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METHODOLOGY FOR THE OPERATIONAL PERFORMANCE ASSESSMENT OF TWOLANE 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 TwoLane 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 TwoLane Highway PTSF ............ ................ 20 3 CONCEPTUAL OVERVIEW OF TWOLANE HIGHWAY FACILITY ANALYSIS METHODOLOGY ........................................22 3.1 Conceptual Framework for Facility Evaluation Methodology ............................ 22 3.1.1 The Definition of a TwoLane 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 twolane highway operation..... 30 3.1.3.2 Effects of intersections on the downstream twolane 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 reeFlow Speed E stim ation ....................................................... .................... 100 5.1.1 Field M easurem ent of FreeFlow Speed...................................................... 101 5.1.2 Estim eating FreeFlow Speeds .......................... ....... ................................. 102 5.2 Performance Measure on the Unaffected TwoLane Highway Segment ......... 103 5.3 Performance Measure on an Affected TwoLane Highway Segment ................ 105 5.4 Service Measure on a TwoLane 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 TWOLANE 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 31. Traffic sim ulation conditions............................................... .......................... 30 32. Service m measure evaluation ............................................... ............................ 41 33. Summary of programs used at each step .......... .............................. .............. 51 34. Sim ulation m odel evaluation........................................................ .............. 52 41. Normal acceleration rates, distance, and elapsed time ............................................ 65 42. Regression m odel sum m ary.................................................... ........................... 66 43. Variable input values (w ith a leftturn bay)............................................................. 73 44. Variable input values (without a leftturn bay) .............................................. 73 45. Regression model (with a leftturn bay)..... ............... ...... .............. 75 46. Regression model (without a leftturn bay)............... ......... ........ ........... 76 47. Upstream effective length with low traffic volume (ft)........................................... 76 48. Composite headway distribution calculation (volume = 15001740 veh/h)............ 83 49. ChiSquared test calculation ......................................................... .............. 85 410. E entering P percent F ollow ing .......................................................................... .... 88 411. Recommended default values for desired speed by vehicle type............................ 90 412. Regression model for the downstream effective length ....................................... 95 413. Comparison of downstream effective length..................................... ............... 98 51. Adjustment (fLs) for lane width and shoulder width .......................................... 103 52. Adjustment (f) for accesspoint density .............................. ... ........... 103 53. Adjustment factor,fATs, to ATS for a segment downstream of a signal.................. 111 54. Downstream length of roadway affected by passing lane.............. .................... 114 55. Factors for estimation of average travel speed within a passing lane ................... 115 56. Variable input values (TW SC intersection)................................... .............. 122 57. Simulation results on the queue length of the TWSC intersection........................ 123 58. LOS criteria for twolane highway facilities....................................................... 126 61. Input data needs for the facilitywide operational analysis ............ ................ 128 62. Average travel speed for the unaffected twolane segments ............ ............... 152 63. Average travel speed for the affected downstream twolane segments................. 153 64. Average travel speed for the affected passing lane segments ............................... 154 65. Control delays at signalized intersections ...................................... 154 B1. Time headway distribution (traffic flow rate = 900 veh/h 1140 veh/h) ........... 171 B2. ChiSquare test calculation (based on Table B) ............................................... 173 B3. Time headway distribution (traffic flow rate = 1200 veh/h 1440 veh/h) ......... 174 B4. ChiSquare test calculation (based on Table B3) ................................. ........... 176 B5. Time headway distribution (traffic flow rate = 1500 veh/h ~ 1740 veh/h) ......... 177 B6. ChiSquare test calculation (based on Table B5) .............................................. 179 C1. Entering Percent Following with a signalized intersection................................... 192 C2. Entering Percent Following with no signalized intersection ................................. 195 LIST OF FIGURES Figure p 21. Screenshot from TW OPAS road editor .................................................................. 15 22. Screenshot from Traffic Analysis Module of IHSDM ........................ ........... 16 23. Screenshot from TRARR road editor........................... ................ 18 24. Screenshot from CORSIM simulation animation (TRAFVU)............................ 19 31. Typical basic twolane, twoway highway segment......................................... 24 32. Typical twolane, twoway highway with a passing lane....................................... 24 33. Typical twolane, twoway highway with an unsignalized intersection ................. 25 34. Typical twolane, twoway highway with a signalized intersection ..................... 26 35. Effect of a signalized intersection on average travel speed.................................... 32 36. Platoon dispersion, 300 ft from the upstream signalized intersection..................... 35 37. Platoon dispersion, 5280 ft from the upstream signalized intersection................. 35 38. Platoon dispersion, 10560 ft from the upstream signalized intersection ............... 36 39. Segment division of a twolane highway with multiple isolated signalized intersections ....... ..................................... ............... 44 310. Facility segmentation of a twolane highway with multiple isolated signalized intersections ....... ..................................... ............... 45 311. Flow diagram of twolane highway facility operational analysis methodology ..... 50 41. L ength of intersection area ............................................................................... 55 42. Schematic distancetime diagram at a signalized intersection ................................ 58 43 Q u eu e length estim ation ............................................................................ .. .... ...... 59 44. Average travel speed along the twolane highway with signal ............................... 74 45. TW OPAS traffic data input interface................................ ................................ 78 46. Composite time headway distribution.............................................. .................. 84 47. Twolane highway traffic flow downstream of a signalized intersection ............... 87 48. Difference in the average travel speed between with and without signalized intersection along the downstream twolane highway............................................. 93 49. Difference in the average travel speed with traffic volume = 1100 veh/h .............. 94 410. Average travel speed variation with traffic volume = 220 veh ............................ 99 51. Downstream operational effects of a signalized intersection on AT..................... 110 52. Effect of a passing lane on average travel speed................................................ 114 53. Traffic stream s at a TW SC intersection ............................................................ 118 54. Guideline for determining the need for a majorroad leftturn bay at a twoway stop controlled intersection............................... .............. 124 55. Length of TW SC intersection area.................................. ....................... .. ........ 125 61. A twolane highway with an isolated signalized intersection ............................... 131 62. Segmentation for a twolane highway facility............................ 143 63. Traffic flow rates at three intersections ........................................... .............. 144 64. A view of a typical passing lane ..................................................... .......... .. 149 A. 1. Passing percentage for various levels of advancing and opposing traffic volume on tw olane high ays ......... ................................. .......... ........... 168 A2. Average travel speed for various levels of advancing and opposing traffic volume on tw olane high ays ......... ................................. .......... ........... 169 A3. Percent timespentfollowing for various levels of advancing and opposing traffic volume e on tw olane high ays ........................................ ..................... ..... 170 B1. Composite time headway distribution (based on Table Bl)................................ 172 B2. Composite time headway distribution (based on Table B3)............................... 175 B3. Composite time headway distribution (based on Table B5)............................. 178 C1. Twolane highway traffic flow downstream of a signalized intersection............... 181 E1. Difference in the average travel speed with traffic volume E2. Difference in the average travel speed with traffic volume E3. Difference in the average travel speed with traffic volume E4: Difference in the average travel speed with traffic volume E5. Difference in the average travel speed with traffic volume F1. Difference in the average travel speed with traffic volume F2. Difference in the average travel speed with traffic volume F3. Difference in the average travel speed with traffic volume F4. Difference in the average travel speed with traffic volume F5. 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 TWOLANE HIGHWAY FACILITIES By Qingyong Yu May 2006 Chair: Scott. S. Washburn Major Department: Civil and Coastal Engineering Traffic engineers have indicated that a facilitybased evaluation methodology for twolane 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 twolane 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 twolane highways with different segment types at the facility level. The scope of analysis provided in the Highway Capacity Manual (HCM) 2000 for twolane 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 twolane 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 twolane 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 timedelayed) 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 towlane 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 twolane 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 Twolane 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 twolane 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 twolane highways, such as passing lanes, twoway stopcontrolled intersections, driveway turnouts, and twoway leftturn 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 twolane highways, there is ongoing demand for analysis methodologies with which to analyze the operating effectiveness of the entire length of twolane 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 facilitybased evaluation methodology for twolane 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 twolane 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 twolane 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 twolane highway segment. From the viewpoint of travelers or transportation engineers, a facility level analysis on a twolane 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 twolane highways with or without passing lane can be evaluated with the methodology in Chapter 20, "TwoLane Highways". Isolated signalized intersections on twolane highways can be evaluated with the methodology in Chapter 16, "Signalized Intersections". The scope of analysis provided in the HCM 2000 for twolane 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 twolane highways, such as decreasing average travel speed, and increasing percent time spentfollowing. The impact between different segment types is a big issue differentiating the facilitylevel analysis from the segmentlevel 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 reacceleration 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 doublecounting the decelerationacceleration 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 twolane 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 (twoway stopcontrolled 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 twolane highway facility, which might include occasional signalized intersections, unsignalized intersection, and other control or roadway treatments. This twolane 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 twolane highway segments are the following: * Basic segmentthis is a segment that consists of a simple twolane cross section, either level or rolling terrain * Basic segments with a continuous specific up or down grade * Threelane cross section segments, with the additional lane being a passing lane * Threelane cross section segments, with the additional lane being a center leftturn lane * Threelane cross section segments, with the additional lane being a rightturn 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 twolane highway with isolated signalized/unsignalized 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 twolane segments and signalized intersections, along with previous research on the effects of signalized intersections on a twolane highway. Task 2: Define the basic conceptual framework, from a segmentation and service measure perspective, for combining twolane highway segments with intersections into a facilitywide operational analysis. Task 3: Investigate traffic operations at the boundary of a twolane 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 TRANSYT7F 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 timespent following. Task 5: Investigate traffic operations at the boundary of a twolane segment and a twoway stopcontrolled intersection (without sharing leftturn lanes), and develop a method that can be used to determine the effective length of the twoway stopcontrolled intersection on through traffic on the major street and rightturn traffic from the major street behind it. Task 6: Join the components (basic twolane segment, upstream signal influence area, signal delay, and downstream signal influence area) into an integrated methodology for the operational analysis of a twolane highway facility. This methodology will be predicated upon the use of an aggregated percenttimedelayed 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 (twolane 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 twolane 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 facilitylevel 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 twolane 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 twolane 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 twolane highway facility. Chapter 3 presents the conceptual framework of the operational analysis procedure for a twolane highway facility, and puts forward the methodology of operational analysis for the twolane highway facilities. The first two steps of the selection of facilitywide 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 freeflow speed, and average travel speed on three kinds of twolane 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 twolane 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 twolane highway facility. Finally previous research on effects of signalized intersections on a twolane 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 twolane 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 TwoLane Highways The Highway Capacity Manual (HCM) published by the Transportation Research Board (TRB) presents the widely accepted standards for analysis of twolane highway capacity and quality of service. In the 1950 HCM, the first version of HCM, the procedure for analysis of twolane highway capacity developed by O. K. Norman was presented. The capacity of a twolane 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 qualityofservice analysis procedure of a twolane highway and their related service measures were revised. In the 1965 HCM, the capacity of a twolane 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 volumetocapacity ratio. A great improvement in analysis of twolane highway capacity and quality of service was achieved in the 1985 HCM. The capacity of a twolane 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 twolane 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 twolane 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 timespentfollowing 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 twolane 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 twolane 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 twoway stopcontrolled (TWSC), allway 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 throughtraffic 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 twolane 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 TimeSpentFollowing (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 TimeDelayed Percent timedelayed 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 freeflow 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 twolane and multilane uninterrupted flow highways [4]. HIGHPLAN maintains fidelity to the HCM 2000 twolane 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 facilitylevel 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 twolane highway operations. 2.2.1 TWOPAS Software TWOPAS (TWOlane PASsing) rural highway simulation software is used for modeling traffic conditions on twolane twoway roadways. This software was used extensively in developing the twolane analysis methodology in the HCM 2000. TWOPAS was first developed in the 1970s by MidWest 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 CaliforniaBerkeley. UCBRURAL provides a menudriven interactive graphical interface with comprehensive input checking, carefully selected default values, and userselected output options including graphic depictions of traffic performance, which is more convenient for users to run TWOPAS model. Figure 21 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 qualityofservice measures for an existing or proposed design. The TAM facilitates use of TWOPAS by feeding it the roadway geometry data stored by IHSDM. Figure 22 shows a view of TAM input interface in IHSDM. I *,, II Figure 21. Screenshot from TWOPAS road editor As a microscopic, stochastically based model, TWOPAS simulates traffic operations on a twolane highway by reviewing the position, speed, and acceleration of each individual vehicle along the roadway at 1second 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 nopassing zones, and reduced speed zones. * Driver Characteristics and preferences including desired speeds, preferred acceleration levels, limitations on sustained use of maximum power, passing and passabort decisions, and realistic behavior in passing and climbing lanes. * Entering Traffic streams generated in response to userspecified flow rate, vehicle mix, immediate upstream alignment, and the percent of traffic platooned. * Driver speed choices in unimpeded traffic based on userspecified distribution of desired speeds; in the impeded traffic based on a carfollowing 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 22. Screenshot from Traffic Analysis Module of IHSDM TWOPAS has the capability to simulate both conventional twolane highways and twolane 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 twolane 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 23 shows an interface of the TRARR road editor. TRARR is designed for twolane 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 23. 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, "stateofthepractice" 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 24 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 * Vehicletypespecific turn percentages * Support Larger Networks * Path Following Capacity Figure 24. 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 twolane highway using the opposing lane. 2.3 Effect of Upstream Signal on TwoLane 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 twolane highway segment in terms of percent timespentfollowing. In their research, the effect of an upstream signalized intersection on the twolane 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 twolane 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 twolane 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 twolane highway directional analysis procedures and deterministic adjustment factors. Step 4: Estimate the level of service based on the criteria suggested in the HCM 2000 twolane highway analysis procedure. CHAPTER 3 CONCEPTUAL OVERVIEW OF TWOLANE 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 twolane highway segments and signalized intersections. This chapter begins with a discussion of the conceptual framework of the operational analysis procedure for a twolane highway facility. It then puts forward a methodology of operational analysis for twolane 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 twolane highway facility, a twolane 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 twolane highway facility, segment types, the features of operational analysis at the facility level, and the proposed methodologies. 3.1.1 The Definition of a TwoLane 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 subsegment is a further division of a segment. Whereas segments are delineated by points (e.g., intersections) or changes in geometric conditions, subsegments for the purpose of discussion in this document are delineated only by changing operational conditions. For example, an isolated signalized intersection on a twolane highway produces operational effects on the upstream segment. The upstream twolane highway segment can be divided into the upstream subsegment within the effective length of the signalized intersection, and the upstream subsegment beyond the effective length of the signalized intersection. Although both subsegments have homogenous geometric conditions, their operational features are different. One subsegment is affected by the downstream signal; the other is not affected. The potential segment types on a twolane highway could include the following: * Basic segment, this is a segment that consists only of a twolane across section. Figure 31 shows a typical view of this type of segment. * Basic segment with continuous specific upgrade or downgrade * Threelane cross section segment, with the additional lane being a passing lane. Figure 32 shows a typical view of this type of segment. * Segment with an unsignalized intersection. Figure 33 shows a typical view of this type of segment. * Threelane cross section segment, with the additional lane being a center leftturn lane or a rightturn lane * Segment terminating into a multilane highway * Segment with an isolated signalized intersection Figure 31. Typical basic twolane, twoway highway segment Figure 32. Typical twolane, twoway highway with a passing lane A twolane highway with signalized intersections is a type of facility composed of isolated signalized intersections, and the basic twolane highway. A twolane 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 33. Typical twolane, twoway highway with an unsignalized intersection Figure 34 shows a typical view of a twolane 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 34. Typical twolane, twoway 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 facilitylevel 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 timespentfollowing is used as the service measure to evaluate the level of service on the basic twolane 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 twolane 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 facilitywide 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 twolane highway with multiple signals, the combination of average travel speed and percent timespentfollowing is used as the service measure to evaluate the level of service on an uninterrupted flow twolane 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 31 gives an example method of aggregating the LOS grades of segments and points weighted by the segment length. SLOS,L, LOS = (31) 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 facilitywide 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 twolane highway segments and signalized intersections. For the twolane methodology (HCM Chapter 20), the method for calculation of average travel speed (ATS) is utilized; however, percent time spentfollowing (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 twolane 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 twolane highway can produce effects on traffic operations of the upstream and downstream twolane highway segment. To illustrate the potential effects of an isolated signalized intersection on the two lane highway operation, CORSIM and TRANSYT7F programs are used to simulate the operations of a twolane highway with an isolated signalized intersection. 3.1.3.1 Effects of intersections on the upstream twolane 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 31. 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 twolane highway based on average travel speed are shown in Figure 35. This figure is directly derived from preliminary simulation runs. Figure 35 shows a comparison of the modeled average speed as it varies along a twolane highway with an isolated signalized intersection and with no isolated signalized intersection under different traffic flow levels. As seen in Figure 35, on the twolane highway segment upstream of the signalized intersection, when vehicles enter the basic twolane highway segment, the difference in the values of average travel speed is very small. The average travel speeds along the twolane 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 twolane highway significantly affects traffic operations on the upstream twolane 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 35. 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 twolane highway operation After passing through the signalized intersection, the vehicle platoon will go into the downstream twolane highway. The platoon dispersion pattern is affected not only by the upstream signalized intersection, but also by the rightturn vehicles and leftturn vehicles from minor streets. There are three movements that contribute to the flow profile, as follows: * through movement from the major street * rightturn movement from the minor street * leftturn movement from another minor street The startandstop operation of signals on the twolane highways tends to create platoons of vehicles that travel along a twolane highway link. Here TRANSYT7F is used to model the dispersion of these platoons as they progress along the downstream twolane highway segment. In TRANSYT7F, 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, )] (32) 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 (33) Where: a : platoon dispersion factor (PDF) Equation 33 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 sitespecific factors such as grades, opposing flow interference and other sources of impedance. The diagrams below illustrate the nature of platoon dispersion on the downstream twolane 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 36) 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 onefull mile, or 5280 feet. Notice that after a fullmile, 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 36. Platoon dispersion, 300 ft from the upstream signalized intersection 2 C Figure 37. Platoon dispersion, 5280 ft from the upstream signalized intersection 6. Cycle Length (Sec) Figure 38. Platoon dispersion, 10560 ft from the upstream signalized intersection The same phenomenon can be observed from the third diagram (Figure 38), 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 twolane highway operations, it is necessary to investigate the effects further when performing an operational performance assessment of twolane highway facilities. To quantify the effect of a signalized intersection on the downstream twolane 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 twolane 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 twolane highway with isolated intersections. Next the section presents an overview of the operational analysis procedures for a twolane 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 twolane 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 spaceaverage 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 twolane highways is that it is not as sensitive as PTSF to the relative balance between passing demand and passing supply. * Percent TimeSpentFollowing (PTSF) Given the platooned nature of traffic on the twolane highway, PTSF represents freedom to maneuver and the comfort and convenience of travel on a twolane highway. However, some researchers [5] think this measure is not appropriate for application to developed, touristoriented 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 spaceaveraged 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 twolane highway segments, but a poor one for the signalized intersection by itself. So ATS, PTSF, or their combination is not a good facilitywide service measure for the facility consisting of twolane 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 twolane 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 timebased 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 twolane 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 freeflow 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 twolane highway, density is much less evenly distributed on a twolane highway than on a freeway or multilane highway [11]. Density is not a good service measure for the twolane highway facility. Percent timespentfollowing does a much better job of representing density; percent timespentfollowing is the percentage of the total travel time that drivers spend traveling in local highdensity 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 twolane highway segments. * Percent TimeDelayed Percent timedelayed 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 interruptedflow 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 delayrelated performance measures, percent timedelayed 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 32. Service measure evaluation Undeveloped Developed Facility incorporating uninterrupted uninterrupted twolane highway twolane twolane Intersection and signalized segments segments influence area intersection Volume/Capacity Ratio F F F F Average Travel Speed G G P P Percent TimeSpentFollowing E F P P PTSF and ATS E E P P Travel Time G G P P Percent FreeFlowSpeed G E P P Density F F F F Control Delay P P E P Percent TimeDelayed G G G G Note: E = excellent, G = good, F = Fair, P = poor Table 32 summarizes the evaluation of potential service measures for a twolane highway with signalized intersections. Based on a review of the advantages and disadvantages of candidate service measures discussed above, it is concluded that percent timedelayed is an appropriate selection as the single service measure for the interrupted flow facility of a twolane highway with signalized intersections. Percent timedelayed 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 twolane 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, nopassing 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 twolane highway with signalized intersections, the signalized intersection is not regarded as a single point, but as a segment with a certain length. Figure 310 shows the division of a twolane highway with multiple isolated signalized intersections. The whole facility is divided into three types of segments, described as follows: * Type 1: the basic twolane 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 twolane 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 39. Segment division of a twolane highway with multiple isolated signalized intersections 0 Q 0 0 Figure 310. Facility segmentation of a twolane highway with multiple isolated signalized intersections 0 Type 1: Basic Twolane 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 twolane highway with signalized intersections using this methodology is provided here. Percent timedelayed is applied as the common service measure for the whole facility composed of twolane 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 freeflow speed. The freeflow speed is used to determine the average travel speed and delay time at each segment. The basic freeflow speed for the twolane 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 freeflow speed on the twolane highway is midblock and as far as possible from the nearest signalized or stopcontrolled intersection. If field observation of freeflow speed is not practical, freeflow speed on the twolane 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 twolane highway sections, and not affected by the signalized intersection, the average travel speed can be calculated using the twolane highway procedure presented in Chapter 20 of HCM 2000. The length of the conventional twolane 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 throughtraffic 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 twolane highway segments and control delay within the signalized intersection are determined, the delay time on the twolane highway segments and the signalized intersection can be calculated using the following equations. Delay time on the twolane highway segment: LH LH DH = H H (34) H FFS Where: DH : delay on the twolane highway segment, s/veh LH : length of twolane highway segment, ft FFS: free flow speed for the twolane highway segment, ft/s SH : average travel speed for twolane highway segment, ft/s Control delay at the signalized intersection: Ds = d,(PF)+ d2 +d3 (35) 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 timedelayed is then computed through dividing total delay time on the entire facility by the total travel time at the freeflow speed on the entire facility. Equation 36 shows the aggregation of point and segment results to obtain an estimate of percent timedelayed for the entire facility. After the facilitywide performance measure, percent timedelayed 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 311 illustrates the analysis procedure for determining LOS on the twolane highway with signalized intersections. 49 Z(D + D,) PTD = H'S LH Ls H,S FFSH FFSs (36) L = LH +Ls H,S Where: PTD: percent timedelayed per vehicle for the entire facility, % DH: delay time per vehicle for the twolane highway segment, s/veh Ds: delay time per vehicle for the signalized intersection influence area, s/veh FFSH: free flow speed for the twolane 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 twolane 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 FreeFlow Speed (FFS)  Determine freeflow speed Type 2: Signalized or Unsignalized Intersection Influence Area ermine effective Compute of the intersection control delay influence area Determine Percent timedelayed  By segment  Over entire facility Determine LOS over entire facility Figure 311.Flow diagram of twolane 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 33. 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 freeflow speed. The methods presented in the HCM 2000 are used field measurement, or estimating freeflow speed. (Chapter 20, Page 204, 205) 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 linearlydecreasing 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 twolane highway segments. The analysis methods presented in Chapter 20 of the HCM 2000 are used to calculate the average travel speed on basic twolane 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 TwoWay StopControlled 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 34 and 35. Step 8: Determine the percent timedelayed and LOS of the entire facility. The percent timedelayed is calculated using Equation 36. LOS is determined from Table 58 (Chapter 5). In this methodology, three simulation programs are selected to simulate traffic operations on the twolane highway in the vicinity of an intersection. The reasons why they were selected are presented in Table 34. Table 34. 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 twolane roadway and includes detailed modeling of traffic signal operations. In addition, the CORSIM simulation model simulates the traffic system on a vehiclebyvehicle 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 oncoming 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 twolane roadway in the vicinity of a traffic signal, and determine the effective length of the signal influence area on the upstream twolane highway segment. TWOPAS is the only simulation program that is able to simulate the passing maneuver operation on the twolane 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 twolane 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 twolane highway, the signalized intersection influence area, and the affected downstream twolane 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 twolane 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 freeflow 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 41 shows an example of how to determine the intersection length in the twolane highway facility with signalized intersections. In this example, a twolane highway with a signalized intersection extends 10 miles, and the isolated intersection is located at the 6mile point. The first 5.75 miles would be regarded as a twolane 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 twolane 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 componentbased perspective. Twolane Highway Segment Intersection Twolane Highway Segment 5.75 M 0.25 3 3.75 _ Figure 41. 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 distancetime diagram shown in Figure 42 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 42 shows the main delay terms at a signalized intersection, and components of the signal influence area. Before Point 1 on the timedistance 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 42, the deceleration distance LD is given by LD = L2 L1 (41) Similarly, the stopping distance Ls is given by Ls = L, L, (42) Similarly, the acceleration distance LA is given by LA = L4 L3 (43) 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 43 illustrates several kinds of conditions for which vehicles pass through a signalized intersection. Figure 43(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 43(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 43(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 + (44) 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 42. Schematic distancetime 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 43. Queue length estimation 4.1.2.1 Determining stopping sight distance The stopping sight distance can be calculated using Equation 45, as follows: SSD = Vt + V 2g a)+G (45) Where: SSD: Stopping Sight Distance, ft Vi: initial vehicle speed, ft/s tr: perceptionreaction 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 perceptionreaction time is taken as 2.5 seconds and a deceleration rate of 11.2 ft/s2 (3.4 m/s2) is assumed. Perceptionreaction time and initial vehicle speed are two important elements in calculating the stopping sight distance. The perceptionreaction 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 perceptionreaction 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. Perceptionreaction 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. Perceptionreaction 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 perceptionreaction time, vehicles still keep the initial speed; at the ending part of perceptionreaction times, drivers begin taking actions to decelerate the vehicles. The AASHTO Green Book [2] suggests a perceptionreaction 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 perceptionreaction 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 perceptionreaction 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 backofqueue 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 46: Q = Q1 + Q2 (46) Where: Q: maximum distance in vehicles over which queue extends from stop line on average signal cycle, veh Q1: firstterm queued vehicles, veh, and Q2 : secondterm 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 47. V, C Q, =PF2 600 (47) 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 48. PF2 (48) 1 1RP 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 49. T 8kX 16k, Q2 = 0.25c, (X 1)+ (X1)2 + L L (49) cLT (cT)2 Where: CL: lane group capacity per lane, veh/lane T: length of analysis period, h kB: secondterm 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 410: 07 kB = 0.12I s3Lg (pretimed signals) \3600) (410) S 06 kB = 0.10I 3600 (actuated signals) \3600) Where: kB: secondterm 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 linearlydecreasing acceleration model. Continuing research [12] has shown that the linearlydecreasing acceleration model better represents both maximum vehicle acceleration capacities as well as actual motorist behavior. The linearlydecreasing acceleration model can be rewritten as a differential equation and integrated to derive the following relationships (treating a grade as being constant), as Equation 411 through 414. 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 (411) at (a Gg) aGg t (412) v= vo ev (412) P I I ) P 8d + v v, t = (413) a_ Gg (a Gg) t(aGg (1 et) (414) d= t voJ (414) 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 linearlydecreasing 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 41 summarizes acceleration rates, distances traveled, and elapsed time for passenger vehicles on level terrain and under normal operating conditions. Table 41. 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 (415) 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 Rsquared value of 0.895. The regression model summary is presented in Table 42. Table 42. 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 Pvalue Intercept 114.408 8.80784 12.9893 5.94E18 X Variable 1 0.105078 0.00495 21.23094 2.79E27 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 leftturn bay, the directional distribution of traffic flow, and the percentage of leftturn 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 twolane 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 PeakHour Factor (PHF), the proportion of trucks and recreational vehicles in the traffic stream, and the directional split (Dfactor). 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 heavyvehicle adjustment factor, and the grade adjustment factor. The conversion can be made using Equation 416 [1]: V Vp = v (416) PHF x f, x fH, Where: vp: passengercar equivalent flow rate for peak 15min period, pc/h V: demand volume for the full peak hour, veh/h PHF: peakhour factor fG: grade adjustment factor fHV: heavyvehicle adjustment factor Traffic data also include the proportions of through vehicles, leftturn vehicles and rightturn vehicle in the traffic stream. The leftturning vehicles may have a negative effect on the flow of the through movements, particularly when higher percentage of leftturning 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 twolane 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 twolane highway because passing opportunities are reduced and eventually eliminated as the opposing traffic volume increases. At an intersection, leftturn vehicles execute their turning maneuvers through the gaps of the opposing through traffic stream. When the opposing through traffic volume is high, leftturn vehicles have less opportunity to execute their turning movements. * Geometric Data Geometric data include the twolane highway geometry and intersection geometry. The basic geometric conditions of the twolane highway and intersection are used to determine the effective length. The existence of exclusive leftor rightturn 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., pretimed, semiactuated, and fullyactuated), the phase plan, cycle length, green time, and clearance intervals. In this study, the simplest and most widely used form of signalization, the twophase pretimed signal, is used. All leftturn and rightturn 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 * Dfactor * percentage of leftturn and rightturn movements * cycle length * ratio of effective green time to cycle length * availability of a leftturn 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 twolane 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 twolane roadway and includes detailed modeling of traffic signal operations. However, CORSIM cannot simulate passing maneuvers using the oncoming lane of traffic. Before making a decision, TWOPAS was used to simulate the traffic operations on the basic twolane 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 twolane 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 twolane 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% nopassing 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 twolane roadway in the vicinity of a traffic signal, and determine the effective length of the signal influence area on the upstream twolane highway segment. In addition, the CORSIM simulation model typically simulates the traffic system on a vehiclebyvehicle 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 twoway, twolane roadway network with an isolated fixedtime signalized intersection was simulated using CORSIM. It extended 3 miles, and the isolated intersection was located at the 1mile point. The attributes of the simulated network were set to fulfill the basic conditions for a twolane 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 pretimed signal Two sets of CORSIM base road network were developed. One is the signalized intersection with a 250foot leftturn bay; the other is the signalized intersection without a leftturn 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 43 and Table 44. The different inputs resulted in a combination of 243 (3x3x3x3x 3=243) simulation scenarios for the base network without a leftturn bay. Ten simulation runs were made for each scenario to account for the variability in stochastic microsimulation program output. A total of 2430 simulated runs were performed. The length of simulation time for each run was 15 minutes. Table 43. Variable input values (with a leftturn bay) Peak Volume Cycle length Percentage of leftturn (pc/h) (sec) g/C and rightturn vehicles 400 60 0.55 5% 800 75 0.65 10% 1200 90 0.75 15% Table 44. Variable input values (without a leftturn bay) Peak Volume Cycle length Percentage of leftturn (pc/h) DFactor (sec) g/C and rightturn 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, leftturn vehicles execute their turning maneuvers through the gaps of the opposing through traffic stream. When the opposing through traffic volume is lower, the leftturn vehicles can execute their turning movements. When the opposing through traffic volume is very high and leftturn vehicles cannot execute their turning movements, the leftturn vehicles can stay temporarily at the leftturn bay, and will not block the advancing through traffic behind them. So when developing the effective length model for the signalized intersection with a leftturn bay, the Dfactor 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 44 illustrates the variations of average travel speed along the twolane 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 twolane 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 44. 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 STwolane Highway With Signal I Twolane Highway Without Signal Intersection 0 5 10 15 20 25 30 Position Along Roadway (1/40 mi) Figure 44. Average travel speed along the twolane highway with signal The regression model for the upstream effective length of a signalized intersection with a leftturn 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 leftturn vehicles in the directional traffic flow The statistical results for the effective length model for the signalized intersection with the leftturn bay (250 ft) are presented in Table 45. 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 tDistribution Table is to.05 = 1.708. All the tstat absolute values are greater than 1.711, so all the variables used in the chosen model are useful. Table 45. Regression model (with a leftturn bay) R2 = 0.95743; Adj R2 = 0.95519 Coefficient tstat 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 leftturn 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 (418) +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 leftturn vehicles in the directional traffic flow The statistical results for the effective length model for the signalized intersection without a leftturn bay are presented in Table 46. 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 tDistribution Table is to.05 = 1.711. All the tstat absolute values are greater than the value of 1.711, so all the variables used in the chosen model are useful. Table 46. Regression model (without a leftturn bay) R2 = 0.77764; Adj R2 = 0.77199 Coefficient tstat 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 47 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 47. 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 twolane highway. The platoon dispersion pattern is affected not only by the upstream signalized intersection, but also by the rightturn 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 twolane 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 twolane 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 twolane highway. The TWOPAS model is used to simulate the effects of a signalized intersection on the downstream twolane 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 45 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 twolane highway operation, the key point is how to accurately decide the EPF at the point immediately downstream of a signalized intersection. Figure 45. 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 twolane 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 419: t % Platooned = 100(1 e 3600) (419) Where: q: hourly flow rate of traffic entering the twolane 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 twolane 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 420: f (t = Ae a) (420) Where: f(t): probability density function, a : userselected 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 (421) ta The percentage of vehicles in platoon with the shifted negative exponential distribution can be calculated using Equation 422: %platoon = 1 P(h > t) =1 [e ^(t ]dt (422) = e (ta)/(ta) 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 freemoving vehicles. According to May [15], the random headway state (Negative exponential distribution) is best suited for very low flow conditions, while the nearlyconstant 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 constantheadway 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 carfollowing or platoon mode and a shifted negative exponential distribution for those freemoving 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 423. %Platooned = 1 P(h > t) 1rPp 1 + P t 2 (423) =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 48. The theoretical shifted negative exponential headway distribution, normal headway distribution, composite headway distribution, and the measured time headway distribution are presented graphically in Figure 46. The ChiSquared 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 ChiSquared test calculations are shown in Table 49. The individual ChiSquared contributions are summed, and the calculated ChiSquared 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 ChiSquared value is determined to be 18.30. Since the calculated Chi Squared value is less than the reference ChiSquared 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 nearlyconstant 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 48. Composite headway distribution calculation (volume = 15001740 veh/h) composite Vehides Not in Platoons Platoon Vehides Distribution t aM a L EM 100% P z P(t 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 46. Composite time headway distribution Table 49. ChiSquared test calculation Time (f0 f) Headway fo f fof (fo )2 / Group 0.0 0.5 22 19 3 10 0.4934 0.5 1.0 140 122 18 310 2.5355 1.01.5 312 307 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 3.03.5 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 5.05.5 13 18 5 27 1.4748 5.5 6.0 7 13 7 43 3.2939 6.06.5 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 8.59.0 2 2 0 0 9.09.5 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 twolane 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 47. The "A" denotes a location immediately downstream of the signalized intersection. As shown in Figure 47, 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 rightturn movements from the minor street; and * Movement 3: Secondary contributing movement. They are leftturn movements from the minor street. As shown in the Figure 47, the total cyclelength 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 rightturn 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 424: VF, EPF, = VP (424) 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 47. Twolane 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 TwoLane 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 cyclebycycle 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 