highway capacity and quality of service was

achieved in the 1985 HCM. The capacity of a two-lane highway was determined to be a

function of the directional split of traffic, ranging from a capacity of 2800 pc/h in both

directions of travel combined for a 50/50 directional split to 2,000 pc/h for a 100/0 split.

In this version, a new level of service measure named "percent time delay" was

developed. Percent time delay is measured as the percentage of vehicles traveling at

headway of 5 sec or less at one or more representative points within the analyzed

roadway.

In Chapter 20 of the HCM 2000, an improved operational analysis procedure for

two-lane highway was presented. Key features of the improved operational analysis

procedure are revised factors for the effects of grades and heavy vehicles, separate

computational procedures for two-lane and directional segments, provision of operational

analysis procedures for passing lanes in level and rolling terrain, climbing lanes on steep

upgrades, and steep downgrades on which some trucks must use crawl speeds [1]. The

combination of average travel speed and percent time-spent-following was determined as

the level of service measure (i.e., the performance measures used to base level of service

upon).









The above discussion reviews the historical development of the HCM procedure for

analysis of two-lane highway capacity and quality of service. The analysis procedure has

been limited to the segment level. The operational analysis methodologies in this chapter

do not address two-lane highways with signalized intersections or with other types of

segments.

2.1.2 HCM Methodology for Signalized and Unsignalized Intersections

In the HCM 2000, Chapter 16 "Signalized htel %eA IiI \ "' contains a methodology

for analyzing the capacity and level of service of signalized intersections [1]. The

methodology addresses the capacity, LOS, and other performance measures for lane

groups and intersection approaches and the LOS for the intersection as a whole. The ratio

of demand flow rate to capacity is used as a capacity utilization measurement. The

capacity analysis methodology for signalized intersections is based on known or

projected signalization plans, and traffic characteristics. The control delay per vehicle is

used as the service measure. In this methodology, the signalized intersection is regarded

as an isolated point location. It does not take into account the potential impact of

downstream congestion on intersection operation.

In the HCM 2000, Chapter 17 "Unsignalizedliiieil 'i iinI'" contains a

methodology for analyzing the capacity and level of service, lane requirements, and

effects of traffic and design features of unsignalized intersections [1]. The analyzed

unsignalized intersections include two-way stop-controlled (TWSC), all-way stop-

controlled (AWSC) intersections, and roundabouts. For a TWSC intersection, LOS is

determined by the computed or measured control delay and is defined for each minor

movement. For an AWSC intersection, control delay is also used to determine LOS.









2.1.3 HCM Methodology for Urban Streets

In the HCM 2000, Chapter 15 "Urban Sti eeil" contains a methodology used to

access the mobility function of the urban street [1]. Four urban street classes are defined

and reflect unique combinations of street function and street design. The degree of

mobility provided is assessed in terms of average travel speed for the through-traffic

stream. Computing the urban street or section speed requires the total time that a vehicle

spends on the urban street. The total time consists of the segment running time and the

intersection control delay of the lane group for through traffic.

The methodology may be used to analyze urban streets that have a traffic signal

spacing of 2 miles or less. To some degree, the analysis procedure is performed at the

facility level, which combines the segment running time and control delay at the

signalized intersection when determining the performance measure (average travel speed)

for the entire facility. However, the potential impacts between roadway segments and

signalized intersections are not taken into account in this methodology.

2.1.4 Performance Measure Definition

Each facility type has a defined method for assessing capacity and level of service

using performance measures. These measures reflect the operating conditions of a

facility, given a set of roadway, traffic, and control conditions. Service measures are the

performance measures used to base level of service upon. In this dissertation, a

methodology of operational performance analysis is developed for the two-lane highway

facility composed of different types of segments. A special service measure will be

selected for this facility to determine its level of service.

The definitions of some performance measures often used in the HCM are

summarized here.









* Volume to Capacity Ratio (v/c)

The v/c ratio is defined as the volume to capacity ratio, often used as a measure of
the sufficiency of existing or proposed capacity.

* Average Travel Speed (ATS)

ATS is defined as the length of the roadway segment under consideration divided
by the average total travel time for all vehicles to traverse that segment during some
designed time interval.

* Percent Time-Spent-Following (PTSF)

PTSF is defined as the average percentage of travel time that vehicles on a given
roadway segment must travel in platoons behind slower vehicles due to the inability to
pass during some designed time interval.

* Travel Time

Travel time is defined as the time spent traversing a section of highway.

* Percent Free Flow Speed (PFFS)

Percent free flow speed is defined as the ratio of vehicle average travel speed to
free flow speed.

* Density

Density is the number of vehicles occupying a given length of highway or lane and
is generally expressed as vehicles per mile per lane.

* Control Delay

Control delay includes "Movements at slower speed and stops on intersection
approaches as vehicles move up in queue position or slow down upstream of an
intersection" [1]. It includes deceleration delay, stopped delay, and acceleration delay.

* Percent Time-Delayed

Percent time-delayed is defined as the percentage of the travel time that vehicles on
a given roadway segment must travel at speeds less than their desired speed (typically the
free-flow speed) due to inability to pass or to delays caused by traffic control.

2.1.5 FDOT HIGHPLAN Software

HIGHPLAN, designed for uninterrupted flow highway level of service analysis for

planning applications, is FDOT's software for two-lane and multilane uninterrupted flow









highways [4]. HIGHPLAN maintains fidelity to the HCM 2000 two-lane and multilane

procedures to the extent possible. However due to some unique characteristics in the

State of Florida, HIGHPLAN incorporates a number of concepts and calculations that

differ significantly from the basic procedures in the HCM 2000.

HIGHPLAN includes an adjustment to account for whether the analysis is at the

segment level or the facility level. If a segment level analysis is performed, it is assumed

that the highway section under consideration is short enough that it does not include any

capacity reducing effects due to the presence of intersecting driveways or cross streets. If

a facility level analysis is chosen, a 10% reduction is applied to the base capacity to

account for driveway and cross street friction. This value is consistent with the capacity

reducing effects of interchanges experienced on Florida freeways [5]. Nonetheless, this is

a gross adjustment necessitated by the lack of a specific facility-level methodology.

2.2 Simulation Methods

The following section provides a brief overview of the TWOPAS, TRARR and

CORSIM simulation models and their potential ability to contribute to the performance

evaluation for the two-lane highway operations.

2.2.1 TWOPAS Software

TWOPAS (TWO-lane PASsing) rural highway simulation software is used for

modeling traffic conditions on two-lane two-way roadways. This software was used

extensively in developing the two-lane analysis methodology in the HCM 2000.

TWOPAS was first developed in the 1970s by Mid-West Research Institute for

the US Federal Highway Administration (FHWA). TWOPAS was revised most recently

in 1998, and was contained in a graphic interface, UCBRURAL, developed by the

University of California-Berkeley. UCBRURAL provides a menu-driven interactive









graphical interface with comprehensive input checking, carefully selected default values,

and user-selected output options including graphic depictions of traffic performance,

which is more convenient for users to run TWOPAS model.

Figure 2-1 shows a view of the UCBRURAL road editor. Recently the TWOPAS

traffic simulation model is built in the Traffic Analysis Module (TAM) of the Interactive

Highway Safety Design Model (IHSDM) to estimate traffic quality-of-service measures

for an existing or proposed design. The TAM facilitates use of TWOPAS by feeding it

the roadway geometry data stored by IHSDM. Figure 2-2 shows a view of TAM input

interface in IHSDM.

I *,, II





















Figure 2-1. Screenshot from TWOPAS road editor

As a microscopic, stochastically based model, TWOPAS simulates traffic

operations on a two-lane highway by reviewing the position, speed, and acceleration of

each individual vehicle along the roadway at 1-second intervals. The operation of each










vehicle is also influenced by the characteristics of the vehicle and its driver, by the

geometric of the roadway, and by the surrounding traffic simulation in a realistic manner

as it advances along the road [6]. TWOPAS incorporates the major features:

* Highway Geometry specified in terms of grades, horizontal curves, lane and
shoulder width, along with passing and climbing lanes.

* Traffic control specified by users, especially passing and no-passing zones, and
reduced speed zones.

* Driver Characteristics and preferences including desired speeds, preferred
acceleration levels, limitations on sustained use of maximum power, passing and
pass-abort decisions, and realistic behavior in passing and climbing lanes.

* Entering Traffic streams generated in response to user-specified flow rate, vehicle
mix, immediate upstream alignment, and the percent of traffic platooned.

* Driver speed choices in unimpeded traffic based on user-specified distribution of
desired speeds; in the impeded traffic based on a car-following model that
simulates driver preferences for following distances, relative leader/follower
speeds, and desire to pass the leader [6].


File Edit View Tools Help


S ProjectlAnalysislHighway
I Policy Review [1r Crash Prediction r Design Consistency r Intersection Review
Evaluation I
-Configuration. -Upstream Alignment
Configuration Name IDefault Increasing Stations Level Tangent
Comment Default TAM configuration file Decreasing Stations Level Tangent v
Change Configuration -Desired Speed
Traffic Flow Mean (mph) Standard Deviation (mph)
Increasing Stations Decreasing Stations Direction of Increasing Stations
Flow Rate (vfhr) 88011 8l Passenger Cars 61.5 5.8ol
Entering Platoons (%) I 79 .0 1 Trucks 59.508[ 4.00]
Percent Trucks (%) 0o.o0l 0.o00 RVs I 59.508 _4.00I
Percent RVs (%) 0.go01 0.001 .Direction of Decreasing Stations
SAuto Generate Platoon Percent passenger Cars 61.5 5.0
rucks 59.5011 4.00
RVs I59.501 4.00l

Loading analysis: Steven
Loading highway new roadway 2/26/05 12:01 PM


Figure 2-2. Screenshot from Traffic Analysis Module of IHSDM









TWOPAS has the capability to simulate both conventional two-lane highways and

two-lane highways with added passing lanes. However, TWOPAS does not have the

ability to simulate traffic turning on or off the highway at driveways, unsignalized

intersections, or signalized intersections.

2.2.2 TRARR Software

TRARR (TRAffic on Rural Roads) was developed in the 1970s and 1980s by the

Australian Road Research Board. TRARR is designed for two-lane rural highways, with

occasional passing lane sections. It is a microscopic simulation model, that is, it models

each vehicle individually. Each vehicle is randomly generated, placed at one end of the

road and monitored as it travels to the other end. Various driver behaviors and vehicle

performance factors determine how the vehicle reacts to changes in alignment and other

traffic. TRARR uses traffic flow, vehicle performance, and highway alignment data to

establish, in detail, the speeds of vehicles along rural roads. This determines the driver

demand for passing and whether or not passing maneuvers may be executed [7]. Figure

2-3 shows an interface of the TRARR road editor.

TRARR is designed for two-lane rural highways, with occasional passing lane

sections. TRARR can be used to obtain a more precise calculation of travel time,

frustration (via time spent following), and benefits resulting from passing lanes or road

realignments. For strategic assessment of road links, TRARR can also be used to evaluate

the relative benefits of passing lanes at various spacing.

Similar to TWOPAS, TRARR has no ability to handle varying traffic flows down

the highway, particularly due to major side roads or signalized intersections. However,

TWOPAS was developed with U.S. data and, therefore, was better representative of U.S.

conditions than TRARR.






















I--- -


Figure 2-3. Screenshot from TRARR road editor

2.2.3 CORSIM Software

CORSIM (CORridor SIMulation), developed by the Federal Highway

Administration, is the core simulation engine in the TSIS (Traffic Software Integrated

System) suite [8]. CORSIM is a comprehensive traffic simulation program, applicable to

surface streets, freeways, and integrated networks with a complete selection of control

devices, such as stop/yield signs, traffic signals, and ramp metering. CORSIM is a

microscopic, discrete time, stochastic, "state-of-the-practice" model used to simulate

traffic operations. It integrates two microscopic traffic simulation models: the arterial

network model, NETSIM, and the freeway model, FRESIM. CORSIM is able to simulate

existing or proposed conditions on very large networks. CORSIM has been applied by

thousands of practitioners and researchers worldwide over the past 30 years and


______-------------_









embodies a wealth of experience and maturity [8]. Figure 2-4 shows an interface

simulating traffic operations at a signalized intersection.

CORSIM has expanded the capabilities of NETSIM and FRESIM with the

following major enhancements:

* HOV lanes in FRESIM

* Freeway ramp metering

* Vehicle-type-specific turn percentages

* Support Larger Networks

* Path Following Capacity























Figure 2-4. Screenshot from CORSIM simulation animation (TRAFVU)

CORSIM can simulate traffic and traffic control system using commonly accepted

vehicles and driver behavior models. However, it does not have the ability to simulate

vehicle passing operations on a two-lane highway using the opposing lane.









2.3 Effect of Upstream Signal on Two-Lane Highway PTSF

In the research of Dixon et al. [3], they developed a methodology to estimate the

effects of a simple isolated signalized intersection on a downstream two-lane highway

segment in terms of percent time-spent-following. In their research, the effect of an

upstream signalized intersection on the two-lane highway segment was to modify the

distribution of entering headways. The condition with no signalized intersection is

represented by assuming the negative exponential distribution of headways for entering

traffic, which is derived from the Poisson distribution for random arrivals. However, the

upstream signalized intersection will modify the headway distribution of the traffic

stream entering the downstream two-lane highway segment.

In TWOPAS, the distribution of headways is defined through the input variable,

Entering Percent Following (EPF), which is the percent of the total number of vehicles in

the direction of travel that are following in platoons, defined as headways less than 3.0

seconds, as they enter the road being analyzed. In Dixon et al.'s research, it was assumed

that as long as the percentage of vehicles following, immediately downstream of the

signalized intersection, could be determined, it was appropriate to represent the effects of

the signalized intersection through the EPF parameter. Vehicle headways were assumed

to follow a random distribution, and EPF was calculated using a cumulative exponential

distribution of headways less than 3.0 seconds.

The analysis procedure of two-lane highway segment affected by the upstream

signalized intersection operations was broken down into four steps.

Step 1: Determine the percentage of vehicle following (EPF) downstream of the
signalized intersection.

Step 2: Determine the Percent Time Spent Following (PTSF) for the downstream
highway section without the upstream signalized intersection.






21


Step 3: Estimate the PTSF for the downstream highway section with the upstream
signalized intersection. In this step, two methods can be used. One method is using
TWOPAS and another method is using the HCM 2000 two-lane highway directional
analysis procedures and deterministic adjustment factors.

Step 4: Estimate the level of service based on the criteria suggested in the HCM 2000
two-lane highway analysis procedure.

















CHAPTER 3
CONCEPTUAL OVERVIEW OF TWO-LANE HIGHWAY FACILITY ANALYSIS
METHODOLOGY

This chapter describes the development of operational analysis procedures for two-

lane highway facilities. The developed methodology would maintain some fidelity to the

HCM by using the existing methodologies for two-lane highway segments and signalized

intersections. This chapter begins with a discussion of the conceptual framework of the

operational analysis procedure for a two-lane highway facility. It then puts forward a

methodology of operational analysis for two-lane highway facilities and presents an

overview of this methodology. Finally, the chapter discusses the selection of a facility-

wide service measure and the first step of this methodology-facility segmentation.

3.1 Conceptual Framework for Facility Evaluation Methodology

To develop a methodology for the operational analysis of a two-lane highway

facility, a two-lane highway with an isolated signalized intersection will be used as a

model. This section discusses the conceptual framework of the operational analysis

procedure for such a configuration. Aspects of the conceptual framework addressed are

the definition of the two-lane highway facility, segment types, the features of operational

analysis at the facility level, and the proposed methodologies.

3.1.1 The Definition of a Two-Lane Highway with Signalized/Unsignalized
Intersections

In the HCM 2000, the primary highway system structure consists of points,

segments, facilities, corridors and areas. A facility is a length of roadway composed of









points and segments. A point is a boundary between segments, in other words, points are

where modal users enter, leave, or cross a facility, or where roadway characteristics

change. A segment is a portion of a facility defined by two end points. Segments are the

primary building blocks of facility analyses. In addition, a sub-segment is a further

division of a segment. Whereas segments are delineated by points (e.g., intersections) or

changes in geometric conditions, sub-segments for the purpose of discussion in this

document are delineated only by changing operational conditions. For example, an

isolated signalized intersection on a two-lane highway produces operational effects on the

upstream segment. The upstream two-lane highway segment can be divided into the

upstream sub-segment within the effective length of the signalized intersection, and the

upstream sub-segment beyond the effective length of the signalized intersection.

Although both sub-segments have homogenous geometric conditions, their operational

features are different. One sub-segment is affected by the downstream signal; the other is

not affected.

The potential segment types on a two-lane highway could include the following:

* Basic segment, this is a segment that consists only of a two-lane across section.
Figure 3-1 shows a typical view of this type of segment.

* Basic segment with continuous specific upgrade or downgrade

* Three-lane cross section segment, with the additional lane being a passing lane.
Figure 3-2 shows a typical view of this type of segment.

* Segment with an unsignalized intersection. Figure 3-3 shows a typical view of this
type of segment.

* Three-lane cross section segment, with the additional lane being a center left-turn
lane or a right-turn lane

* Segment terminating into a multilane highway

* Segment with an isolated signalized intersection

































Figure 3-1. Typical basic two-lane, two-way highway segment


Figure 3-2. Typical two-lane, two-way highway with a passing lane









A two-lane highway with signalized intersections is a type of facility composed of

isolated signalized intersections, and the basic two-lane highway. A two-lane roadway

generally extends from one signalized intersection to the next signalized intersection.

This type of facility is typically located in a rural area, but the signal may be present in a

small town.


Figure 3-3. Typical two-lane, two-way highway with an unsignalized intersection

Figure 3-4 shows a typical view of a two-lane highway with a signalized

intersection. The main features are as follows:

* Roadside development is not intense.

* Density of traffic access point is not high.

* Signalized intersections are more than 2 miles apart.

* These conditions result in a smaller number of traffic conflicts, smoother flow, and
dissipation of the platoon structure.

































Figure 3-4. Typical two-lane, two-way highway with a signalized intersection

3.1.2 Service Measure Consistency

LOS is a qualitative designation of the operational conditions within a traffic

stream based on performance measures such as speed, travel time, freedom to maneuver,

traffic interruptions, comfort, and convenience. Six levels of service are defined in the

HCM, using the letters A through F for each type of facility, where A is good, and F is

bad. The performance measure chosen to base LOS upon is referred to as a service

measure. For application in the segment LOS analysis, every type of segment has its own

service measure based on to determine its LOS.

When performing the facility-level operational analysis, occasional inconsistencies

can arise because of different service measures being applied. For example, in the two-

lane highway with an isolated intersection, the combination of average travel speed and

percent time-spent-following is used as the service measure to evaluate the level of









service on the basic two-lane highway segment, however the service measure for a

signalized intersection is based on control delay. In the HCM 2000, the measure of

operational quality used for point locations is not related to highway segment. Thus,

anomalies are possible when changing from one facility type to another.

Therefore selecting an appropriate service measure is a key issue in the

development of operational analysis for the two-lane highway at the facility level. There

are basically two methodological approaches that can be taken for an operational analysis

of a facility composed of different types of segment. They are:

1. Each segment uses the service measures) already specified for it in the HCM 2000.
The LOS of the entire facility is determined by combining the LOS of each segment
in some manner.

2. A common service measure is used for each segment and point. LOS of the entire
facility is determined by the aggregated service measure.

With the first methodology, no unified facility-wide service measure is applied for

the segments of the entire facility. Each segment or point uses its own service measures)

defined in the HCM 2000. Because of different service measures (e.g., ATS, PTSF, or

control delay) being applied, inconsistencies can arise. For example, when determining

the level of service of a two-lane highway with multiple signals, the combination of

average travel speed and percent time-spent-following is used as the service measure to

evaluate the level of service on an uninterrupted flow two-lane highway segment;

however the service measure for a signalized intersection is based on control delay. Thus,

anomalies are possible when changing from one segment type to another.

Another drawback of this methodology is the aggregation of the point and segment

LOS grades into an estimate of the LOS grade for the entire facility. In the HCM 2000,

the measure of operational quality used for point locations is not related to highway









segments. It is very difficult to combine the LOS of points with that of segments.

Equation 3-1 gives an example method of aggregating the LOS grades of segments and

points weighted by the segment length.


SLOS,L,
LOS = (3-1)
ZL,
1=1
Where:

LOS: the level of service of the entire facility,

LOS,: the level of service of segment i,

L,: the length of segment i, ft, and

n: the number of segments.

With this approach, segment LOS values are weighted by the segment length;

however, LOS is not a quantitative value. It is simply a measure of user satisfaction for

that service along the roadway. It is difficult to accurately convert the LOS grade into the

corresponding numerical value for aggregation. Even though a certain conversion method

is available, because each segment type has its own strategy to determine the LOS, every

segment type needs a unique conversion method, which makes the LOS combination

method somewhat complicated and possibly subjective.

In the HCM 2000, Chapter 15, the average travel speed is used as the service

measure on the urban street with multiple signalized intersections at a spacing of 2.0

miles or less. The method using a common service measure for a facility consisting of

multiple different segment types is a good reference. In the second methodology, a

common service measure would be applied to every segment of the entire facility. The

service measures at each segment are aggregated to obtain an estimate of service measure









for the entire facility. The LOS of the entire facility is determined by this aggregated

service measure. The unified facility-wide service measure not only avoids many

disadvantages of the application of multiple service measures, but also provides a

Measure of Effectiveness (MOE) describing traffic operations in terms discernible by

motorists from the scope of the entire facility.

The proposed second method would also maintain some fidelity to the Highway

Capacity Manual by using the existing methodologies for two-lane highway segments

and signalized intersections. For the two-lane methodology (HCM Chapter 20), the

method for calculation of average travel speed (ATS) is utilized; however, percent time-

spent-following (PTSF) is not utilized. For signalized intersections (HCM Chapter 16),

the current method for the calculation of control delay is utilized.

By using a time/delay based service measure, this method will be similar to the

current HCM methodology for urban streets. For transportation agencies looking to

analyze the impacts of adding a lane (or lanes) to a two-lane highway, along with adding

some signalized intersections, thus possibly changing the classification to an urban

arterial in some sections, this will provide for consistency in the analyses (assuming the

LOS thresholds are set accordingly). This methodology will be completely presented and

explained in Section 3.2.

3.1.3 Impacts of Signalized Intersection on Adjacent Highway Segments

Another important issue in the development of an operational analysis at the

facility level is the impacts with different segment types. Continuing research has shown

that installing a signalized intersection on a two-lane highway can produce effects on

traffic operations of the upstream and downstream two-lane highway segment.









To illustrate the potential effects of an isolated signalized intersection on the two-

lane highway operation, CORSIM and TRANSYT-7F programs are used to simulate the

operations of a two-lane highway with an isolated signalized intersection.


3.1.3.1 Effects of intersections on the upstream two-lane highway operation

When vehicles approach the signalized intersection facing a red signal indication,

drivers will safely stop their vehicles with sufficient sight distance to avoid entering the

intersection or colliding with queued vehicles. Here CORSIM is used to model the

variation of average travel speed as vehicles approach the upstream signalized

intersection.

Six CORSIM simulations are made with 30 replicate runs for each. The six

conditions are as follows:

Table 3-1. Traffic simulation conditions
Traffic Volume (veh/h) With or Without Signal
1 600 With
2 600 Without
3 1000 With
4 1000 Without
5 1400 With
6 1400 Without


The operational effects of a signalized intersection on the two-lane highway based

on average travel speed are shown in Figure 3-5. This figure is directly derived from

preliminary simulation runs. Figure 3-5 shows a comparison of the modeled average

speed as it varies along a two-lane highway with an isolated signalized intersection and

with no isolated signalized intersection under different traffic flow levels. As seen in

Figure 3-5, on the two-lane highway segment upstream of the signalized intersection,

when vehicles enter the basic two-lane highway segment, the difference in the values of









average travel speed is very small. The average travel speeds along the two-lane highway

with an isolated signalized intersection are very much in agreement with those with no

isolated signalized intersection. When near to the signalized intersection (about 1000 ft

before the stop line of signalized intersection), the difference in average travel speed

becomes very large. The average travel speed under the condition with an isolated

signalized intersection drops dramatically because of queuing in front to the signal. After

the signalized intersection, average traffic speed quickly increases and returns to its

former level.

So installing a signalized intersection on a two-lane highway significantly affects

traffic operations on the upstream two-lane highway segment based on average travel

speed, and the effective length of a signalized intersection is greater than its actual length.

The effective length of the upstream influence area of a signalized intersection is defined

from the dividing point, at which vehicles begin decelerating to the stop line of this

signalized intersection












Operational Effects of an Isolated Signalized Intersection on Average Travel Speed


--Traffic Flow = 600 vph

--Traffic Flow= 1000 vph

Traffic Flow= 1400 vph

Without Signalized Intersection


1000


Intersection


1500 2000
Position Along Roadway (ft)


Figure 3-5. Effect of a signalized intersection on average travel speed


Q.
E
o 30
QC
c)
Q.



20
- 25
I-







10
5


0


2500


3000


3500


45 r r 4 r4 r4 0 0 F'i F'i r'i









3.1.3.2 Effects of intersections on the downstream two-lane highway operation

After passing through the signalized intersection, the vehicle platoon will go into

the downstream two-lane highway. The platoon dispersion pattern is affected not only by

the upstream signalized intersection, but also by the right-turn vehicles and left-turn

vehicles from minor streets. There are three movements that contribute to the flow

profile, as follows:

* through movement from the major street

* right-turn movement from the minor street

* left-turn movement from another minor street

The start-and-stop operation of signals on the two-lane highways tends to create

platoons of vehicles that travel along a two-lane highway link. Here TRANSYT-7F is

used to model the dispersion of these platoons as they progress along the downstream

two-lane highway segment. In TRANSYT-7F, for each time interval (step), t, the arrival

flow downstream is found by the following recurrence equation [9]:



v(t+P)= F v, +[(1- F) vl, )] (3-2)
Where:

Vft+;, : predicted flow rate (in time interval of the predicted platoon);

v,: flow rate of the initial platoon during step t;

/p: an empirical factor, generally 0.8;

T: the cruise travel time on the link in steps; and

F: a smoothing factor

F =(1l+ a .. T) 1 (3-3)


Where:









a : platoon dispersion factor (PDF)

Equation 3-3 is based on field studies by Hillier and Rothery [10]. The factor a

has been found by researchers to best represent measured dispersion on typical urban

streets in the U.S. when it was set at 0.35. This PDF will vary to consider site-specific

factors such as grades, opposing flow interference and other sources of impedance.

The diagrams below illustrate the nature of platoon dispersion on the downstream

two-lane highway of a signalized intersection. As traffic moves downstream, the initially

tight platoon formed from the departing queue tends to disperse the farther downstream it

travels. Because drivers tend to maintain safe headways, or spacing, between vehicles

and often travel at different speeds, the platoon tends to spread out a few moving ahead

and some dropping back. The flow rate decreases with time as the platoon reaches each

point of observation. They are the "snapshots" of the traffic flow at the different

observation stations of the downstream link (the average traffic flow is 1200 veh/h).

The first diagram (Figure 3-6) illustrates a platoon after it has traveled 300 feet

after being stopped at the upstream signalized intersection. The most intense portion of

the platoon is at a rate higher than 1870 veh/h, and the lowest portion is at a rate near 0

veh/h. The platoon has spread out extremely unevenly. At this point, the timing plan of

the upstream signal and traffic streams from the minor streets produce significant effects

on the pattern of platoon dispersion.

As traffic moves downstream, the initially tight platoon formed from the departing

queue tends to disperse the farther downstream it travels. The second diagram (Figure 3-

7) illustrates the same platoon after traveling one-full mile, or 5280 feet. Notice that after

a full-mile, the most intense portion of the platoon is a rate slightly higher than 1500










veh/h, whereas after 300 feet the most intense portion of a platoon is approximately 1900

veh/h. At this point, the platoon has spread out to cover the whole portion of the cycle.

The effect produced by the upstream signal on the platoon dispersion becomes smaller.











i-













Figure 3-6. Platoon dispersion, 300 ft from the upstream signalized intersection












2-
C-


Figure 3-7. Platoon dispersion, 5280 ft from the upstream signalized intersection

















6.









Cycle Length (Sec)



Figure 3-8. Platoon dispersion, 10560 ft from the upstream signalized intersection

The same phenomenon can be observed from the third diagram (Figure 3-8), which

illustrates the same platoon after traveling 2 miles, or 10560 feet. The platoon has spread

out more evenly and covered the whole portion of the cycle. The most intense portion of

the platoon is about 1400 veh/h, which is near to the average flow rate of 1200 veh/h. At

this point, the effect produced by the upstream signal on the platoon dispersion is

negligible.

Based on the above analysis, it can be determined that the upstream signalized

intersection and traffic streams from the cross street alter the pattern of platoon

dispersion. The degree of platoon dispersion in turn directly affects vehicle delay, speed,

queuing, and other measures of effectiveness.

Given the potential impact of a signalized intersection on downstream two-lane

highway operations, it is necessary to investigate the effects further when performing an

operational performance assessment of two-lane highway facilities. To quantify the









effect of a signalized intersection on the downstream two-lane highway segment, a key

issue is to determine this effective length of influence area, downstream segment of the

signalized intersection.

3.2 Methodological Approach

Based on the discussion in the former section, using a common service measure for

the entire facility is preferred. A two-lane highway with an isolated signalized

intersection will be used as a model. This section begins with a discussion of service

measure selection, facility segmentation for a two-lane highway with isolated

intersections. Next the section presents an overview of the operational analysis

procedures for a two-lane highway with an isolated signalized intersection.

3.2.1 Service Measure Selection

In this methodology, a common service measure is applied to every segment of the

entire facility. The LOS of the entire facility is determined by this aggregated service

measure. One of the key steps in the methodology is the selection of a service measures)

used to define the overall level of service for the facility. Based on the features of the

two-lane highway with occasional signalized and unsignalized intersection, some

candidate service measures are estimated. They are described as follows:

* Volume to Capacity Ratio (v/c)

The v/c ratio is often used as a measure of the sufficiency of existing or proposed

capacity. According to the 2000 HCM, this v/c ratio measure of capacity sufficiency

of the overall intersection is a good indication of whether the physical geometry

design features and the signal design provide sufficient capacity for the intersection.

But the ratio is not sensitive to speeds and travel time. With an acceptable LOS grade,

a v/c ratio may indicate that the same facility is operating at or near all capacity.









Conversely, road segments operating at deficient levels of service may have an

acceptable v/c ratio in cases where the adjoining intersections are not operating

efficiently.

Generally, the v/c ratio is used as a measure of the sufficiency of existing or proposed

capacity. The ratio however, is not sensitive to speeds and travel time. The v/c ratio is

better as a measure of the capacity sufficiency, but not good as a measure of the

quality of service. The combination of v/c ratio and other performance measures may

be better.

S Average Travel Speed (ATS)

ATS reflects the mobility function of traffic facilities. Speed, as represented by ATS, is

a very important part of the LOS definition and is also easy for the public to

understand. And it is easily calculated using the data that is already being collected.

As a space-average measure, ATS can be estimated in the field by travel time studies

or by measure of spot speeds. One potential drawback to the use of average travel

speed as the single service measure for two-lane highways is that it is not as sensitive

as PTSF to the relative balance between passing demand and passing supply.

* Percent Time-Spent-Following (PTSF)

Given the platooned nature of traffic on the two-lane highway, PTSF represents

freedom to maneuver and the comfort and convenience of travel on a two-lane

highway. However, some researchers [5] think this measure is not appropriate for

application to developed, tourist-oriented sections, such as US Route 1 in the Florida

Keys, on which motorists are more concerned about the ability to maintain a

reasonable speed. PTSF is also a space-averaged measure, which is difficult to

measure directly in the field. While the HCM suggests that it be estimated as the









percentage of vehicles traveling at a headway of 3 seconds or less at a representative

point, the LOS estimation is very sensitive to the headway threshold [11].

Both ATS and PTSF are measured over a section of roadway. In the highway structure

system of the HCM, the signalized intersection is regarded as a point, or a segment

with a short length, so ATS, PTSF, or their combination is a conceptually adequate

service measure for two-lane highway segments, but a poor one for the signalized

intersection by itself. So ATS, PTSF, or their combination is not a good facility-wide

service measure for the facility consisting of two-lane highway segments and

signalized intersections.

* Travel Time

Travel time, particularly in the context of reliability, is gaining momentum as a

performance and service measure for some types of facilities. Travel time is

essentially the same performance measure as speed (it is simply the reciprocal).

However, just like speed, travel time alone is not sufficient as a service measure over

a length of two-lane highway facility. It would also need to be qualified per some

unit distance (e.g., min/mi). In this situation, it is generally a simple task to convert

to other time-based measures if so desired. Currently, for the purposes of the HCM

2000 methodologies, speed is still generally used in preference to travel time.

* Percent Free Flow Speed (PFFS)

PFFS is defined as the ratio of vehicle average travel speed to free flow speed.

Washburn, et al. [5] proposed percent free flow speed as the primary performance

measure for two-lane highways in developed areas. This measure makes some sense

for these areas due to the fact that drivers probably do not have much expectation for









passing in these areas and they are willing to tolerate following other vehicles as long

as their speed is close to the desired free-flow speed.

* Density

Density is used as the primary service measure for the types of uninterrupted flow

facilities, such as freeway and multilane highway. Given the platooned nature of

traffic on a two-lane highway, density is much less evenly distributed on a two-lane

highway than on a freeway or multilane highway [11]. Density is not a good service

measure for the two-lane highway facility. Percent time-spent-following does a much

better job of representing density; percent time-spent-following is the percentage of

the total travel time that drivers spend traveling in local high-density conditions. An

additional difficulty with density is that direct measurement of it in the field is

difficult, requiring a vantage point for photographing, videotaping, or observing

significant lengths of highway. Furthermore, conceptually it does not work for

signalized intersections.

* Control Delay

Control delay includes "Movements at slower speed and stops on intersection

approaches as vehicles move up in queue position or slow down upstream of an

intersection" [1]. It is the principal service measure for evaluating LOS at

intersections, which are point locations within a traffic network. However, the

measure of operational quality of effectiveness used for point locations can not be

used for highway segments, such as two-lane highway segments.

* Percent Time-Delayed

Percent time-delayed is defined as the percentage of the travel time that vehicles on a

given roadway segment must travel at speeds less than their desired speed due to










inability to pass or traffic control during some designated time interval. Percent time-

delayed is a good performance measure for interrupted-flow facilities, such as two-

lane highways with occasional signalized intersections. It reflects the effects of speed

reductions by motorists due to restrictive roadway geometry, traffic control, and other

traffic, and represents the degree to which drivers are forced to travel at speeds less

than their desired speed.

Just like other delay-related performance measures, percent time-delayed also has a

direct economic interpretation and can be used in economic studies if the monetary

value of a traveler's delay can be established. The primary drawback of percent time-

delayed as a performance measure is the difficulty of measuring it in the field.

Table 3-2. Service measure evaluation
Undeveloped Developed Facility incorporating
uninterrupted uninterrupted two-lane highway
two-lane two-lane Intersection and signalized
segments segments influence area intersection
Volume/Capacity Ratio F F F F
Average Travel Speed G G P P
Percent Time-Spent-Following E F P P
PTSF and ATS E E P P
Travel Time G G P P
Percent Free-Flow-Speed G E P P
Density F F F F
Control Delay P P E P
Percent Time-Delayed G G G G
Note: E = excellent, G = good, F = Fair, P = poor


Table 3-2 summarizes the evaluation of potential service measures for a two-lane

highway with signalized intersections. Based on a review of the advantages and

disadvantages of candidate service measures discussed above, it is concluded that percent

time-delayed is an appropriate selection as the single service measure for the interrupted-

flow facility of a two-lane highway with signalized intersections. Percent time-delayed is

a measure that directly relates to the driver's experience. It not only represents freedom to









maneuver and the comfort and convenience of travel on a two-lane highway, but also

reflects the effects of speed reductions due to traffic control (e.g., signalized intersection,

stop sign), and due to restrictive geometric features (e.g., vertical grade, horizontal curve,

no-passing zone), and other traffics (e.g., opposite traffic flow, heavy vehicles).

3.2.2 Facility Segmentation

To perform an operational analysis for a facility consisting of different segment

types, and obtain the LOS of the facility, the entire facility is divided into several

segments. Thus, the analysis methodology must prescribe how to segment the facility.

In the HCM 2000, Chapter 15, Urban Streets, presents the methodology for

evaluating arterials in urban and suburban areas with multiple signalized intersections at a

spacing of 2.0 miles or less. In this methodology, the urban street is divided into

segments, which is the full distance from one signalized intersection to the next. Figure 3-

9 illustrates the segmentation method for this methodology. Running time is computed

for each segment, along with control delay at each signalized intersection. In this

methodology, the signalized intersection is regarded as a point location within a traffic

network, and control delay is regarded as a typical point performance measure without

covering any distance. In the HCM 2000 [1], the definition of control delay implies that

control delay happens not at a point, but actually within a certain distance. Although the

time lost due to slow movement before and after a stop is technically part of the running

time, it is also included in control delay. Thus, this segment division method introduces

error due to the segment between intersections being longer than they should.

In the HCM 2000, Chapter 16, SignalizedIntersections, presents the methodology

for evaluating isolated signalized intersections. In this methodology, the signalized

intersection is regarded as a single isolated traffic control installation. So the length of the









signal influence area is not a key factor in determining control delay, or in the decision of

LOS based on control delay.

When evaluating highways with multiple signalized intersections, the signalized

intersection should not be regarded as an isolated point. The impacts between signalized

intersections and highway segments should be taken into account. In Sections 3.1.3.1

and 3.1.3.2, it has been shown that the installation of a signalized intersection actually

affects the operations on the highway segments, and the signal influence area does extend

a certain length. So when evaluating a two-lane highway with signalized intersections,

the signalized intersection is not regarded as a single point, but as a segment with a

certain length.

Figure 3-10 shows the division of a two-lane highway with multiple isolated

signalized intersections. The whole facility is divided into three types of segments,

described as follows:

* Type 1: the basic two-lane highway. This type of segment may be located in the
upstream or downstream of the signalized intersection, but beyond the signal
effective length. These segments are not affected by signalized intersections.

* Type 2: the signal influence area. In the highway structure system of HCM 2000,
the signalized intersection is defined as a point; the boundary between segments. In
this operational analysis methodology, it will be regarded as a segment with a
certain length, which is composed of not only its own actual length, but also the
deceleration and acceleration lengths. The length of the signal influence area
corresponds to the three components of control delay-deceleration delay, stop
delay, and acceleration delay.

* Type 3: the affected downstream segment. This type of segment is still the two-lane
highway, but affected by the upstream signalized intersection. Potential operational
effects on this segment are produced by the upstream signalized intersection and
traffic flows coming from the cross street. Note the length of this type of segment
does not include the acceleration length of the signal influence area.

The lengths of these different segment types should add up to the total length of the

analyzed facility.









I I I
I I I



I I I




Roadway Segments


Figure 3-9. Segment division of a two-lane highway with multiple isolated signalized intersections






















0


Q


0


0


Figure 3-10. Facility segmentation of a two-lane highway with multiple isolated signalized intersections


0


Type 1: Basic Two-lane highway

Type 2: Signalized Intersection Influence Area

Type 3:Affected DownstreamSegrnent


....................
.....................
....................
.....................
....................
.....................
im 6 0601i. 10: 10: 10: M: :Mim
. . . . . .
. . . . . .
. . . . . .
. . . . . .
. . . . . .


I i, i, i, I i









3.2.3 Overview of Computational Methodology

In this methodology, a common service measure would be applied to every

segment of the entire facility. The service measures at each segment are aggregated to

obtain an estimate of the overall service measure for the entire facility. The LOS of the

entire facility is determined by this aggregated service measure.

An example of analyzing a two-lane highway with signalized intersections using

this methodology is provided here. Percent time-delayed is applied as the common

service measure for the whole facility composed of two-lane highway segments and

signalized intersections.

The first step in this analysis is to segment the facility based on the features of

segment type. The second step is to determine the free-flow speed. The free-flow speed is

used to determine the average travel speed and delay time at each segment. The basic

free-flow speed for the two-lane highway is observed at basic conditions and ranges from

45 to 65 mile/h, depending on the highway's characteristics. The speed study should be

conducted at a representative site within the study section. The best location to measure

free-flow speed on the two-lane highway is mid-block and as far as possible from the

nearest signalized or stop-controlled intersection. If field observation of free-flow speed

is not practical, free-flow speed on the two-lane highway may be estimated using the

method presented in the HCM 2000.

The next step in the analysis is to perform operational analysis at the point and

segment levels. At the first type of segment, which is the basic two-lane highway

sections, and not affected by the signalized intersection, the average travel speed can be

calculated using the two-lane highway procedure presented in Chapter 20 of HCM 2000.









The length of the conventional two-lane highway segment is determined by the actual

placement of the signalized intersection within the analysis section.

At the second type of segment, which is the signalized intersection influence area,

the control delay is the portion of the total delay for a vehicle approaching and entering a

signalized intersection. Control delay concludes the delays of initial deceleration, move-

up time in the queue, stops, and acceleration. It can be calculated using the signalized

intersection procedure presented in Chapter 16 for the through-traffic lane group. The

length of the signal influence area includes the deceleration length, stopping length, and

acceleration length.

The third type of segment is the downstream segment, affected by the upstream

signalized intersection, and the traffic flow coming from the cross streets. The potential

impacts of the signalized intersection on this segment will be assessed further in the term

of average travel speed. The effective length of influence area downstream of the

signalized intersection is also decided. For the analysis of this type of segment, statistical

methods and TWOPAS simulation model will be used to quantify the impacts. The

methodology will be presented in Chapter 4.

Once average travel speed on the two-lane highway segments and control delay

within the signalized intersection are determined, the delay time on the two-lane highway

segments and the signalized intersection can be calculated using the following equations.

Delay time on the two-lane highway segment:

LH LH
DH = H H (3-4)
H FFS

Where:


DH : delay on the two-lane highway segment, s/veh









LH : length of two-lane highway segment, ft

FFS: free flow speed for the two-lane highway segment, ft/s

SH : average travel speed for two-lane highway segment, ft/s

Control delay at the signalized intersection:

Ds = d,(PF)+ d2 +d3 (3-5)

Where:

Ds: control delay per vehicle at the signalized intersection, s/veh

d,: uniform control delay, s/veh

d2: incremental delay, s/veh

d3 : initial queue delay, s/veh

PF: uniform delay progression adjustment factor

After estimates of delay time at the segment and point levels are obtained, segment

and point delays are then added together to obtain the entire facility estimate. Percent

time-delayed is then computed through dividing total delay time on the entire facility by

the total travel time at the free-flow speed on the entire facility. Equation 3-6 shows the

aggregation of point and segment results to obtain an estimate of percent time-delayed for

the entire facility. After the facility-wide performance measure, percent time-delayed is

obtained, the facility's LOS grade can be determined based on the LOS table. An initial

set of thresholds will be established as part of this research, but further research on this

issue will likely be warranted. Figure 3-11 illustrates the analysis procedure for

determining LOS on the two-lane highway with signalized intersections.






49


Z(D + D,)
PTD = H'S
LH Ls
H,S FFSH FFSs
(3-6)
L = -LH +Ls
H,S
Where:

PTD: percent time-delayed per vehicle for the entire facility, %

DH: delay time per vehicle for the two-lane highway segment, s/veh

Ds: delay time per vehicle for the signalized intersection influence area, s/veh

FFSH: free flow speed for the two-lane highway segment, ft/s

FFSs: free flow speed for the signalized intersection influence area, ft/s

L: length of the entire facility, ft

LH: length of the two-lane highway segment, ft and

Ls: length of the signalized intersection influence area, ft








50




Input
---- Roadway data
---- Traffic data
---- Control data





Divide the facility into segments




Free-Flow Speed (FFS)
---- Determine free-flow speed






Type 2:
Signalized or
Unsignalized Intersection
Influence Area







ermine effective Compute
of the intersection control delay
influence area













Determine Percent time-delayed
----- By segment
----- Over entire facility




Determine LOS over entire facility


Figure 3-11.Flow diagram of two-lane highway facility operational analysis methodology









In developing this methodology, some simulation and analysis methods were used

at each methodological step. Table 3.3 summarizes those programs and methods used.

Table 3-3. Summary of programs used at each step
Step 1: Divide the facility into segments.
Facility is divided into segments based on its geometric conditions. Segments in the
facility are not regarded as isolated. The interactions between different segments are also
taken into account.
Step 2: Determine the free-flow speed.
The methods presented in the HCM 2000 are used field measurement, or estimating
free-flow speed. (Chapter 20, Page 20-4, 20-5)
Step 3: Determine segment length.
3.1 Determine the length of the signalized intersection influence area
The length of signal influence area is the sum of three components, deceleration distance,
queue length, and acceleration distance. Acceleration distance can be determined using
the linearly-decreasing acceleration model. The deceleration distance and queue length
are determined using the CORSIM simulation program and regression analysis.
3.2 Determine the length of the affected downstream segment
The length of the affected downstream segment is determined using the TWOPAS
simulation program and regression analysis. The method is built upon work done
previously by Dixon, et al.
3.3 Determine the length of the TWSC intersection influence area
The length of TWSC influence area is the sum of three components, deceleration
distance, queue length, and acceleration distance. The Synchro/SimTraffic program was
used to determine the queue length.
Step 4: Calculate the unaffected average travel speed on basic two-lane highway
segments.
The analysis methods presented in Chapter 20 of the HCM 2000 are used to calculate the
average travel speed on basic two-lane highway segments.
Step 5: Calculate control delay at the signalized or unsignalized intersection influence
area.
The analysis methods presented in Chapter 16 of the HCM 2000 are used to calculate
control delay at the signalized intersection.
The analysis methods presented in Chapter 17 of the HCM 2000 are used to calculate
control delay at the Two-Way Stop-Controlled intersection.
Step 6: Determine average travel speed on the affected downstream segment.
An adjustment factor is used to account for the effects of the upstream signalized
intersection on the downstream highway segment. The values of adjustment factor are
determined using the TWOPAS simulation program and regression analysis.
Step 7: Determine the delay time at every segment.
The delay time at every segment is calculated using Equations 3-4 and 3-5.
Step 8: Determine the percent time-delayed and LOS of the entire facility.
The percent time-delayed is calculated using Equation 3-6.
LOS is determined from Table 5-8 (Chapter 5).









In this methodology, three simulation programs are selected to simulate traffic

operations on the two-lane highway in the vicinity of an intersection. The reasons why

they were selected are presented in Table 3-4.

Table 3-4. Simulation models evaluation


Simulation
Model
CORSIM


Evaluation


CORSIM, developed by the Federal Highway Administration, is the
most widely used and accepted traffic simulation model in the U.S. It has
the ability to simulate traffic operations on a two-lane roadway and includes
detailed modeling of traffic signal operations. In addition, the CORSIM
simulation model simulates the traffic system on a vehicle-by-vehicle basis
by updating roadway position, speed, acceleration, and other state variables
in discrete time steps. The ability to calibrate, modify, and manipulate these
parameters is a key characteristic of the CORSIM simulation model
amenable for use to determine the effective length of the signal influence
area.
CORSIM cannot simulate passing maneuvers using the on-coming
lane of traffic. However, experience shows that drivers usually do not
undertake passing maneuvers in the vicinity of a traffic signal. Under this
assumption, it is feasible to use a program such as CORSIM to model
vehicular operations on a two-lane roadway in the vicinity of a traffic signal,
and determine the effective length of the signal influence area on the
upstream two-lane highway segment.


TWOPAS is the only simulation program that is able to simulate the
passing maneuver operation on the two-lane highway using the opposing
lane, and was developed with U.S. data. Meanwhile the input variable,
Entering Percent Following reflects the potential effects of a signalized
intersection on the downstream two-lane highway operations.
In this study, TWOPAS was used to simulate the effects of the
signalized intersection on the downstream segment.
Synchro is a complete software package for modeling and optimizing
traffic signal timing. SimTraffic is a companion product to Synchro for
performing microscopic simulation and animation. SimTraffic uses a
Synchro file for input. It is very convenient to obtain the queue information
from its simulation output.
In Synchro, there are two options for reporting the intersection
statistical information, the Synchro method or the HCM method. The HCM
method is used to determine the queue length to maintain fidelity to the
existing HCM.


TWOPAS


Synchro
and
SimTraffic














CHAPTER 4
DEVELOPMENT OF FACILITY SEGMENTATION COMPUTATIONS

The methodology developed in Chapter 3 divides the entire facility into three types

of segments. They are the basic two-lane highway, the signalized intersection influence

area, and the affected downstream two-lane highway segment. In this methodology, the

overall LOS for the facility is calculated by aggregating the service measure values of the

segments, as weighted by segment length. The focus of this chapter is the determination

of the length of each of the component segments of a two-lane highway facility.

Here the relation of the signalized intersection influence area and the affected

segment downstream of the signalized intersection is clarified again. The components of

the signal influence area include deceleration distance, stopping distance, and

acceleration distance, which are consistent with those of control delay defined in the

HCM 2000-deceleration delay, stop delay, and acceleration delay. The segment delay

time for the signalized intersection influence area is determined by the intersection

control delay. The affected downstream segment is still affected by the upstream

signalized intersection. As the traffic stream discharges from the upstream intersection

into the downstream highway segment, it will take some distance for traffic to return to

the same flow condition as before the influence of the signal. The delay time for the

affected downstream segment is determined by the difference in free-flow travel time and

actual travel time.

This chapter includes two sections. Section 1 presents three methods to determine

the length of a signalized intersection influence area and their advantages and









disadvantages are evaluated. Section 2 explores the methodology to determine the length

of the downstream segment affected by the upstream signal. How to accurately define the

headway distribution and calculate the parameter of EPF is discussed in this section.

Finally, this methodology is verified by comprehensive comparisons with other

simulation programs.

4.1 Effective Length of the Influence Area Upstream of the Signalized Intersection

This section discusses the methodology of determining the effective length of the

signalized intersection influence area. Three methods are presented. The first method is to

apply the recommended length in FDOT's 2002 Level/Quality of Service Handbook; the

second one determines the length of a signalized intersection influence area using the

HCM equations; the third one is to apply simulation method.

4.1.1 Recommended Length in FDOT's 2002 Level/Quality of Service Handbook

In FDOT's 2002 Level/Quality of Service Handbook, for a preliminary engineering

analysis FDOT recommends breaking the facility into uninterrupted and interrupted flow

segments [4]. The interruptedflow intersection segments, "intersection influence areas,

extend 0.5 miles in length centered on the midpoint of the crossingfacility. The LOS for

this influence area is determined by the intersection LOS. Figure 4-1 shows an example

of how to determine the intersection length in the two-lane highway facility with

signalized intersections.

In this example, a two-lane highway with a signalized intersection extends 10

miles, and the isolated intersection is located at the 6-mile point. The first 5.75 miles

would be regarded as a two-lane highway segment, the next 0.5 miles would be regarded

as the intersection area, and the last 3.75 miles would be regarded as a two-lane highway

segment.









The recommended length in FDOT's 2002 Level/Quality of Service Handbook is

only a simplified value. It does not take into account any actual factors such as traffic

conditions and signal timing plans in the field. A new method to determine the effective

length of the signalized intersection influence area under specific conditions is presented

here from a component-based perspective.

Two-lane Highway Segment Intersection Two-lane Highway Segment



5.75 M 0.25- 3 3.75 _












Figure 4-1. Length of intersection area

4.1.2 Components of the Signal Influence Area

The signalized intersection influence area is the place where control delay happens.

Control delay is defined as the total delay due to the signalized intersection and includes

deceleration delay, stop delay, and acceleration delay. The length of the signalized

intersection influence area should be consistent with control delay, and its components

correspond to those of the control delay. That is, the components of the signalized

influence are deceleration length, stopping length, and acceleration length. The detailed

distance-time diagram shown in Figure 4-2 is useful for defining the general shape of the









relationship of control delay (Time), and the length of the signalized intersection area

(Distance) associated with a specific vehicle.

Figure 4-2 shows the main delay terms at a signalized intersection, and

components of the signal influence area. Before Point 1 on the time-distance diagram, the

vehicle is moving at a relatively uniform speed. From Point 1 to Point 2, the vehicle

decelerates until it stops at Point 2 to join the standing queue before the signalized

intersection. The vehicle remains stopped between Points 2 and 3. Between Points 3 and

Point 4, the vehicle accelerates until it reaches a uniform speed again at Point 4. Notice

that Point 3 is the stop bar.

In Figure 4-2, the deceleration distance LD is given by

LD = L2- L1 (4-1)
Similarly, the stopping distance Ls is given by

Ls = L, L, (4-2)

Similarly, the acceleration distance LA is given by

LA = L4 L3 (4-3)


To determine the overall length of the signal influence area, the lengths of each of

the three components must be determined. The method to determine the lengths of these

three components will be discussed in the following section.

Figure 4-3 illustrates several kinds of conditions for which vehicles pass through a

signalized intersection. Figure 4-3(a) shows the condition for which vehicles are near the

intersection facing a red signal indication and a queue exists in front of the intersection,

so drivers will safely stop their vehicles within sufficient sight distance to avoid entering

the intersection or colliding with queued vehicles. For this condition, the effective length









is equal to the sum of stopping sight distance (SSD) and queue length. At the end of the

red period, the queue length increases to the maximum value.

Figure 4-3(b) shows the condition for which vehicles are near the intersection

facing a green signal indication, a queue exists in front of the intersection, and drivers do

not need to stop their vehicle completely, but still need to decelerate. For this condition,

the effective length is still equal to the sum of SSD and queue length. At the end of the

green period, the queue length decreases to the minimum value. Vehicle approaches the

signal under different conditions. Here the average queue length is used.

Figure 4-3(c) shows the condition for which vehicles are near the intersection

facing a green signal indication, and no queue exists in front of the intersection. In this

case, the effective length is equal to SSD only. When a vehicle randomly arrives at the

intersection, it may encounter any condition, where queue length is at a maximum,

median, or not present. Based on the above discussion, the upstream effective length of

the signalized intersection influence area can be calculated as the summation of stopping

sight distance and average queue length. That is,

L = SSD + (4-4)

Where:

Lu: effective length of influence area upstream of signalized intersection, ft

SSD: Stopping Sight Distance, ft

Q : average queue length, ft

In the above equation, SSD corresponds to the distance traveled during

perception/reaction time plus the braking/deceleration distance, and Q corresponds to

the stopping distance (i.e., distance over which queued vehicles are stopped).



















Acceleration
distance

-j


Queue
length


Deceleration
distance


Free flow speed /
trajectory /
/
/
/


Control delay


I I Acceleration ends


'I Approach delay
s.A to .bP a ............................... bar.......................................................................................


Stopped delay


anpad = nf


- _- I... ;-.. .... oo..................................


Decele tion begins


-- ........................................................................ ..................................................................................................


Vehicle /5
trajectory



E4


Time


Figure 4-2. Schematic distance-time diagram at a signalized intersection


;IL


J









-

Y Y
Safe Braking Distance Queue Length
(a)
I



Safe Braking Distance Queue Length
(b)
I

I

Safe Braking Distance


Signal is Red
Signal is Green


Figure 4-3. Queue length estimation

4.1.2.1 Determining stopping sight distance

The stopping sight distance can be calculated using Equation 4-5, as follows:


SSD = Vt + V
2g a)+G


(4-5)


Where:

SSD: Stopping Sight Distance, ft

Vi: initial vehicle speed, ft/s

tr: perception-reaction time, sec

a: deceleration rate, ft/s


0

0









g: gravitational constant, ft/s

G: roadway grade (+for uphill and for downhill), percent/100

This equation is from AASHTO's "Green Book" [2]. In this equation, the
perception-reaction time is taken as 2.5 seconds and a deceleration rate of 11.2 ft/s2 (3.4
m/s2) is assumed.
Perception-reaction time and initial vehicle speed are two important elements in

calculating the stopping sight distance. The perception-reaction time is the time it takes

to initiate the physical response, which includes the detection, identification, and decision

elements involved in responding to a stimulus. The perception-reaction time used to

calculate the stopping sight distance, when vehicles are near to the signalized intersection

should be analyzed from the features of actions taken by drivers when near the signalized

intersection.

* Vehicle deceleration when approaching an intersection is an expected event.
Perception-reaction time varies depending on whether the event is expected or
unexpected, with expected events logically requiring less time.

* Vehicle deceleration when approaching an intersection is a relatively simple task.
Perception-reaction time varies with the complexity of the task. The simpler the
task, the shorter the time required for a response.

Decelerating vehicles approaching the signalized intersection is an expected event,

and it is also a fairly simple task. At the first part of perception-reaction time, vehicles

still keep the initial speed; at the ending part of perception-reaction times, drivers begin

taking actions to decelerate the vehicles. The AASHTO Green Book [2] suggests a

perception-reaction time of 2.5 seconds, which is a design recommendation, accounting

for unexpected events or obstacles in the roadway. Based on this recommended value and

the characteristics of actions taken by drivers nearing a signalized intersection, the

perception-reaction time is assumed to be in the range of 1 second (1 second is typically









used for yellow interval timing calculations). It is also assumed that the latter part of this

perception-reaction time will consist of some vehicle deceleration as a driver will lift

their foot off the accelerator in preparation for applying the vehicle's brakes.

Initial vehicle speed is another important element of stopping sight distance. The

travel speed is generally inversely proportional to the traffic volumes. When the traffic

volume is lower, vehicles approach the intersection at a higher speed; when the traffic

volume is higher, vehicles approach the intersection at a relatively lower speed.

4.1.2.2 Determining average queue length

Appendix G of Chapter 16 in the HCM 2000 puts forward the concept of the

average back-of-queue measure [1] at signalized intersections. In this model the back of

queue is the number of vehicles that are queued depending on arrival patterns of vehicles

and vehicles that do not clear the intersection during a given green phase. The average

back of queue is used as the average queue length, and can be calculated using Equation

4-6:



Q = Q1 + Q2 (4-6)
Where:

Q: maximum distance in vehicles over which queue extends from stop line on

average signal cycle, veh

Q1: first-term queued vehicles, veh, and

Q2 : second-term queued vehicles, veh

The first term, Q1, represents the number of vehicles that arrive during the red

phases and during the green phase until the queue has dissipated. The first term is

calculated using equation 4-7.









V, C
Q, =PF2 600 (4-7)
1- min(1.0, X) C

Where:

PF2: adjustment factor for effects of progression

VL: lane group flow rate per lane, veh/h

C: cycle length, sec

g: effective green time, sec, and

XL: ratio of flow rate to capacity

Qi represents the number of vehicles that arrive during the red phases and during

the green phase until the queue has dissipated. The adjustment factor for effects of

progression is calculated by Equation 4-8.



PF2 (4-8)
1 1-RP JL

Where:

PF2: adjustment factor for effects of progression, veh

VL: lane group flow rate per lane veh/h

SL: lane group saturation flow rate per lane, veh/h

C: cycle length, sec

g: effective green time, sec, and

Rp: platoon ratio

The second term, Q2, is an incremental term associated with randomness of flow

and overflow queues that may result because of temporary failures. This value can be an









approximate cycle overflow queue when there is no initial queue at the start of the

analysis period. The second term of the average back of queue can be computed using

Equation 4-9.

T 8kX 16k,
Q2 = 0.25c, (X -1)+ (X-1)2 + L L (4-9)
cLT (cT)2

Where:

CL: lane group capacity per lane, veh/lane

T: length of analysis period, h

kB: second-term adjustment factor related to early arrivals, and

QbL: initial queue at start of analysis period, veh

The second term adjustment factor related to early arrivals is calculated using

Equation 4-10:

07
kB = 0.12I s3Lg (pretimed signals)
\3600)
(4-10)
S 06
kB = 0.10I 3600 (actuated signals)
\3600)

Where:

kB: second-term adjustment factor related to early arrivals

SL: lane group saturation flow rate per lane, veh/h

g: effective green time, sec

I: upstream filtering factor for platoon arrivals
4.1.2.3 Determining acceleration distance

Another component of the signal influence area, acceleration distance after the

signalized intersection stop bar, can be determined using a linearly-decreasing









acceleration model. Continuing research [12] has shown that the linearly-decreasing

acceleration model better represents both maximum vehicle acceleration capacities as

well as actual motorist behavior. The linearly-decreasing acceleration model can be

rewritten as a differential equation and integrated to derive the following relationships

(treating a grade as being constant), as Equation 4-11 through 4-14. It should be noted

that this is only part of the full derivation. The full derivation can be found in most traffic

flow theory textbooks, for example [13].

Iv
= a pv + Gg (4-11)
at

(a Gg) aGg t (4-12)
v-= vo ev (4-12)
P I I ) P

8d + v v,
t = (4-13)
a_ Gg

(a Gg) t(aGg (1- et) (4-14)
d= t -voJ (4-14)
P P P


Where:

v: speed at the end of the acceleration cycle, ft/s

vo: speed at the beginning of the acceleration cycle, ft/s

a, p : acceleration model parameters, based on the design vehicle type

g: gravitational constant, ft/s

G: roadway grade (+for uphill and for downhill), percent/100

t: time for vehicle to accelerate from beginning speed, vo, to ending speed, v, sec

d: distance for vehicle to accelerate from beginning speed, vo, to ending speed, v, ft









The equations presented above arising from the linearly-decreasing acceleration

model are not quite as simple or as easy to apply as their counterparts based on constant

acceleration rates, but they are processed readily by a computer.

Transportation and Traffic Engineering Handbook [14] also contained one of the

most comprehensive summaries of previous research and field studies of maximum and

normal acceleration and deceleration rates. Table 4-1 summarizes acceleration rates,

distances traveled, and elapsed time for passenger vehicles on level terrain and under

normal operating conditions.

Table 4-1. Normal acceleration rates, distance, and elapsed time
Initial Final Speed (mph)
Speed 15 30 40 50 60
Acceleration Rate 3.3 3.3 3.3 3.1 2.9
0 (mph/s)
Elapsed Time (sec) 4.5 9.1 12.1 15.9 20.9
Distance Traveled (ft) 49 200 354 574 929
Acceleration Rate 3.3 2.9 2.5
30 (mph/s)
Elapsed Time (sec) --- --- 3.0 6.8 11.8
Distance Traveled (ft) 154 374 729
Acceleration Rate 2.6 2.3
40 (mph/s)
Elapsed Time (sec) --- --- --- 3.8 8.8
Distance Traveled (ft) 220 575
Acceleration Rate 2.0
50 (mph/s)
Elapsed Time (sec) --- --- --- --- 5.0
Distance Traveled (ft) 355
Source: Reference 14.

After the SSD, back of queue, and acceleration length are determined, the length of

the signalized intersection influence area can be calculated as the summation of the three

components. That is,


Ls = SSD + Q + LA


(4-15)










Where:

Ls: length of a signalized intersection influence area, ft

LA: acceleration length, ft

The components of the signal influence area, SSD, back of queue, and acceleration

length, are consistent with those of control delay defined in the HCM 2000, which are

deceleration delay, stop delay, and acceleration delay. A regression model was developed

for the relationship of control delay calculated using the methodology presented in the

HCM 2000, and the length of the signal influence area as the summation of SSD, average

back of queue, and acceleration length. The results indicate that the assumption of a

linear relationship is reasonable with an adjusted R-squared value of 0.895. The

regression model summary is presented in Table 4-2.


Table 4-2. Regression model summary
1. SUMMARY OUTPUT:
Regression
Statistics
Multiple R 0.9469
R Square 0.8966
Adjusted R Square 0.8946
Standard Error 23.9621
Observations 54.0000

2. ANOVA:
df SS MS F
Regression 1.0000 258814.8753 258814.9 450.7529
Residual 52.0000 29857.5439 574.1835
Total 53.0000 288672.4193

Coefficients Standard Error t Stat P-value
Intercept -114.408 8.80784 -12.9893 5.94E-18
X Variable 1 0.105078 0.00495 21.23094 2.79E-27
Lower 95% Upper 95% Lower 95.0% Upper 95.0%
-132.082 -96.7335 -132.082 -96.7335
0.095146 0.115009 0.095146 0.115009









In this methodology, the length of a signal influence area is calculated as the

summation of its components. In determining the length of each component, especially

the SSD and back of queue, several significant factors are not reflected in the calculation

formulas, such as the availability of a left-turn bay, the directional distribution of traffic

flow, and the percentage of left-turn vehicles in the traffic flow. A new methodology is

explored in the next section to fully take into account all major contributing factors,

which can affect the length of a signalized intersection influence area.

4.1.3 Simulation and Regression Analysis

To fully account for all significant contributing factors affecting the length of a

signalized intersection influence area, the method of regression analysis method is

applied. Ideally, field data would largely be used to develop the regression model.

However, in many cases, available study sites are either too limited and/or data cannot be

collected without great complication. Additionally, it is often difficult to collect enough

field data to provide a statistically valid sample size. In this study, the simulation method

is applied to simulate the operations of a two-lane highway with a signalized intersection.

The overall procedure consists of the following four major steps:

1. Select the potential contributing factors that are expected to have an impact on the
effective length.

2. Select the appropriate simulation model.

3. Develop the simulation model to simulate the effects of contributing factors on
effective length.

4. Develop the regression model.

These steps are discussed in detail in the following sections.









4.1.3.1 Contributing factor selection

The contributing factors considered include those that are expected to affect the

effective length. Many factors can produce effects on the effective length of a signalized

intersection. In the following section, traffic data, geometric data, and signal data are

discussed, respectively.

* Traffic Data

Traffic data include the hourly traffic volume, a Peak-Hour Factor (PHF), the

proportion of trucks and recreational vehicles in the traffic stream, and the

directional split (D-factor). Traffic flow rate can be used to represent the traffic

conditions by making adjustments to the hourly traffic demand. These adjustments

are the PHF, the heavy-vehicle adjustment factor, and the grade adjustment factor.

The conversion can be made using Equation 4-16 [1]:

V
Vp = v (4-16)
PHF x f, x fH,

Where:

vp: passenger-car equivalent flow rate for peak 15-min period, pc/h

V: demand volume for the full peak hour, veh/h

PHF: peak-hour factor

fG: grade adjustment factor

fHV: heavy-vehicle adjustment factor

Traffic data also include the proportions of through vehicles, left-turn vehicles and

right-turn vehicle in the traffic stream. The left-turning vehicles may have a negative

effect on the flow of the through movements, particularly when higher percentage of

left-turning vehicles may result in lane overflow or obstruction of the through









movements. The directional distribution of traffic flow is another important

characteristic of traffic stream. On two-lane highways, lane changing and passing are

possible only in the face of oncoming traffic in the opposite lane. There is a strong

interaction between the directions of travel on a two-lane highway because passing

opportunities are reduced and eventually eliminated as the opposing traffic volume

increases. At an intersection, left-turn vehicles execute their turning maneuvers

through the gaps of the opposing through traffic stream. When the opposing through

traffic volume is high, left-turn vehicles have less opportunity to execute their turning

movements.

* Geometric Data

Geometric data include the two-lane highway geometry and intersection geometry.

The basic geometric conditions of the two-lane highway and intersection are used to

determine the effective length. The existence of exclusive left-or right-turn lanes,

along with the storage lengths of such lanes should be noted, as these are important

factors in determining the effective length.

* Signal Data

The signalization conditions include control mode (i.e., pre-timed, semi-actuated, and

fully-actuated), the phase plan, cycle length, green time, and clearance intervals. In

this study, the simplest and most widely used form of signalization, the two-phase

pre-timed signal, is used. All left-turn and right-turn movements are made on a

permitted basis from shared or exclusive lanes. The cycle length and effective green

time are selected as contributing factors to determine the effective length.









Based on the above discussion on traffic, geometric, and signalization conditions,

contributing factors are selected for calibration of the upstream length of roadway

affected by the signalized intersection. They are:

* peak volume

* D-factor

* percentage of left-turn and right-turn movements

* cycle length

* ratio of effective green time to cycle length

* availability of a left-turn bay

4.1.3.2 Simulation model selection

The next step is to select a simulation model to simulate traffic operations on a two-

lane highway with a signalized intersection. As reviewed in Chapter 2, TWOPAS rural

highway simulation model has the ability to simulate traffic operations on a conventional

two-lane roadway. However, the model has no ability to simulate traffic turning on or off

the highway at driveways and does not handle signalized intersections. Therefore, the

TWOPAS simulation model is not appropriate to determine the effective length of the

influence area upstream of the signalized intersection.

CORSIM, developed by the Federal Highway Administration, is the most widely

used and accepted traffic simulation model in the U.S. It has the ability to simulate traffic

operations on a two-lane roadway and includes detailed modeling of traffic signal

operations. However, CORSIM cannot simulate passing maneuvers using the on-coming

lane of traffic.

Before making a decision, TWOPAS was used to simulate the traffic operations on

the basic two-lane roadway to study the relation of passing demand, passing capacity, the









percentage of passing zones, the advancing traffic volume, and the opposing traffic

volume. CORSIM was used to determine the features that affected performance measure

variation on the two-lane highway segment upstream the signalized intersection. These

results are presented in Appendix A. After large quantities of simulations, the following

conclusions can be drawn from the study:

* Although on the two-lane highway, passing operations can be performed using the
opposite lane in the face of oncoming traffic, the percentage of vehicles
undertaking passing maneuvers is rarely more than 6% of the traffic volume under
different conditions of advancing traffic flow rate and opposing traffic flow rate.

* At the same advancing traffic volume level, the difference in average travel speed
at the different opposing traffic volume levels is very small, less than 2%; the
difference in the average travel speed between 100% no-passing zones and 0% no-
passing zones is also small. As the advancing traffic flow rate increases, the
difference decreases and gradually becomes negligible.

* The variance in travel speed due to a downstream signalized intersection is much
larger than due to following a slower leading vehicle.

As vehicles approach a signal (i.e., within the influence area of the signalized

intersection), the spacing between vehicles decreases, and following vehicles are unlikely

to pass leading vehicles. Experience has shown that as drivers approach a signal, they

generally will be more cautious; thus usually not undertaking passing maneuvers and

possibly slowing down even if the signal indication is green. The roadway is also often

marked with solid yellow dividing lines (i.e., no passing) in the vicinity of traffic signals.

Under this assumption, it is feasible to use a program such as CORSIM to model

vehicular operations on a two-lane roadway in the vicinity of a traffic signal, and

determine the effective length of the signal influence area on the upstream two-lane

highway segment. In addition, the CORSIM simulation model typically simulates the

traffic system on a vehicle-by-vehicle basis by updating roadway position, speed,

acceleration, and other state variables in discrete time steps. The ability to calibrate,









modify, and manipulate these parameters is a key characteristic of the CORSIM

simulation model amenable for use to determine the effective length of the signal

influence area.

4.1.3.3 Simulation model experimental design

A two-way, two-lane roadway network with an isolated fixed-time signalized

intersection was simulated using CORSIM. It extended 3 miles, and the isolated

intersection was located at the 1-mile point. The attributes of the simulated network were

set to fulfill the basic conditions for a two-lane highway and signalized intersection

according to the HCM 2000. These were defined as:

* Design speed greater than or equal to 60 mi/h

* Lane widths greater than or equal to 12 ft

* Clear shoulder wider than or equal to 6 ft

* Level terrain

* All passenger cars in traffic stream

* Two phase pre-timed signal

Two sets of CORSIM base road network were developed. One is the signalized

intersection with a 250-foot left-turn bay; the other is the signalized intersection without a

left-turn bay. Once the base road networks were developed, the values for the

contributing variables were systematically changed to model different scenarios. The

values for each contribution variable are displayed in Table 4-3 and Table 4-4. The

different inputs resulted in a combination of 243 (3x3x3x3x 3=243) simulation scenarios

for the base network without a left-turn bay. Ten simulation runs were made for each

scenario to account for the variability in stochastic micro-simulation program output. A









total of 2430 simulated runs were performed. The length of simulation time for each run

was 15 minutes.

Table 4-3. Variable input values (with a left-turn bay)
Peak Volume Cycle length Percentage of left-turn
(pc/h) (sec) g/C and right-turn vehicles
400 60 0.55 5%
800 75 0.65 10%
1200 90 0.75 15%


Table 4-4. Variable input values (without a left-turn bay)
Peak Volume Cycle length Percentage of left-turn
(pc/h) D-Factor (sec) g/C and right-turn vehicles
400 0.50 60 0.55 5%
700 0.55 75 0.65 8%
1100 0.60 90 0.75 11%

At an intersection, left-turn vehicles execute their turning maneuvers through the

gaps of the opposing through traffic stream. When the opposing through traffic volume is

lower, the left-turn vehicles can execute their turning movements. When the opposing

through traffic volume is very high and left-turn vehicles cannot execute their turning

movements, the left-turn vehicles can stay temporarily at the left-turn bay, and will not

block the advancing through traffic behind them. So when developing the effective length

model for the signalized intersection with a left-turn bay, the D-factor is not included as a

contributing factor.

4.1.3.4 Regression model development

After simulation, average travel speeds at the interval of 0.025 miles along the two-

lane roadway were obtained from the CORSIM output file. Figure 4-4 illustrates the

variations of average travel speed along the two-lane highway with an isolated signalized

intersection.







74



Based on the variation of average travel speed, the effective length of the signalized


intersection on the upstream two-lane highway segment can be measured from the


bifurcation point, at which point vehicles begin decelerating to the stop line of the


signalized intersection, such as the section AO in Figure 4-4. After extracting the needed


data, regression analysis was performed to establish the model of the upstream effective


length with contributing factors.


Upsteam Effective Length


40-

35




I-
i30-



1 20

> 15
STwo-lane Highway With Signal I
Two-lane Highway Without Signal
Intersection

0 5 10 15 20 25 30
Position Along Roadway (1/40 mi)



Figure 4-4. Average travel speed along the two-lane highway with signal

The regression model for the upstream effective length of a signalized intersection


with a left-turn bay is developed as follows:


Len- p = 43.2463 + 4.2688 x (V/100)2 + 5.2178 x Cycle (417)

57.3041 x (V/100) x%LT 5.2444 x Cycle x g_C

Where:


Leneff up upstream effective length of a signalized intersection, ft


V: traffic flow rate, veh/h


Cycle: cycle length, sec









g C: ratio of effective green time to the cycle length, and

%LT: percentage of left-turn vehicles in the directional traffic flow

The statistical results for the effective length model for the signalized intersection

with the left-turn bay (250 ft) are presented in Table 4-5. For a significance level of 0.05

(or 95% confidence), a =0.05, and the degrees of freedom, n (k + 1) = 30 5 = 25 df.

The critical t value obtained from t-Distribution Table is to.05 = 1.708. All the t-stat

absolute values are greater than 1.711, so all the variables used in the chosen model are

useful.


Table 4-5. Regression model (with a left-turn bay)
R2 = 0.95743; Adj R2 = 0.95519
Coefficient t-stat
Intercept 43.2463 4.84765
V/100(Q) 4.2668 29.38653
Cycle (L) 5.2178 11.41796
V/100(L) x %LT(L) -57.3041 -3.05196
Cycle (L) x gCRatio (L) -5.2444 -9.45781
(L) Linear; (Q) Quadratic

The regression model for the upstream effective length of a signalized intersection

without a left-turn bay is developed as follows:

Lenef p = 3074.49 + 5.89 x (V/100)2- 440.00 x DFactor
+1.69 x Cycle 7336.59 x g _C + 4758.52 x (g _C)2 (4-18)
+1171.01 x (V/100) x (%LT)2

Where:

Leneffp: upstream effective length of a signalized intersection, ft

V: traffic flow rate, veh/h

DFactor: percentage of traffic traveling in the peak direction

Cycle: cycle length, sec









g C: the ratio of effective green time to the cycle length, and

%LT: the percentage of left-turn vehicles in the directional traffic flow

The statistical results for the effective length model for the signalized intersection

without a left-turn bay are presented in Table 4-6. For a significance level of 0.05 (or

95% confidence), a =0.05, and the degrees of freedom, n (k + 1) = 30 5 = 24 df. The

critical t value obtained from t-Distribution Table is to.05 = 1.711. All the t-stat absolute

values are greater than the value of 1.711, so all the variables used in the chosen model

are useful.

Table 4-6. Regression model (without a left-turn bay)
R2 = 0.77764; Adj R2 = 0.77199
Coefficient t-stat
Intercept 3074.49 3.97573
V/100(Q) 5.89 20.44190
Dfactor (L) -440.00 -2.08639
Cycle (L) 1.69 2.40322
gCRatio (L) -7336.59 -3.08700
gCRatio (Q) 4758.52 2.60546
V/100(L) x %LT(Q) 1171.01 3.98667
(L) Linear; (Q) Quadratic

When calculating the upstream effective length, Table 4-7 is used for the following

conditions:

(1): The maximum g/C value for this regression model is 0.8.

(2): When the traffic flow rate is less than or equal to 300 veh/h

Table 4-7. Upstream effective length with low traffic volume (ft)
g/C
V (veh/h) 0.5 0.6 0.7 0.8
100 160 130 110 90
200 180 150 130 110
300 210 180 160 140









4.2 Effective Length of the Influence Area Downstream of the
Signalized Intersection

After passing through the signalized intersection, the vehicle platoon will travel

into the downstream two-lane highway. The platoon dispersion pattern is affected not

only by the upstream signalized intersection, but also by the right-turn vehicles and left-

turn vehicles from minor streets.

This section begins with the discussion of Entering Percent Following (EPF) in

the TWOPAS model and headway distribution. Then the effect of the signalized

intersection on the downstream two-lane highway segment is quantified through the

parameter of EPF. Next, the methodology using TWOPAS simulation to determine the

effective length of a signalized intersection on the downstream segment is presented.

Finally CORSIM simulation is used to validate this methodology.

4.2.1 Entering Percent Following of TWOPAS

A study by Dixon et al. [3] concluded that the potential effect of a signalized

intersection on the downstream two-lane highway operations was to modify the

distribution of headways. The condition with no signalized intersection is represented by

assuming randomly distributed headways for entering traffic. However, the signalized

intersection in the upstream will modify the headway distribution of the traffic stream

entering the two-lane highway.

The TWOPAS model is used to simulate the effects of a signalized intersection on

the downstream two-lane highway. In TWOPAS, the distribution of headway is defined

through the input variable, Entering Percent Following (EPF), which is the percentage of

the total vehicles in the direction of travel that are following in platoons when they enter

the road being analyzed. Figure 4-5 illustrates an interface of TWOPAS for inputting









traffic data. In this interface, EPF is identified in the text, '% Traf in Platoons' in Dixon

et al.'s study, it was assumed that it was appropriate to represent the effects of a

signalized intersection through the EPF parameter, the percentage of vehicles following

immediately downstream of a signalized intersection. To analyze the potential effect of a

signalized intersection on the downstream two-lane highway operation, the key point is

how to accurately decide the EPF at the point immediately downstream of a signalized

intersection.




















Figure 4-5. TWOPAS traffic data input interface

4.2.2 Headway Distribution

The time headway distribution between vehicles is an important flow characteristic

that affects the safety, level of service, driver behavior, and capacity of a transportation

system. Previous research [15] has established that the shape of the time headway

distribution varied considerably as the traffic flow rate increased. In Dixon et al.'s study,

the negative exponential distribution is used to define the headway distribution for the

different traffic flow levels. For example, for the basic two-lane highway without a









signalized intersection, the EPF parameter is calculated using a cumulative exponential

distribution for headways less than or equal to 3.0 seconds, using Equation 4-19:

t
% Platooned = 100(1- e 3600) (4-19)

Where:

q: hourly flow rate of traffic entering the two-lane highway, veh/h

t: headway criteria used to define when vehicles are following, (3.0 sec)

The simple negative exponential distribution could not completely capture the

features of headway distribution. To accurately quantify the effect of an isolated

signalized intersection on the downstream two-lane highway segment, the shifted

negative exponential distribution and composite distribution are introduced into the

Dixon et al. methodology to calculate the EPF parameter.

4.2.2.1 Shifted negative exponential distribution

Under very low volume conditions, all the vehicles may be thought of as traveling

independent of one another. Any point in time is as likely to have a vehicle arriving as

any other point in time. This situation will be classified as the random headway state. The

negative exponential distribution can be used to define the time headway distribution for

this condition. However, drivers typically maintain a minimum time headway for safety

considerations, although their perception of the minimum safe headway is often too low.

Thus, the shifted negative exponential distribution can better define the time headway

distribution under very low volume conditions. The probability density function of the

shifted negative exponential distribution is given by equation 4-20:



f (t = Ae- a) (4-20)


Where:









f(t): probability density function,

a : user-selected parameter greater than or equal to zero that affects the shift of

the

distribution, sec, and

A : parameter that is a function of the mean time headway and a .

A can be calculated as:

A (4-21)
t-a
The percentage of vehicles in platoon with the shifted negative exponential

distribution can be calculated using Equation 4-22:

%platoon = 1 P(h > t)

=1 [e ^(t ]dt (4-22)

= -e (t-a)/(t-a)
4.2.2.2 Composite distribution

As the traffic flow rate increases, there is increasing interaction between vehicles.

Gerlough et al. [16] proposed that the traffic flow consisted of two classes of vehicles:

constrained vehicles and free-moving vehicles. According to May [15], the random

headway state (Negative exponential distribution) is best suited for very low flow

conditions, while the nearly-constant headway state (Normal distribution) is best suited

for very high flow conditions. The intermediate headway state lies between the two

boundary conditions of the random- and constant-headway states. The composite model

is a better alternative to represent the headway distribution as the traffic flow level

increases. The composite model approach utilizes the combination of a normal headway

distribution for these constrained cars that are in the car-following or platoon mode and a

shifted negative exponential distribution for those free-moving vehicles. The composite









distribution represents the time headway distribution well when the traffic flow rate is

higher. The percentage of vehicles in platoon with the composite distribution can be

calculated using Equation 4-23.


%Platooned = 1- P(h > t)
1rPp 1 + P t- 2 (4-23)
=1- Pe a) + Pt e 2 s dt

Where:

Pp: proportion of vehicles in platoon, %

PNP: proportion of vehicles not in platoon, %

t : mean headway of the vehicles in platoon, sec

tN : mean headway of the vehicles not in platoon, sec

a : the minimum time headway for vehicles not in platoon, sec

s: standard deviation of normal distribution

t: time headway being investigated, sec

t : mean headway, sec/veh

In the composite distribution, there are four independent parameters that need to be

specified: mean and standard deviation of the normal distribution, the proportion of

vehicles in platoon, and the minimum time headway for vehicles not in platoon.

Numerous calculations and sensitivity analyses of a matrix of the four independent

parameters need to be conducted to find the "best" composite model distribution for each

traffic flow level. An example is given here to show how to find an appropriate

composite distribution for the traffic flow of 1636 veh/h. Detailed calculations of the

theoretical time headway for this traffic flow level are shown in Table 4-8. The









theoretical shifted negative exponential headway distribution, normal headway

distribution, composite headway distribution, and the measured time headway

distribution are presented graphically in Figure 4-6. The Chi-Squared test is used to

access statistically how closely the measured distribution is similar to the theoretical

composite distribution. An example is given to compare the measured time headway

distribution for the traffic flow level of 1636 veh/h with a composite distribution. The

Chi-Squared test calculations are shown in Table 4-9. The individual Chi-Squared

contributions are summed, and the calculated Chi-Squared value is found to be 13.94.

The number of degrees of freedom is determined to be 10 based on 15 time intervals and

4 parameters required for the composite distribution. Assuming a 0.05 significance level

the reference Chi-Squared value is determined to be 18.30. Since the calculated Chi-

Squared value is less than the reference Chi-Squared value, the hypothesis is not rejected

and the conclusion is that there is no evidence of a statistical difference between the two

distributions.

Although the composite distribution is the combination of a normal headway

distribution and a shifted negative exponential distribution, when the traffic flow rate is

lower, a larger difference occurs between the composite distribution and the measured

distribution. So in this study, the shifted negative exponential distribution and composite

distribution are used together to mathematically describe time headway distribution,

including boundary conditions of random headway state and nearly-constant headway

state, and the intermediate headway state. Detailed calculations of the theoretical time

headway for all four traffic flow levels are presented in tabular form and figure in

Appendix B.









Table 4-8. Composite headway distribution calculation (volume = 1500-1740 veh/h)
composite
Vehides Not in Platoons Platoon Vehides Distribution

t aM a L EM 100% P z P(t 0.0 0.0 1.5 0.0000 0.0000 -3.000 0.0013 0.0215 0.0147 0.0147 24
0.5 0.0 1.5 0.0000 0.0000 -2.000 0.0228 0.1359 0.0927 0.0927 152
1.0 0.0 1.5 0.0000 0.0000 -1.000 0.1587 0.3413 0.2327 0.2327 381
1.5 0.0 1.5 0.0000 1.0000 0 0.0000 0.0000 0.5 0.3413 0.2327 0.2327 381
2.0 0.0 1.5 0.0000 1.0000 0.1813 0.0577 1.0000 0.8413 0.1359 0.0927 0.1503 246
2.5 0.3 1.5 0.2000 0.8187 0.2321 0.0738 2.0000 0.9772 0.0215 0.0147 0.0885 145
3.0 0.8 1.5 0.5333 0.5866 0.1663 0.0529 3.0000 0.9987 0.0013 0.0009 0.0538 88
3.5 1.3 1.5 0.8667 0.4204 0.1192 0.0379 4.0000 1 0.0379 62
4.0 1.8 1.5 1.2000 0.3012 0.0854 0.0272 0.0272 45
4.5 2.3 1.5 1.5333 0.2158 0.0612 0.0195 0.0195 32
5.0 2.8 1.5 1.067 0.1546 0.0438 0.0139 0.0139 23
5.5 3.3 1.5 2.2000 0.1108 0.0314 0.0100 0.0100 16
6.0 3.8 1.5 2.5333 0.0794 0.0225 0.0072 0.0072 12
6.5 4.3 1.5 2.8667 0.0569 0.0161 0.0051 0.0051 8
7.0 4.8 1.5 3.2000 0.0408 0.0116 0.0037 _0.0037 6
7.5 5.3 1.5 3.5333 0.0292 0.0083 0.0026 0.0026 4
8.0 5.8 1.5 3.8667 0.0209 0.0059 0.0019 0.0019 3
8.5 6.3 1.5 4.2000 0.0150 0.0043 0.0014 0.0014 2
9.0 6.8 1.5 4.5333 0.0107 0.003 0.0010 _________0.0010 2
9.5 7.3 1.5 4.867 0.0077 0.0077 0.0024 0.0024 4
I I I 1.0000 163


0.3182,Ep = 1.5sec,s = 0.5sec,P = 0.6818


7tp = 3.7 sec, a = 2.2sec, sp = 1.5sec, Pp













Composite Distribution ( Mean Headway= 2.2 sec)


0.05



0.00,



-0.05


Headway (sec)


Figure 4-6. Composite time headway distribution









Table 4-9. Chi-Squared test calculation
Time (f0 -f)
Headway fo f fo-f (fo -)2 /
Group
0.0 0.5 22 19 3 10 0.4934
0.5- 1.0 140 122 18 310 2.5355
1.0-1.5 312 307 4 19 0.0616
1.5 2.0 294 307 -13 164 0.5342
2.0 2.5 209 198 10 102 0.5158
2.5 3.0 125 117 9 74 0.6293
3.0-3.5 78 71 7 47 0.6638
3.5 4.0 46 50 -4 15 0.2955
4.0 4.5 30 36 -5 30 0.8433
4.5 5.0 21 26 -5 21 0.8143
5.0-5.5 13 18 -5 27 1.4748
5.5 6.0 7 13 -7 43 3.2939
6.0-6.5 7 9 -3 8 0.8607
6.5 7.0 7 7 0 0 0.0044
7.0 7.5 3 5 -2 5
7.5 8.0 3 3 -1 1 1.9678
8.0 8.5 0 2 -2 6
8.5-9.0 2 2 0 0
9.0-9.5 1 1 0 0 0.4183
> 9.5 3 1 -2 4
1320 1320 0 AL= 15.41
ZCALC = 15.41


n= (I- -p)
2 2e
%CALC < ref


(16 1) 4 = 11. Significance Level = 0.05, ,rf = 19.70.

15.41 <19.70; Therefore, do not reject null hypothesis


4.2.3 Determining Entering Percent Following

Dixon et al. [3] concluded that it was appropriate to represent the effects of a

signalized intersection on the downstream two-lane highway operations through the EPF

parameters, as long as the percent following immediately downstream of a signalized

intersection can be determined. In this study, the methodology for determining Entering

Percent Following is based on Dixon et al.'s methodology. The main difference from

their methodology is the application of distributions for time headway. As discussed in









Section 4.2.2, the shifted negative exponential distribution and composite distribution are

introduced into this methodology. Estimation of the percentage of entering traffic

following is based on a flow profile immediately downstream of the signalized

intersection. A flow profile immediately downstream of the signalized intersection at

location "A" is shown in the Figure 4-7. The "A" denotes a location immediately

downstream of the signalized intersection. As shown in Figure 4-7, there are three

movements that contribute to the flow profile:

* Movement 1: Primary contributing movement. They are through movements from
the upstream major street;

* Movement 2: Secondary contributing movement. They are right-turn movements
from the minor street; and

* Movement 3: Secondary contributing movement. They are left-turn movements
from the minor street.

As shown in the Figure 4-7, the total cycle-length is divided into three states. The

above three movements are charged through the three states. They are:

* First state: Discharged from the through movement queue during the first phase

* Second state: Discharge from the through movement without a queue plus any
right-turn on red executed during the first phase

* Third state: Discharge from the right and left turn movements during the second
phase

Entering percent following at location A can be estimated using equation 4-24:



VF,
EPF, =
VP (4-24)

VF Z= VF

Where:

EPFa: percent of vehicles following at Point A, immediately downstream of a









signalized intersection,

VFa: total number of vehicles following per cycle at location A, veh

VF,: total number of vehicles following per cycle from movement i, veh, and

Va: total number of vehicles per cycle at location A, veh


Figure 4-7. Two-lane highway traffic flow downstream of a signalized intersection

Source: Dixon, Michael P., Michael Kyte, and Satya Sai Kumar Sarepali. Effects of
Upstream Signalized Intersections on Two-Lane Highway Operations, Transportation
Research Board, Washington D.C., 2004
To determine the EPFa, the key point is to decide on the value of the denominator,

Va, and numerator, VFa. Because Va is the summation of the cycle-by-cycle volumes from

movements 1, 2, and 3, it can be determined if volumes for movements 1, 2 and 3 and the

cycle length are known. This leaves the estimation of VFa, the number of vehicles