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Estimating Freeway Travel Time as a Function of Demand Using Simulation

Permanent Link: http://ufdc.ufl.edu/UFE0022782/00001

Material Information

Title: Estimating Freeway Travel Time as a Function of Demand Using Simulation
Physical Description: 1 online resource (137 p.)
Language: english
Creator: Yennamanni, Ramakrishna
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: demand, simulation, travel, volume
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This study tries to model the freeway travel time. Specifically, this study contributes to the literature by developing models that are easy to use, make accurate predictions, and represent field conditions better. Moreover, the models developed in this study are applicable to all the freeway segment types and thus are more versatile that the existing models, which does not distinguish the different types of freeway segments. The models developed as part of this thesis can be quickly applied to study freeway corridors under several situations, which include freeway construction work-zones, traffic incidents, and lane drops. These models can be used to estimate freeway travel time easily, quickly compared to a full-scale simulation of the corridor.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Ramakrishna Yennamanni.
Thesis: Thesis (M.S.)--University of Florida, 2008.
Local: Adviser: Elefteriadou, Ageliki L.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022782:00001

Permanent Link: http://ufdc.ufl.edu/UFE0022782/00001

Material Information

Title: Estimating Freeway Travel Time as a Function of Demand Using Simulation
Physical Description: 1 online resource (137 p.)
Language: english
Creator: Yennamanni, Ramakrishna
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: demand, simulation, travel, volume
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This study tries to model the freeway travel time. Specifically, this study contributes to the literature by developing models that are easy to use, make accurate predictions, and represent field conditions better. Moreover, the models developed in this study are applicable to all the freeway segment types and thus are more versatile that the existing models, which does not distinguish the different types of freeway segments. The models developed as part of this thesis can be quickly applied to study freeway corridors under several situations, which include freeway construction work-zones, traffic incidents, and lane drops. These models can be used to estimate freeway travel time easily, quickly compared to a full-scale simulation of the corridor.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Ramakrishna Yennamanni.
Thesis: Thesis (M.S.)--University of Florida, 2008.
Local: Adviser: Elefteriadou, Ageliki L.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022782:00001


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1 ESTIMATING FREEWAY TRAVEL TIME AS A FUNCTION OF DEMAND USING SIMULATION By RAMAKRISHNA YENNAMANI A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2008

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2 2008 Ramakrishna Yennamani

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3 To my parents

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4 ACKNOWLEDGMENTS I thank the University o f Florida and the Depa rtment of Civil and Co astal Engineering for giving me the opportunity to participate in a Tr ansportation Project and produce unique research. I thank my committee, comprising of Dr. Lily Elefteriadou, Associate Professor, Committee Chair, and primary advisor; Dr. Siva Sriniv asan, Assistant Professo r; and Dr. Yafeng Yin, Assistant Professor. I thank them for the advice, guidance, and feedback throughout the research and writing of the report. I tha nk the group of masters and doctoral candidat es that provided me with the technical support and gu idance when needed. Finally, I thank my friends and family for encouragement throughout this endeavor.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ............................................................................................................... 4LIST OF TABLES ...........................................................................................................................7LIST OF FIGURES .........................................................................................................................8LIST OF ABBREVIATIONS ........................................................................................................ 14ABSTRACT ...................................................................................................................... .............15 CHAP TER 1 INTRODUCTION .................................................................................................................. 171.1 Background ...................................................................................................................171.2 Objectives and Scope ....................................................................................................181.3 Organization ..................................................................................................................182 LITERATURE REVIEW .......................................................................................................192.1 Travel Time Models fo r Planning Applications ........................................................... 192.2 Travel Time Estimation for Real-Time Applications ................................................... 232.3 Travel Time Data Collection Techniques ..................................................................... 242.4 Variables for Scenario Development ............................................................................ 252.5 Summary and Conclusions ............................................................................................273 METHODOLOGY ................................................................................................................. 293.1 Simulation Model Selection ..........................................................................................293.2 Development and Simulation of S cenarios for Variable Selection ...............................303.3 Scenarios for Database Development ........................................................................... 313.4 Development of Analytical T.T. Models ...................................................................... 313.5 Comparison of Analytical Models to Simulator ........................................................... 314 SIMULATION OF SCENARIOS ..........................................................................................344.1 Identification of Variables and Their Range of Values ................................................ 344.2 Development of Scenarios ............................................................................................ 354.2.1 Basic Freeway Segment .................................................................................... 354.2.2 Merge Segment .................................................................................................434.2.3 Diverge Segment ...............................................................................................514.2.4 Weaving segment .............................................................................................. 60

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6 5 ANALYTICAL MODELS ................................................................................................... 1085.1 Model Structure ...........................................................................................................1085.1.1 Models for Uncongested Conditions ............................................................... 1095.1.2 Models for Congested Conditions ...................................................................1105.1.3 Application ...................................................................................................... 1115.2. Travel Time Models for BFS ...................................................................................... 1125.3 Travel Time Models for Merge Segment .................................................................... 1155.4 Travel Time Models for Diverge Segment ................................................................. 1175.5 Travel Time Models for Weaving Segment ................................................................ 1195.6 Travel Time Models for Bottleneck ............................................................................ 1206 COMPARISION with Other ANalytical Models .................................................................1297 CONCLUSIONS & RECOMMENDATIONS ..................................................................... 1317.1 Summary .................................................................................................................. ...1317.2 Conclusions .................................................................................................................1317.3 Model Applications .....................................................................................................1327.4 Further Research .........................................................................................................133REFERENCES .................................................................................................................... ........134BIOGRAPHICAL SKETCH .......................................................................................................137

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7 LIST OF TABLES Table page 4-1 Range of values for each variable that m ay affect T.T. along basic freeway segments .... 714-2 Range of values for each variable th at may affect T.T. along merge segment .................. 714-3 Range of values for each variable th at may affect T.T. along diverge segment ................ 714-4 Range of values for each variable in weaving segment ..................................................... 714-5 Input values simulated for basic freeway segments ...........................................................724-6 Impact of study vari ables on T.T. of BFS .......................................................................... 724-7 Input values simulated for a merge segment ...................................................................... 724-8 Impact of study variable s on T.T. of merge segment ........................................................ 734-9 Input values simulated for a diverge segment .................................................................... 734-10 Impact of study variables on T.T. of diverge segment ...................................................... 734-11 Variable values for weaving segment ................................................................................ 744-12 Impact of study variables on T.T. of weaving segment ..................................................... 745-1 BFS uncongested model statistics .................................................................................... 1225-2 BFS congested T.T. range model summary ..................................................................... 1225-3 Merge uncongested model summary ............................................................................... 1225-4 Merge congested T.T. range model statistics and estimates ............................................ 1225-5 Diverge uncongested model summary ............................................................................. 1235-6 Diverge congested T.T. range model summary ............................................................... 1235-7 Weaving segment uncongested model summary ............................................................. 1235-8 Weaving segment congested T.T. range model summary ............................................... 1245-9 Bottleneck T.T. model summary ..................................................................................... 124

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8 LIST OF FIGURES Figure page 2-1 Comparison of BPR, MTC, Akcelik and 1994 HCM T.T. functions for q/c<1.5 (source: Rupinder Singh, 1999) ......................................................................................... 282-2 Comparison of BPR, MTC, Akcelik and 1994 HCM T.T. functions for q/c <2 (source: Rupinder Singh, 1999) ......................................................................................... 283-1 Methodology flow chart .....................................................................................................334-1 Picture of a basic freeway segment. ................................................................................... 744-2 Variation of TT per mile with demand (lanes = 2, FFS = 50 mph, length of basic freeway segment = 5000 ft, and downs tream capacity = 1515 veh/hr/lane) ..................... 754-3 Variation of TT per mile with demand for various values of downstream capacity (lanes = 2, length of basic freeway segment = 5000 ft and FFS is 55 mph) ...................... 754-4 Variation of TT per mile with demand for different values of speed (Lanes = 2, length of basic freeway Segment = 5000 ft, and downstream capacity = 2250 veh/hr/lane) .................................................................................................................. ......764-5 Variation of TT per mile with different values of speed (lanes = 2, length of basic freeway segment = 5000 ft and downs tream capacity = 1324 veh/hr/lane) ...................... 764-6 Variation of TT per mile with different values of speed (lanes = 2, length of basic freeway segment = 5000 ft and downstream capacity = 849 veh/hr/lane) ........................ 774-7 Variation of TT per mile with demand fo r different lengths of the BFS (lanes = 2, length of basic freeway segment = 5000 ft and downstream capacity = 2250 veh/hr/lane) .................................................................................................................. ......774-8 Variation of TT per mile with demand fo r different lengths of the BFS (lanes = 2, FFS = 55 mph, and downstream cap acity = 1324 veh/hr/lane) ......................................... 784-9 Variation of TT per mile with demand for various lengths of the BFS (lanes = 2, FFS = 55 mph, and downstream capacity = 849 veh/hr/lane) ................................................... 784-10 Variation of TT per mile with demand for various values of number of lanes of the BFS (FFS = 55 mph, length of basic freew ay segment = 5000 ft and downstream capacity = 2250 veh/hr/lane) ..............................................................................................794-11 Variation of TT per mile with demand for various values of number of lanes of the BFS (FFS = 55 mph, length of basic freew ay segment = 5000 ft and downstream capacity = 850 veh/hr/ane) .................................................................................................79

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9 4-12 Variation of TT per mile with demand for the downstream segment with (number of lanes = 2, FFS = 55 mph) ................................................................................................... 804-13 Variation of TT per mile with demand for the downstream segment with (number of lanes = 2, FFS = 55 mph) ................................................................................................... 804-14 Time series plot between TT per mile of the downstream bottleneck and the number of vehicles in the downstream bottleneck .......................................................................... 814-15 Time series plot between TT per mile of the upstream segment and the number of vehicles in the upstream segment ...................................................................................... 814-16 Sketch of a merge freeway segment. ................................................................................. 824-17 Variation of TT per mile with demand (lanes = 2, FFS = 50 mph, length of entry section = 500 ft, ramp demand = 100 ve h/hr/ln, and downstream capacity = 1689 veh/hr/lane) .................................................................................................................. ......824-18 Variation of TT per mile with demand (lanes = 2, FFS = 50 mph, length of entry section = 500 ft, and ramp demand = 100 veh/hr/ln) ......................................................... 834-19 Variation of TT per mile with demand fo r different values of speed (lanes = 2, FFS = 50 mph, length of entry section = 500 ft and ramp demand = 100 veh/hr/ln, and downstream capacity = 2400 veh/hr/lane) ......................................................................... 834-20 Variation of TT per mile with demand fo r different values of speed (lanes = 2, FFS = 50 mph, length of entry section = 500 ft and ramp demand = 100 veh/hr/ln, and downstream capacity = 1689 veh/hr/lane) ......................................................................... 844-21 Variation of TT per mile with demand fo r different values of speed (lanes = 2, FFS = 50 mph, length of entry section = 500 ft and ramp demand = 100 veh/hr/ln, and downstream capacity = 1324 veh/hr/ln) ............................................................................. 844-22 Variation of TT per mile with demand for different values of ramp demand (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 2491 veh/hr/ln) ...................................................................................................................854-23 Variation of TT per mile with demand for different values of ramp demand (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 1689 veh/hr/lane) ...............................................................................................................854-24 Variation of TT per mile with demand for different values of ramp demand (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 1324 veh/hr/lane) ...............................................................................................................864-25 Variation of TT per mile with demand for different values of # lanes (length of entry section = 500 ft, and FFS = 50 mi/hr, ra mp demand = 100 veh/hr/ln, and downstream capacity = 2400 veh/hr/lane) ..............................................................................................86

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10 4-26 Variation of TT per mile with demand for different values of # lanes (length of entry section = 500 ft, and FFS = 50 m i/hr, ra mp demand = 100 veh/hr/ln, and downstream capacity = 1685 veh/hr/lane) ..............................................................................................874-27 Variation of TT per mile with demand for different values of length of entry section (# Lanes = 2, FFS = 50 mi/hr, ramp demand = 100 veh/hr/ln, and downstream capacity = 2400 veh/hr/lane) ..............................................................................................874-28 Variation of TT per mile with demand for different values of length of entry section (# lanes = 2, FFS = 50 mi/hr, ramp demand = 100 veh/hr/ln, and downstream capacity = 1689 veh/hr/lane) ..............................................................................................884-29 Variation of TT per mile with demand for different values of length of entry section (# lanes = 2, FFS = 50 mi/hr, ramp demand = 100 veh/hr/ln, and downstream capacity = 1324 veh/hr/lane) ..............................................................................................884-30 Time series plot between TT per mile of the downstream bottleneck and the number of vehicles in the downstream bottleneck .......................................................................... 894-31 Time series plot between TT per mile of the upstream segment and the number of vehicles in the upstream segment ...................................................................................... 894-32 Sketch of a diverge freeway segment. ............................................................................... 904-33 Variation of TT per mile with demand (lanes = 2, FFS = 50 mph, length of entry section = 500 ft, ramp Exit % = 5, and downstream capacity = 1515 veh/hr/lane) .......... 904-34 Variation of TT per mile with demand for different values of downstream segment capacity (lanes = 2, FFS = 50 mph, length of entry section = 500 ft, and ramp exit % = 5) .....................................................................................................................................914-35 Variation of TT per mile with demand fo r different values of speed (lanes = 2, FFS = 50 mph, length of entry section = 500 ft and ramp exit % = 5, and downstream capacity = 2137 veh/hr/lane) ..............................................................................................914-36 Variation of TT per mile with demand fo r different values of speed (lanes = 2, FFS = 50 mph, length of entry section = 500 ft and ramp exit % = 5, and downstream capacity = 1689 veh/hr/lane) ..............................................................................................924-37 Variation of TT per mile with demand fo r different values of speed (lanes = 2, FFS = 50 mph, length of entry section = 500 ft and ramp exit % = 5, and downstream capacity = 1324 veh/hr/lane) ..............................................................................................924-38 Variation of TT per mile with demand for different values of off-ramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 2136 veh/hr/ln) ...................................................................................................................93

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11 4-39 Variation of TT per mile with demand for different values of off-ramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 m i/hr, and downstream capacity = 1689 veh/hr/ln) ...................................................................................................................934-40 Variation of TT per mile with demand for different values of off-ramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 1324 veh/hr/ln) ...................................................................................................................944-41 Variation of TT per mile with demand for different values of length of entry section (# lanes = 2, FFS = 50 mi/hr, ramp demand = 100 veh/hr/ln, and downstream capacity = 2136 veh/hr/lane) ..............................................................................................944-42 Variation of TT per mile with demand for different values of length of entry section (# lanes = 2, FFS = 50 mi/hr, ramp demand = 100 veh/hr/ln, and downstream capacity = 1689 veh/hr/lane) ..............................................................................................954-43 Variation of TT per mile with demand for different values of length of entry section (# lanes = 2, FFS = 50 mi/hr, ramp demand = 100 veh/hr/ln, and downstream capacity = 1324 veh/hr/lane) ..............................................................................................954-44 Variation of TT per mile with demand for different values of # lanes (length of entry section = 500 ft, and FFS = 50 mi/hr, off -ramp exit % = 5, and downstream capacity = 2136 veh/hr/lane) ............................................................................................................964-45 Variation of TT per mile with demand for different values of # lanes (length of entry section = 500 ft, and FFS = 50 mi/hr, off -ramp exit % = 5, and downstream capacity = 1689 veh/hr/lane) ............................................................................................................964-47 Time series plot between TT per mile of the upstream segment and the number of vehicles in the upstream segment ...................................................................................... 974-49 Variation of TT per mile with demand (# lanes = 2, FFS = 50 mph, length of entry section = 500 ft, ramp exit % = 5, an d downstream capacity = 1696 veh/hr/lane) .......... 984-50 Variation of TT per mile with demand for different values of downstream segment capacity (lanes = 2, FFS = 50 mph, length of entry section = 500 ft, and ramp exit % = 5) .....................................................................................................................................994-51 Variation of TT per mile with demand fo r different values of speed (lanes = 2, FFS = 50 mph, length of entry section = 500 ft and ramp exit % = 5, and downstream capacity = 2209 veh/hr/lane) ..............................................................................................994-52 Variation of TT per mile with demand fo r different values of speed (lanes = 2, FFS = 50 mph, length of entry section = 500 ft and ramp exit % = 5, and downstream capacity = 1696 veh/hr/lane) ............................................................................................100

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12 4-53 Variation of TT per mile with demand fo r different values of speed (lanes = 2, FFS = 50 m ph, length of entry section = 500 ft and ramp exit % = 5, and downstream capacity = 1326 veh/hr/lane) ............................................................................................1004-54 Variation of TT per mile with demand for different values of off-ramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 2209 veh/hr/ln) .................................................................................................................1014-55 Variation of TT per mile with demand for different values of off-ramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 1696 veh/hr/ln) .................................................................................................................1014-56 Variation of TT per mile with demand for different values of off-ramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 1326 veh/hr/ln) .................................................................................................................1024-57 Variation of TT per mile with demand for different values of length of entry section (# lanes = 2, FFS = 50 mi/hr, ramp demand = 100 veh/hr/ln, and downstream capacity = 2209 veh/hr/lane) ............................................................................................1024-58 Variation of TT per mile with demand for different values of length of entry section (# lanes = 2, FFS = 50 mi/hr, ramp demand = 100 veh/hr/ln, and downstream capacity = 1696 veh/hr/lane) ............................................................................................1034-59 Variation of TT per mile with demand for different values of length of entry section (# lanes = 2, FFS = 50 mi/hr, ramp demand = 100 veh/hr/ln, and downstream capacity = 1326 veh/hr/lane) ............................................................................................1034-60 Variation of TT per mile with demand for different values of # lanes (length of entry section = 500 ft, and FFS = 50 mi/hr, off -ramp exit % = 5, and downstream capacity = 2209 veh/hr/lane) ..........................................................................................................1044-61 Variation of TT per mile with demand for different values of # lanes (length of entry section = 500 ft, and FFS = 50 mi/hr, off -ramp exit % = 5, and downstream capacity = 1696 veh/hr/lane) ..........................................................................................................1044-62 Variation of TT per mile with demand for different values of ramp demand (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 2491 veh/hr/ln) .................................................................................................................1054-63 Variation of TT per mile with demand for different values of ramp demand (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 1689 veh/hr/lane) .............................................................................................................1054-64 Variation of TT per mile with demand for different values of ramp demand (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 1324 veh/hr/lane) .............................................................................................................106

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13 4-65 Time series plot between TT per mile of the downstream bottleneck and the number of vehicles in the downstream bottleneck ........................................................................ 1064-66 Time series plot between TT per mile of the upstream segment and the number of vehicles in the upstream segment .................................................................................... 1075-1 Variation of TT per mile with demand (lanes = 2, FFS = 50 mph, length of basic freeway segment = 5000 ft, and downs tream capacity = 1515 veh/hr/lane) ................... 1255-2 Sigmoid curve ............................................................................................................. .....1255-3 Comparison of average HCM speed and model speed .................................................... 1265-4 Variation of maximum T.T. with demand for a series of length of basic freeway segment ....................................................................................................................... .....1265-5 Variation of travel time with time interval ...................................................................... 1275-6 Variation of TT per mile with demand for various values of downstream capacity (lanes = 2, length of basic freeway segment = 5000 ft and FFS is 55 mph) .................... 1275-7 Variation of TT per mile with capacity for various values of demand (lanes = 2, length of basic freeway segment = 5000 ft and FFS is 55 mph)......................................1286-1 Variation of upstream segment T.T. with demand for several anal ytical models with capacity at 1515 veh/hr/ln ................................................................................................130

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14 LIST OF ABBREVIATIONS T.T Travel time BFS Basic freeway segment BPR Bureau of Public Roads MTC Metropolitan Transportation Commission d Demand C Capacity Cd Downstream segment capacity q Flow

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15 Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science ESTIMATING FREEWAY TRAVEL TIME AS A FUNCTION OF DEMAND USING SIMULATION By Ramakrishna Yennamani December 2008 Chair: Lily Elefteriadou Major: Civil Engineering Analytical T.T. models using demand have been developed in the past, and are applicable for both under-saturated and overs aturated conditions. These mode ls are consistent with each other and make accurate T.T. predictions at lower demand levels or in unsaturated conditions. However, at high levels of demand or congestion th ese models are not consistent with each other and have not been compared with field data. Furt her, some of the existing models, such as BPR, consider flows greater than the capacity, which is unrealistic. Thus there is a need for further advancement in the T.T. estimation models whic h make accurate predictions at both saturated and unsaturated congestion levels. Moreover most of the existing models such as BPR and MTC do not consider the queuing phenomenon explicitl y. Thus analytical models which consider formation and dissipation of queue and also consider the delay asso ciated with these queues in estimation of T.T. is required. Besides analytical models, simulation has also been used in the past for estimation of the T.T. given demand. However, analytical models of T.T. have not been developed using results obtained from simulation. A preliminary list of variables that may affect the T.T. are considered. These variables are used for simulation so that the significant variables can be selected for further consideration. Not

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16 all of the freeway segments require the same set of inputs to estimate travel time, therefore each segment type is considered separately. Th e Highway Capacity Manual (HCM) 2000 considers the following freeway segments: 1) Basic fr eeway segment 2) Merge segment 3) Diverge segment 4) Weaving segment. Lane Width, number of lanes, driver Popula tion, free flow speed (FFS, freeway demand, length of the freeway segment are considered as important variables that may affect the travel time of a basic freeway segment. The same variables whic h are considered for the basic freeway segment are also considered for all the other segments with the addition of the on-ramp demand and length of the entry segment for merge segment, with the addition of the off-ramp demand and length of the entry segment for diverge segment, with the addition of the on-ramp demand, offramp demand, and length of the en try segment for weave segment.

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17 CHAPTER 1 INTRODUCTION 1.1 Background Travel tim e (T.T.) estimation has been extens ively researched because of its important applications, such as pre-trip traveler informa tion (Jha et.al 1998), route trip guidance systems (Balke et.al 1995), and traffic management (Pal en, 1997). Such applications require accurate short-term T.T. predictions, which have been made possible due to the advancement of surveillance technologies. These can measure and transmit information such as volume, speed and occupancy. These traffic parameters can be used for real time estimation of T.T. Most of the models developed thus far are based on speed to estimate short-term T.T. However there are other important applications of T.T. estimation, for example planning applications. Planning applicati ons essentially involve the assessment of the transportation infrastructure at a future time to estimate its performance. Based on appropriate performance measures, decisions can be made regarding impr ovement alternatives. Planning applications for freeways are very important as the congestion le vels on intercity highways and freeways are high and are likely to increase further (TRB special re port, 1991). Such high levels of congestion have serious impacts on the regional economic development (Bhat 1995). Planning applications are based on future trav el demand where speed data for those future conditions are not known. Analytical T.T. models using demand have been developed, and are applicable for both under-saturated (Davidson 1966, HCM 2000) and oversaturated conditions (Bureau of Public Roads 1964, Akcelik 2003). These models are consistent with each other and make accurate T.T. predictions at lower demand levels and unsaturated conditions. However, at high levels of demand and congested conditions, these models are not consistent with each other and have not been compared w ith field data (Akcelik 2003).

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18 Most of the existing models do not consider queuing explicitly. Thus, further advancement in the T.T. estimation models is needed to improve prediction particularly for congested conditions. These models should also consider the formation and dissipation of queues. 1.2 Objectives and Scope The objectiv e of this thesis is to develop analytical models for estimating T.T. for freeway corridors as a function of demand. Given the difficu lty in obtaining field da ta particularly with respect to demand, simulation will be used in the development of the analytical models. The following tasks were undertaken: 1. Select important variables which may impact freeway corridor T.T. as identified in the literature 2. Using these variables, devel op scenarios and simulate them to select the significant variables that affect freeway T.T. 3. Using the significant variables identified above, finalize the scenarios considered and simulate them to generate data for the development of analytical models 4. Develop analytical T.T. models based on the simulation results 5. Compare the analytical models developed in task 4 to other planning T.T. models 1.3 Organization The rest of this docum ent is organized as follows. Chapter 2 discusses the literature relevant to the topic. The methodology developed to achieve the stat ed objectives is described in Chapter 3. Chapter 4 describes the development and simulation of scenarios for generating the database. This data is used to develop T.T. an alytical models, which are presented in Chapter 5. These analytical models are compared to other planning T.T. models and the results are presented in Chapter 6. Chapter 7 summarizes th e important findings from this research.

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19 CHAPTER 2 LITERATURE REVIEW This chapter reviews literature relevant to th e topic. First, the state-of-the art on T.T. models used in planning applications are review ed (Section 2.1). Next, th e state-of-art on T.T. models for real tim e applications are review ed in (Section 2.2). Va rious data collection techniques which can be used to estimate or me asure T.T. are reviewed in Section 2.3. Section 2.4 discusses variables found to impact T.T. Finally a summary of the lite rature review findings is provided in Section 2.5. 2.1 Travel Time Models for Planning Applications This section reviews literature on T.T es timation for planning applications, and the advantages and disadvantages of ea ch of these methods are studied. T.T. estimation models for planning applications can be broadly classi fied on the basis of saturation levels considered. Wh ile some models can be applie d only for unsaturated conditions, other models can be applied for both unsaturat ed conditions (demand/capacity < 1) and over saturated conditions (demand/capacity > 1). Models of the former type, such as the HCM speed flow curve, can be used to pr edict the T.T.s for unsaturated conditions. However these models cannot be used for oversaturated conditions, and thus they cannot be used to predict T.T.s in future years as the traffic demand in future years usually falls in oversat urated conditions (Singh 1999). There are three T.T. estimation models which are applicable in over saturated conditions and each of these is discussed below (1) Bureau of Public Roads (BPR) mode l (Bureau of Public Roads, 1964): (2-1) Where,

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20 T = travel time = free flow travel time q = flow C = Capacity Spiess (1990) evaluated the popular BPR function and found se veral drawbacks. Some of the limitations of the BPR function are (1) they are not strictly incr easing functions at low volume (2) there is no upper limit on the slop e of the volume delay function. Developing on these drawbacks of the BPR function he investigated the set of necessary conditions which a valid volume delay function should satisfy. The functions which satisfy these conditions are called conical volume delay functions. He cited an application of these conical volume delay functions as an input to the tr affic assignment for the city of Basel, Switzerland. He found that the convergence speed for traffic assignment was high for conical volume delay functions as compared to the BPR function. The first limitation highlighted by Spiess (1990) is not validated by any field data. On the other hand, HCM 2000 describes the speed flow rela tion, based on field data, as a relatively flat curve under non congested conditions. The BPR function models travel time for the study segment independent of the downstream conditions. When the downstream segment is a bottleneck, all the upstream segments of the bottleneck experience congested conditions. Thus, exclud ing the impact of the downstream conditions is one of the f undamental limitations of BPR function. Miruchandani et al. (2003) have highlighted that the popular BPR model and the conical volume delay functions are limited to uninterrupted flow. Further, they have highlighted that analytical volume delay functions do not model congestion and dissipation effects. (2) Metropolitan Transpor tation Commission (MTC) mode l (Singh et.al, 1995):

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21 (2-2) Where, = travel time = free flow travel time q = flow C = Capacity Akcelik (2003) argues that for oversaturated traffic conditions the T.T. should increase linearly with flow. Contrary to this argument the T.T. estimated using the MTC model varies exponentially with flow for overs aturated conditions. Thus the MTC model is not theoretically justified from queuing theory. Similar to the BPR function, MTC function m odels travel time for the study segment independent of the downstream conditions. When th e downstream segment is a bottleneck all the upstream segments of the bottleneck experien ce congested conditions. Thus, excluding the impact of the downstream conditions is one of the fundamental limitations of MTC function. Further, the length of the segment is also not considered by both BPR and MTC functions. As the length of the segment increases the percenta ge of the segment that experiences congestion keeps decreasing. Thus the length of the segment is also believed to be an important variable, which is not addressed by both BPR and MTC functions. (3) Akceliks model estimates average T.T. over a given time period: 20 5 0{0.25*[(/1){(/1)(8*(/1)/()}]}atttqCqCJqCCt (2-3) Where, t= T.T. t0= free flow T.T. t = time period for which the specified demand persists q= flow C= capacity = Delay parameter

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22 These three models estimate T.T. significantl y different from one another. Singh (1999) studied the T.T. predicted by BPR, MTC, and Ak celik models for oversaturated conditions. The comparison of the BPR, MTC, Akcelik and 1994 HCM are shown in Figure 2-1 and Figure 2-2. It can be observed from Figure 2-1 and Figur e 2-2 that under uncongest ed conditions, all the above four travel time functions make similar predictions. However, unde r congested conditions, these four travel time functions make different travel time predictions. While, the BPR function is insensitive to increases in flow for oversat urated conditions, the MTC model predicts T.T. which varies non-linearly with increase in flow Akceliks model predicts T.T. which varies linearly with increase in flow. Singh (1999) conc luded that Akceliks model best describes the T.T. for oversaturated conditions. The fundamental limitation of all the a bove four functions is that they do not consider the im pact of the downstream conditions on the travel time of the study segment. There are several differences between Akcelik s travel time function and other functions (BPR and MTC). One key difference is that, whil e Akceliks travel time function considers the time period over which the average travel time is reported, BPR and MTC travel time functions do not consider the time period over which th e average travel time is reported. Another difference is that, while the BPR and MTC functi ons are more macroscopic and mainly focus on planning applications, the Akce liks function is microscopic a nd focuses on making realistic estimate of travel time. Miruchandani et al. (2003) have developed simulation-based T.T. estimation, for modeling the impacts of congestion, dissipa tion, and interrupted flow, using the CORSIM software. Their simulation modeling included several factors such as lane changing behavior, gap acceptance,

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23 intersection control, start up loss ti mes, vehicle headways, and pedestrian traffic. They used this simulation-based estimation of T.T., for their traffic assignment process. 2.2 Travel Time Estimation fo r Real-Time Applications This section reviews literature on T.T estima tion models for real time applications. These models are for short term prediction of T.T. Th e advantages and disadvantages of each of the methods are also studied. Finally the usability of these models to planning applications is studied. Most models estimate and report either T.T. or, its equivalent, sp eed. The most widely used methods for freeway T.T. prediction use da ta collected from loop detectors. For methods that use loop detector data, vehicle length is an important parameter for estimating speed (or T.T.). These models either use a constant value of effective vehicle length (Petty and Peter Bickel 1998) or use the vehicle length measur ed for each vehicle (Dailey 2004). Dailey (2004) claimed that models that use a constant effectiv e vehicle length are inaccu rate (greater than 80%) under high levels of congestion. While the models that use vehicle le ngth for each individual vehicle for estimation of speed are more accurate (greater than 90%). Instead of estimating speed and then T.T., T.T. can also be directly measured by vehicle reidentification. Using dual loop detectors the vehicl e length can be direc tly estimated. Several approaches have been proposed to estimate ve hicle length including Kalman filtering (Dailey 2004) and Exponential smoothed technique (He lling 2002). Once the vehicle length is known, the vehicle can be re-identified using its lengt h as its signature (Coifman 1998). By identifying the vehicle at both the upstream and down-stream the T.T. can be measured. Mirchandani et al. (2004) have shown that instead of identifying a si ngle vehicle, a platoon can be identified at both the upstream and down-stream points. Using this technique they could match 90 % of the platoons. Thus the T.T. of all vehicles in the platoon can be measured. The vehicle re-

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24 identification technique works well only under congested conditions. Smith et al. (2004) conducted sensitivity analysis on T.T. estimation us ing single loop detector data. They estimated T.T. at various levels of congestion and found that T.T. is overestimated as the congestion level decreases, by as much as 1 minute per mile. An important issue regarding T.T. estimati on is the T.T. prediction interval, the time period for which the predictions are made (for ex ample the next 10 minutes). Chien et al (2003) have shown that although accurate (97%) short term T.T. predictions have been possible using flow and speed data modeled using simple re gression techniques, w ithout considering the historical data accurate prediction of T.T.s fo r longer periods could not be made. This is attributed to the unknown flows th at are to arrive for the next one hour, and the speeds of the vehicles that are to arrive, which is also unknown. 2.3 Travel Time Data Collection Techniques In this section various T.T. da ta collection technologies a nd their applications for T.T. m easurement are also reviewed. There are numerous techniques for T.T. data collection. Kim et.al ( 1995) classified these techniques into three categories: 1) Spot speed measurement techniques (measure speed only) 2) Vehicle tracking techniques (measure vehicle T.T.s) 3) Trip maker tracking techniques (measure traveler trip times than vehicle trip times). Further, Kim et.al (1995) evaluated the relative advantages of the above thr ee classes of techniques. Spot speed measurement techniques measure the instantaneous speed either at a fixed lo cation, such as road side sensors, or at fixed time, such as aerial photography. These spot speed measurement techniques provide economically efficient solutions for acquiring large volumes of sp eed data at a given location. Vehicle tracking techniques measure T.T. along the trip. These technique s include the floating car technique, non-instrumented vehicle tracking, and passive probe technique. Microwave radar

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25 detection systems (RTMS) use microwaves to detect traffic and measure traffic related parameters such as volume and speed. EIS traffic solutions (2006) have tested the accuracy with which RTMS can measure traffic by comparing the traffic data collected using RTMS with manually collected data. They f ound that RTMS can be used to accurately measure traffic in general (98%). 2.4 Variables for Scenario Development This sec tion reviews the literature to identify a preliminary list of variables that may affect the travel time. These variables will be used fo r simulation so that the significant variables can be selected for furt her consideration. The Highway Capacity Manual (HCM) 2000 cons iders the following freeway segments: 1) Basic freeway segment, 2) Merge segment, 3) Diverge segment, and 4) Weaving segment. Not all of these segments require the same set of inputs to estimate travel time, therefore each segment type is considered separately. For the basic freeway segment, the HCM 2000 lis ts the following variables as important for operational analysis: 1) Lane Width: If the lane widt hs are less than 12 ft, driver s tend to reduce their speed for driving close to one another laterally. 2) Number of lanes: Under moderately or h eavily congested conditi ons, lane changing might facilitate faster travel. 3) Driver Population: Non commuter driver popul ations have different driving behavior compared to regular commuters (HCM 2000). 4) Free flow speed (FFS): Under uncongested co nditions, with higher free flow speed, there is an opportunity to travel faster 5) The demand: the demand is directly related to T.T. as, higher traffic results in congestion and lower T.T.

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26 In addition to the factors listed in HCM 2000, other factors that can impact travel time of a basic freeway segment are also considered These factors are listed below. 6) Length of the freeway segment: The length of the segment woul d affect the T.T./mile as a function of the queue length or the congested portion of the segment. For a merge segment, the HCM 2000 considers the same variables as the basic freeway segment with the addition of the following: 1. Demand from on-ramp: Higher the demand from on-ramp, the extent of merging will be higher and results in high levels of c ongestion thus resulti ng in higher T.T. 2. Length of the entry segment: The entry segment stores the queue that needs to get past the merging point bottleneck. With longer entr y segment, more vehicles can be queued, which results in higher travel time. For a diverge segment, the HCM 2000 considers th e same variables as the basic freeway segment with the addition of the following: 1. Demand on off-ramp: Higher the demand on off -ramp, more vehicles exit out of the system. This reduces congestion t hus resulting in lower T.T. 2. Length of the entry segment: The entry segment stores the queue that needs to get past the merging point bottleneck. With longer entr y segment, more vehicles can be queued, which results in higher travel time. For a weaving segment, the HCM 2000 considers the same variables as the basic freeway segment with the addition of the following: 1) Demand from on-ramp: Higher the demand from on-ramp the extent of merging will be higher and results in high levels of c ongestion thus resulti ng in higher T.T. 2) Demand on off-ramp: Higher the demand on off -ramp, more vehicles exit out of the system. This reduces congestion t hus resulting in lower T.T. 3) Length of the entry segment: The entry segment stores the queue that needs to get past the merging point bottleneck. With longer entr y segment, more vehicles can be queued, which results in higher travel time. 4) Weaving Length: The length of the weaving segment restricts the space under which all the required lane changes have to be made Thus with decrease in weaving length, the intensity of lane changes increases and thus speed decreases. Thus, the resulting travel time increases (HCM 2000).

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27 2.5 Summary and Conclusions Analytical T .T. models using demand have been developed, and are applicable for both under-saturated and oversaturated conditions. Thes e models are consistent with each other and make accurate T.T. predictions at lower demand le vels or in unsaturated conditions. However, at high levels of demand or congestion these models ar e not consistent with e ach other and have not been compared with field data. Further, some of the existing models, such as BPR, consider flows greater than the capacity, which is unrealistic. Thus there is a need for further advancement in the T.T. estimation models which make accurate predictions at both saturated and unsaturated congestion levels. Moreover, most of the existing models (BPR and MTC) do not consider the queuing phenomenon explicitly. Thus analytical mode ls which consider formation of queue and dissipation of queues and also consider the delay associated with these queues in estimation of T.T. is required. Besides analytical models, simulation has also been used for direct estimation of T.T.. However, analytical models of T.T. have not been developed using results obtained from simulation. A preliminary list of variables that may aff ect the travel time are considered. These variables will be used for simulation so that the significant variables can be selected for further consideration. Not all of the freew ay segments require the same se t of inputs to estimate travel time, therefore each segment type is consider ed separately. The Highway Capacity Manual (HCM) 2000 considers the following freeway segm ents: 1) Basic freeway segment, 2) Merge segment, 3) Diverge segment, and 4) Weaving segment. Lane Width, number of lanes, driver Population, free flow speed (FFS) freeway demand, length of the freeway segment were considered as importa nt variables that may affect the travel time of a basic freeway segment. The same variables which are considered for the basic freeway

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28 segment are also considered with the addition of the on-ramp demand and length of the entry segment for merge segments, with the addition of the off-ramp demand and length of the entry segment for diverge segments, with the addition of the on-ramp demand, off-ramp demand, and length of the entry segment for weave segments. Figure 2-1. Comparison of BPR, MTC, Akcelik and 1994 HCM T.T. functions for q/c<1.5 (source: Rupinder Singh, 1999) Figure 2-2. Comparison of BPR, MT C, Akcelik and 1994 HCM T.T. functions for q/c <2 (source: Rupinder Singh, 1999)

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29 CHAPTER 3 METHODOLOGY This section presents the m ethodology devel oped to accomplish the objectives stated in Chapter 1. The methodology is outlined in Figure 3-1. First, a simulation m odel is selected to suit the needs of the project (Section 3.1). Next, scenarios ar e developed and simulated to identify the most important variables that may af fect T.T. in the simulator (Section 3.2). Using these important variables, a set of scenarios is developed and simulated to obtain a database for analytical model development (Sec tion 3.3). Analytical models are developed using this database (Section 3.4). Section 3.5 discu sses the comparison of the proposed analytical models to other T.T. estimation models. 3.1 Simulation Model Selection Although most of the m icro-simulation packages available are capable of simulating large networks, they differ in the level of detail used to conduct analysis and also differ in the basic algorithms used (car following, lane changing, e.t.c.). Thus depending on the requirements of the application, appropriate soft ware has to be selected. There are several software packages, in cluding AIMSUN, PARAMICS, VISSIM, and CORSIM, that suit the general requirements of this study. More specifically, the software should be able to replicate and provide T.T. for differe nt types of freeway segments. Any of the above listed micro-simulation packages could be used fo r this purpose. The CORSIM software package was readily available for use for this study, t hus the CORSIM software package was used. CORSIM was developed by FHWA. It has a se parate module for freeway analysis called FRESIM. It is widely used among transportatio n professionals, relatively well documented, and also requires only modest ne twork coding. Moreover, the support from McTrans is readily

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30 available for any problems that might arise while using CORSIM. It can also model freeway corridors under various levels of congestion. 3.2 Development and Simulation of Scenarios for Variable Selection The study corridor is broken down in to freeway segments, as described in Section 2.4. Segmenting the corridor in to these segments en ables easy estimation of analytical models for each of these three segments, as the number of variables re mains relatively small. After developing analytical models for T.T. for each of the four classes of segments, the T.T. for the entire corridor is estimated as the sum of the T.T. of all the segments. To develop the analytical models for each cla ss of the freeway segments, first, important variables that can affect the T.T. for each segmen t are identified. For each of these variables, the possible range of values is se lected within the normal field conditions. Within the range of possible values for each variable, a few values are selected and are considered for the development of scenarios. Once specific values are chosen for each variable, scenarios are developed using these values. A scenario repres ents a state where each variable is assigned a specific value among the possible values. The variables selected for de veloping scenarios are classi fied into the following groups. 1. Basic freeway segment: Lane width, number of lanes, driver population, free flow speed (FFS), demand, and length of the freeway segment. 2. Merge segments: In addition to the variables considered for the basic freeway segment, the following variables are considered: Demand from on-ramp, length of the entry segment. 3. Diverge segment: In addition to the variables considered for the basic freeway segment, the following variables are considered: Demand on off-ramp, length of the entry segment. 4. Weaving segment: In addition to the variables considered for the basic freeway segment, the following variables are considered: Demand from on-ramp, demand on off-ramp, length of the entry segment, weaving Length.

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31 In addition to the above variables, some other va riables were also found to be important, such as: length of the acceleration and dece leration lane. However, both the length of the acceleration and deceleration lane are dependent on the free flow speed. As the free flow speed is varied, the length of the acceleration lane and deceleration lane is adjusted to its design length according to the guidelines mentioned in green book. Lane width was not included for developing s cenarios because it was already included in estimation of free flow speed. Driver population f actor and percent of trucks were not included for developing scenarios to contain the numbe r of scenarios within a reasonable range. 3.3 Scenarios for Database Development Based on the results of the prelim inary experi ments, important variab les are identified and the list of scenarios to be used is prepared. These scenarios are simulated and T.T. is extracted for each scenario. A database is developed using the simulated data. This database is in the form of an (MxN) matrix, where each of the M rows is a specific scenario and each of the N columns is a variable, either the T.T. itself or one of the several variables that have been considered in the development of scenarios. Such a database is developed for each segment type. 3.4 Development of Analytical T.T. Models Af ter simulating the scenarios and developi ng the database, analytical models are developed for each freeway segment type. Regression models are developed with T.T. as the dependent variable and the other variables us ed for developing scenarios as independent variables. 3.5 Comparison of Analytical Models to Simulator The analytical m odels are applied to predict T.T. on freeway segments under saturated/congested conditions. Similarly, other anal ytical models from the literature are applied on freeway segments under saturated/congested conditions. Comparisons are drawn on the

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32 predicted T.T. using the analytic al models developed as part of this thesis along with other analytical models in literature.

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33 Figure 3-1. Methodology flow chart Simulation of various scenarios for selecting important variables Development of analytical travel time models based on simulation results Compare T.T. estimates from Analytical Models developed in this study and existing travel time estimation models Selection of Simulation model Recommendations Simulation of scenarios for developing database

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34 CHAPTER 4 SIMULATION OF SCENARIOS This chapter discusses th e identification of variables for developing simulation scenarios, the simulation process, and the se lection of variables for inclusi on in the analytical models. The variables identified from the l iterature are discussed in Sect ion 4.1. Next, the development and simulation of scenarios along with the selection of the variables found to affect T.T. in the simulation are presented in Section 4.2. 4.1 Identification of Variable s and Their Range of Values To develop the analy tical models for each class of the freeway segments, first, the variables that may affect the T.T. for each type of segment identified from the literatu re (Section 2.4) are reviewed, and a reasonable range of values is obtained. The range of values is selected such that they reflect the commonl y found values in field and also generate reasonable number of scenarios. These variables along with their range of values are listed in Table 4-1, Table 4-2, Table 4-3, and Table 4-4. As discussed in Section 2.4, the downstream conditions can impact the traffic flow of the study segment, more so if the downstream segmen t is a bottleneck. In this study the impact of downstream segment is analyzed by varying its capacity. Although there is no standard procedure to design the downstream segment so that it reaches a particular capacity, five different road configurations were develope d such that the throughput from the downstream segment varies uniformly over a large range of values. These different road configurations include, free flow speed of 15 mph and 25 mph, single lane closure, lane closure with rubber necking factor. Rubber necking f actor reflects the intensity of the incident or work zone.

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35 4.2 Development of Scenarios This section presents the scenarios developed for each type of freeway segments, identified in Section 2.4. 4.2.1 Basic Freeway Segment A basic freeway segm ent does not have any on-ramps or off-ramps. A sketch of a basic freeway segment is shown in Figure 4-1. The basic freeway segment shown in Figure 4-1 consists of two links, the subject freeway segmen t, which is located between the entry and exit points and the segment downstream of the subjec t segment. This downstream segment acts as a bottleneck and is used in this study to control the number of vehicles that can exit the subject freeway segment. This is achieved in the simulation by varying the geometry and driver behavior characteristics of the downstream segment. Each variable under considera tion was tested whether it has any influence on the T.T. per mile of the basic freeway segment. This was accomp lished by varying the values of each variable systematically and observing the T.T. per mile. It should be noted that, an initialization period of 15 minutes was used in all the simulation r uns. Some of the simulation runs reached the equilibrium within the initialization period, wh ile a majority of scenarios did not reach equilibrium within the initiali zation period. While the travel time derived from the simulation runs that did not reach equilibrium depend on the initialization period, this has not been considered in this study. A detailed description of the vari ables evaluated is given below. Demand per lane: Number of vehicles attempting to enter the subject segment. If the demand exceeds capacity then a queue is formed in the bottleneck and also upstream of the entrance of the subject segment. In this case the number of vehicles actually entering the segment

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36 could be lower than the demand. Eight different values of demand are used, ranging from 1000 veh/hr/ln to 9999 veh/hr/ln. Downstream capacity: The maximum number of vehicl es exiting from the downstream section. Although there is no sta ndard procedure to design the downstream segment so that it reaches a particular capacity, five different road configurations were de veloped such that the throughput varies uniformly over a large range of values. Free-Flow speed: The average speed on a section when there is very low demand. Four different speeds were tested; 55 mph, 60 mph, 65 mph, and 70 mph. Number of lanes: The number of through lanes in each direction. This study tested 2-lane segments, 3-lane segments, and 4-lane segments. Length of the BFS segment: This study tested segment le ngth equal to 5000 ft, 10,000 ft, 15,000 ft, 20,000 ft, and 25,000 ft. The complete set of values tested is shown in Table 4-5, and scenarios were developed for each combination of these for a basic freeway segment. 2400 different scenarios were created for basic freeway segment. Each of these scenarios was simulated 10 times and the average travel ti me, density, and number of vehicles exiting the downstream segment were computed. The run time for simulating all of these 2400 scenarios 10 times was about 48 hrs on a .39 Ghz core 2 duo CPU with 3 GB memory. Preliminary analysis was conducted to evaluate the impacts of each of these variables on the T.T. per mile. Figure 4-2 shows that the T.T. remains relatively constant until demand reaches downstream capacity. The impact of dema nd per lane is very significant when the downstream segment has reduced capacity. Once demand reaches downstream capacity, T.T.

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37 starts to linearly increase with demand and then the relationship flattens out to a maximum value of T.T. (at approximately 2,250 veh/ln). To find the impact of downstream capacity on T.T., the downstream capacity is varied from no capacity reduction (2250 veh/hr/ln) to very low capacity (848 veh/hr/ln). Figure 4-3 presents the relationship between downstream capac ity and T.T. As shown, the T.T. plots consist of three parts. In the first part, when de mand is lower than the downstream capacity, the relationship between T.T. and demand is relatively flat, i.e. T.T. is not affected by demand. In the second part, when demand exceeds the downstream segment capacity, T.T. starts increasing linearly with demand. In the third and final part, when demand exceeds downstream segment capacity considerably, the linearly increasing T.T. curve flattens out and eventually becomes a constant value. As illustrated in Figure 4-3, the downstream capacity has a very significant impact on T.T. Because of the high impact of the reduced dow nstream capacity, the impact of the remaining variables on T.T. is presented in two cases; a) when there is no reduction in capacity of the downstream section and b) when there is reduction in the capacity of the downstream section. To find the impact of free-flow speed on T.T., th e free-flow speed is varied from 55 mph to 70 mph and the relationship between T.T. and demand for each of the free-flow speeds is observed. Figure 4-4 presents the relationship be tween T.T. and demand for different free-flow speeds when there is no downstream bottleneck. As shown there is significant difference in the T.T. per mile between each of the FFS. Therefore FFS is an important vari able in the estimation of T.T. when there is no downstream bottleneck. As the speed increases, the T.T. per mile decreases. When there is no reduction in downstream segment capacity, with higher FFS the vehicles can travel faster and the T.T. decrease s. The relationship between T.T. and demand is a

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38 set of parallel lines, one for each speed. The T.T. increases linearly by a relatively small amount, with increasing demand. To find the impact of free-flow speed on T.T. when there is a downstream bottleneck, the free-flow speed is varied from 55 mph to 70 mph and the relationship between T.T. per mile and demand is observed for each of these FFS. Figure 45 presents the relations hip between T.T. and demand for different free-flow speeds when the downstream segment has reduced capacity equal to 1324 veh/hr/ln. As shown, as the FFS increases, the difference in T.T. per mile between each of the FFSs decreases until the demand reaches the downstream segment capacity. Once demand reaches the downstream segment capacity, congesti on starts to occur and vehicles can no longer travel at free flow conditions, and there is no chan ge in T.T. with increase in FFS. As shown in the Figure 4-5, the T.T. remains relatively co nstant until demand reaches downstream capacity. Once demand reaches downstream capacity, T.T. st arts to linearly increase with demand and then the relationship flattens out to a maximu m value of T.T. (at approximately 2,000 veh/ln). The downstream capacity is further reduced to 849 veh/hr/ln and the relationship between T.T. and demand for different free-flow speeds is presented in Figure 4-6. As shown in the Figure 4-6, as the FFS increases, the difference in T.T. per mile between each of the free flow speed decreases until the demand reaches downstr eam segment capacity. Once demand reaches downstream segment capacity, congestion starts to occur and vehicles ca n no longer travel at free-flow conditions, and there is no change in T.T. with increase in free-flow speed. To find the impact of length of the BFS on T.T., the length of the BFS is varied from 5,000 ft to 25,000 ft and the relationship between T.T. and demand for each of the lengths of BFS is observed. Figure 4-7 presents the relationship betw een T.T. and demand for different lengths of BFS when there is no downstream bottleneck. As shown, there is no significant difference in the

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39 T.T. per mile between each of the lengths of th e basic freeway segment. Therefore the length of the basic freeway segment is not an important vari able in the estimation of T.T. when there is no downstream bottleneck. This tre nd is observed because when the downstream segment has no reduction in capacity, free flow c onditions prevail in the basic freeway segment. Thus the T.T. increases with the length of the BFS almost linearl y, which results in a constant T.T. per mile for different lengths of the BFS. As shown in the Figure 4-7, the T.T. rema ins relatively constant with increasing demand, when there is no reduction in downstream capacity. To find the impact of the length of the BFS on T.T. when there is a downstream bottleneck, the length of the BFS is varied from 5,000 ft to 25,000 ft and the relationship between T.T. per mile and demand is observed for each of these lengths. Figure 4-8 presents the relationship between T.T. and demand for different free-flow speeds when the downstream segment has reduced capacity equal to 1324 veh/hr /ln. As shown, there is significant difference in the T.T. per mile between each of the lengths of the basic freeway segment. Therefore the length of the basic freeway segment is an important variable in the estimation of T.T. when there is a downstream bottleneck. As shown in the Fi gure 4-8, the T.T. per mile decreases with increasing length of the segment. When the segm ent is very long the queuing of vehicles is mostly concentrated at the downstream end of th e segment, with the upstream part operating at free flow conditions. As the segment length increa ses, the section with free flow conditions increases, thus the average speed of the segmen t increases and the T.T. decreases as shown in Figure 4-8. As shown in the Figure 4-8, the T.T. remains relatively constant until demand reaches downstream capacity. Once demand reaches downstream capacity, T.T. starts to linearly increase with demand and then the relationship flattens out to a maximum value of T.T.

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40 The downstream capacity is further reduced to 849 veh/hr/ln and the relationship between T.T. and demand for different le ngths of the basic freeway segm ent is presented in Figure 4-9. As shown, there is significant diffe rence in the T.T. per mile betw een each of the lengths of the basic freeway segment. Therefore the length of the basic freeway segment is an important variable in the estimation of T.T. when there is no downstream bottleneck. As shown in the Figure 4-9, once demand reaches downstream capac ity, T.T. starts to linearly increase with demand and then the relationship flattens out to a maximum value of T.T. (at approximately 2,250 veh/ln). To find the impact of the number of lanes on T.T. when there is no downstream bottleneck, the number of lanes is varied from 2 lanes to 4 lanes and the relationship between T.T. and demand for each of those configurations is observed. Figure 4-10 presents the relationship between T.T. and demand as a function of the number of lanes when there is no downstream bottleneck. As shown, there is no significant diffe rence in the T.T. per mile between each of these configurations. Therefore the number of lanes is not an impor tant variable in the estimation of T.T. when there is no downstream bottleneck. As shown in the Figure 4-10, the T.T. remains relatively constant with incr easing demand, when there is no reduction in downstream capacity. It should be noted that the dema nd here and everywhere else in the document refers to vehicles that are attempting to use the facility on a per lane basis. Thus, while testing the impact of number of lanes, demand refers to demand per lane and not the total demand. To find the impact of the number of lanes on T.T. when there is a downstream bottleneck, the number of lanes is varied from 2 lanes to 4 lanes and the relationship between T.T. and demand for each of these configurations is observed. Figure 4-11 presents the relationship between T.T. and demand as a function of nu mber of lanes when there is a downstream

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41 bottleneck. As shown, there is no significant diffe rence in the T.T. per mile between each of these configurations. Therefore the number of lanes is not an impor tant variable in the estimation of T.T. when there is a downstream bottl eneck. As shown in the Figure 4-11, once demand reaches downstream capacity, T.T. starts to linearly increase with demand and then the relationship flattens out to a maximum valu e of T.T. (at approximately 2,250 veh/ln). To find the impact of downstream capacity on the T.T. per mile of the downstream segment, the downstream capacity is varied fr om no capacity reduction (2240 veh/hr) to very low capacity (848 veh/hr). Figure 4-12 presents the relationship between downstream capacity and T.T per mile of the downstream segment. As shown in Figure 4-13, travel time per mile of the downstream segment decr eases exponentially with dow nstream segment capacity. To find the impact of downstream capacity on the T.T. per mile of the downstream segment, the downstream capacity is varied fr om no capacity reduction (2240 veh/hr) to very low capacity (848 veh/hr). Figure 4-13 presents the relationship between downstream capacity and T.T per mile of the downstream segment. As s hown, the T.T. plots do not have a clear 3 part curve similar to the upstream travel time plots. To find the impact of the number of vehicles in the is a downstream bottleneck on the T.T. of the downstream bottleneck, a particular co mbination of demand and downstream segment capacity values are chosen such that a queue is formed after the simulation is run for a while. As shown in the Figure 4-14, the T.T. per of the dow nstream bottleneck closely follows the trend of the number of vehicles in the downstream bottleneck. Therefore the number of vehicles in the downstream bottleneck is found to be an important variable in the estimati on of T.T. within the downstream bottleneck when ther e is a downstream bottleneck. As shown in the Figure 4-14,

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42 once downstream bottleneck gets saturated with traffic, T.T. starts to flatten out to a maximum value of T.T. To find the impact of the number of vehicles in the is a upstream se gment on the T.T. of the upstream segment, a particular combina tion of demand and downs tream segment capacity values are chosen such that a queue is formed af ter the simulation is run for a while. As shown in the Figure 4-15, the T.T. per of the upstream segm ent closely follows the trend of the number of vehicles in the downstream bottleneck. Therefore the number of vehicles in the upstream segment is found to be an important variable in the estimation of T.T. within the upstream segment when there is a upstream segment. As shown in the Figure 4-15, once upstream segment gets saturated with traffic, T.T. starts to flatten out to a maximum value of T.T. Summary: Based on the investigation made from the plots (Figure 4-2 to Figure 4-15) describing the variation of T.T. as a function of several factors, the following observations were made: 1) The relationship between T.T. and demand (F igure 4-2) can be characterized by the following; (1) when demand is less than the downstream segment capacity the T.T. remains relatively constant (2) when demand is equal to downstream capacity the T.T. starts to increase at an ex ponential rate (3) when the exponentially increasing T.T. suddenly starts to flatten and reaches a ma ximum T.T. Although the shape of the T.T. plot against demand is relatively similar to the BPR and other functions, when the demand is less than the capacity, the shape differs significantly in the congested region. While the traditional models predict exponentially incr easing T.T. once the demand exceeds capacity, the analysis conducted in this study suggests that the T.T. curve flattens after a partic ular point. 2) The capacity of the downstream segment plays a key role in the prediction of T.T. The variation of T.T. with demand varies si gnificantly depending on whether the demand is greater than or less than the downstream capac ity (Figure 4-3). Thus the impact of all other variables is broken-down into 2 cases : (1) when there is no downstream bottleneck (2) when there is a downstream segment bottleneck. 3) FFS significantly affects T.T. when there is no downstream bottleneck (Figure 4-4). However if there is a downstream bottleneck, the FFS does not impact the T.T. (Figure 45 & Figure 4-6).

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43 4) The length of the basic freeway segment is no t significant when there is not bottleneck (Figure 4-7). However when there is a downstream bottleneck, the length of basic free flow segment becomes significant, under conge sted conditions (Figure 4-8 and Figure 49). It is observed that as the length of the basic freeway segment increases, the T.T. decreases for a given demand. For segments with higher length, the impact of downstream congestion on the upstream end is lo wer than that of a shorter segment, and thus higher average speeds are re ported for longer segments. 5) The number of lanes shows no significant im pact on T.T. neither for presence of a downstream segment bottleneck nor when ther e is no bottleneck (Figure 4-10 & Figure 411). From the simulation analysis in this section, it is observed that vari ation of T.T. with demand primarily depends on whether or not demand exceeds the downstream segment capacity. It is also observed that the im pact of any variable (with the exception of downstream segment capacity) on T.T. of any freeway segment depe nds on the downstream segment capacity. Table 4-6 summarizes the impact of each of the vari ables on travel time when there is no downstream segment bottleneck and when there is a downstream segment bottleneck. 4.2.2 Merge Segment The m erge segment tested consists of four fr eeway links and a ramp link. The first link is the entry link which spans from the beginning of the merge segment to the point where the ramp meets the freeway (Figure 4-16). The second link is the merging section, which spans along the length of the acceleration lane. The third link is immediately downstream of the merging section and extends till the exit point. The fourth and final link is the downstream section, which starts from the exit point of the merge segment and sp ans for a fixed length (2000 ft). This downstream segment is used to control the number of vehicles that can move out of the merge segment, in other words the downstream capacity. This is achieved in the simulation by varying the geometry, traffic control, and driver behavior characteristic s of the downstream segment. A brief description of the vari ables considered to develop me rge operating scenarios is given below.

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44 Demand per lane: Number of vehicles attempting to enter the subject segment. If the demand exceeds capacity then a queue is formed upstream of the entrance of the subject segment. In this case the number of vehicles ac tually entering the segment could be lower than the demand. Eight different values of demand are used, ranging from 1000 veh/hr/ln to 9999 veh/hr/ln. Downstream capacity: The maximum number of vehicl es exiting from the downstream section. Although there is no standard way to design the downstream segment to achieve a particular capacity, five different road configurations were de veloped such that the throughput varies uniformly over a large range of values. Ramp Demand per lane: Number of vehicles attempting to enter the ramp segment. Three different values of demand are used: 100, 300, and 500 veh/hr/ln. FFS: The average speed on a section when there is very low demand. Four different speeds were tested; 55 mph, 60 mph, 65 mph, and 70 mph. Number of lanes: The number of through lanes in each direction. This study tested 2-lane segments, 3-lane segments, and 4-lane segments. Length of the entry segment: The length of the section of road starting from the entry point of the merge segment to the beginning of the acce leration lane. The complete set of values tested is provided in Table 4-7, and scenarios are developed for each combination of these for a merge segment. 6075 different scenarios were created for merge freeway segment. Each of these scenarios is simulated 10 times and the average travel time density, and number of vehicles exiting the system are computed. The run time for simula ting all of these 3375 s cenarios 10 times takes about 150 hrs on a core 2 duo CPU with 3 GB memory.

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45 Preliminary analysis was conducted to evaluate the impacts of each of these variables on the T.T. per mile. Figure 4-17 shows that the T.T. remains relatively constant until demand reaches downstream capacity. The impact of dema nd per lane is very significant when the downstream segment has reduced capacity. Once demand reaches downstream capacity, T.T. starts to linearly increase with demand and th en flatten out to a maximum value of T.T. (at approximately 2,250 veh/ln). To find the impact of downstream capacity on th e T.T., the downstream capacity is varied from full capacity (4500 veh/hr/ln) to very low capacity (250 veh/hr/ln). Figure 4-18 presents the relationship between downstr eam capacity and the T.T. As shown in Figure 4-18 the T.T. plot with demand has two char acteristic points similar to the basic freeway segment. As illustrated in Figure 4-18 the downstream capacity has a very significant impact on T.T. Similar to the basic freeway segment case, the imp act of remaining variables on T.T. is presented in two cases; no reduction in capac ity and reduction in capacity. To find the impact of free-flow speed on T.T., th e free-flow speed is varied from 50 mph to 70 mph and the relationship between T.T. and demand for each of the free-flow speeds is observed. Figure 4-19 presents the relationship be tween T.T. and demand for different free-flow speeds when there is no downstream bottleneck. Similar to the basic freeway segment case, FFS is found as an important variable in the es timation of T.T., when there is no downstream bottleneck, and the relationship between T.T. and de mand is a set of parallel lines, one for each speed. The T.T. linearly increases, by a ve ry minimal value, with increase in demand. To find the impact of free-flow speed on T.T. when there is a downstream bottleneck, the free-flow speed is varied from 50 mph to 70 mph and the relationship between T.T. per mile and demand is observed for each of these FFS. Figure 4-20 presents the relationship between T.T.

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46 and demand for different free-flow speeds when the downstream segment has reduced capacity equal to 1689 veh/hr/ln. As show n, as the FFS increases, the differe nce in T.T. per mile between each of the FFS decreases until the demand reaches the downstream segment capacity. Once demand reaches downstream segment capacity, conge stion starts to occur and vehicles can no longer travel at free flow conditions Thus there is no change in T. T. with increase in FFS. As shown in the Figure 4-20, the T.T. remains relatively constant until demand reaches downstream capacity. Once demand reaches downstream capacity, T.T. starts to linearly increase with demand and then the relationship flattens out to a maximum value of T.T. (at approximately 2,000 veh/ln) The downstream capacity is further reduced to 1324 veh/hr/ln and th e relationship between T.T. and demand for different free-flow speeds is presented in Figure 4-21. As shown, as the FFS increases, the difference in T.T. per mile be tween each of the FFS starts increasing after the demand reaches downstream segment capacity. As shown in the Figure 4-21, once demand reaches downstream capacity, T.T. starts to linearly increase with demand and then the relationship flattens out to a maximum valu e of T.T. (at approximately 2,000 veh/ln). To find the impact of on-ramp demand on T.T., the length ramp-demand is varied from 100 veh/hr/ln to 500 veh/hr/ln and the relationship between T.T. and demand for each value of on-ramp demand is observed. Figure 4-22 presents the relationship between T.T. and demand for different on-ramp demand when there is no downstream bottleneck. As shown, there is no significant difference in the T.T. per mile be tween each of the on-ramp demands. Therefore onramp demand is not an important variable in the estimation of T.T. when there is no downstream bottleneck.

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47 To find the impact of on-ramp demand on T.T. when there is a downstream bottleneck, the ramp-demand is varied from 100 veh/hr/ln to 500 veh/hr/ln and th e relationship between T.T. and demand for each value of on-ramp demand is observed. Figure 4-23 presents the relationship between T.T. and demand for different on-ramp demand when there is a downstream bottleneck. As shown, there is no significant difference in th e T.T. per mile between each of the on-ramp demands. Therefore on-ramp demand is not an impor tant variable in the estimation of T.T. when there is no downstream bottleneck. To find the impact of free-flow speed on T.T. when there is a downstream bottleneck, the free-flow speed is varied from 50 mph to 70 mph and the relationship between T.T. per mile and demand is observed for each of these FFS. Figure 4-23 presents the relationship between T.T. and demand for different free-flow speeds when the downstream segment has 1321 veh/hr/ln as reduced capacity. The downstream capacity is further reduced to 1324 veh/hr/ln and th e relationship between T.T. and demand for different on-ramp demands is presented in Figure 4-24. As shown, as the FFS increases, the difference in T.T. per mile between each of the on-ramp demand starts increasing after the demand reaches downstream se gment capacity. As shown in the Figure 4-24, once demand reaches downstream capacity, T.T. star ts to linearly increase with demand and then the relationship flattens out to a maximum va lue of T.T. (at approximately 2,000 veh/ln). To find the impact of number of lanes on T.T. when there is no downstream bottleneck, the number of lanes is varied from 2 lanes to 4 lanes and the relationship between T.T. and demand for each of the number of lanes is observed. Figu re 4-25 presents the relationship between T.T. and demand for different number of lanes when there is no downstream bottleneck. As shown, there is no significant difference in the T.T. pe r mile between each of the number of lane

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48 configurations. Therefore number of lanes segment is not an importa nt variable in the estimation of T.T. when there is no downstream bottleneck. As shown in the Figure 4-25, the T.T. remains relatively constant with incr easing demand, when there is no reduction in downstream capacity. It should be noted that the demand here and everywhere else in the document refers to vehicles that are attempting to use the facility on a per lane basis. Thus, while testing the impact of number of lanes, demand refers to demand per lane and not the total demand. To find the impact of the number of lanes on T.T. when there is a downstream bottleneck, the number of lanes is varied from 2 lanes to 4 lanes and the relationship between T.T. and demand for each of the number of lanes is observed. Figure 4-26 presents the relationship between T.T. and demand for different number of lanes when there is a downstream bottleneck. As shown, there is no significant difference in the T.T. per mile between each of the number of lane configurations. Therefore number of lanes segment is not an important variable in the estimation of T.T. when there is a downstr eam bottleneck. As shown in the Figure 4-26, once demand reaches downstream capacity, T.T. starts to linearly increase with demand and then the relationship flattens out to a maximum valu e of T.T. (at approximately 2,250 veh/ln). To find the impact of length of the entry segm ent on T.T. per mile of merge segment, the length of the entry segment is varied from 500 ft to 10,000ft and for each length we plot the graph between T.T. and demand, as shown in Figure 4-27. As shown, there is no significant variation in T.T. per mile for different seri es of length of the entry segment when the downstream segment has no reduction in capacity. This trend is observed because when the downstream segment has no reduction in capacity, uncongested conditions prevail in the merge segment. Thus the T.T. increases with length of the entry segment almost linearly, which results in a constant T.T. per mile for diffe rent lengths of the entry segment.

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49 To find the impact of length of the entry segm ent on T.T. per mile of merge segment when there is a downstream bottleneck, the length of the entry segment is varied from 500 ft to 10,000ft and for each length we plot the graph be tween T.T. and demand, as shown in Figure 428. As shown in Figure 4-28, there is significant variation in T.T. pe r mile for different series of length of the entry segment when the downstream segment has a reduction in capacity. As shown in the Figure 4-28, the T.T. remains relative ly constant until demand reaches downstream capacity. Once demand reaches downstream capacity, T.T. starts to linearly increase with demand and then the relationship flattens out to a maximum value of T.T. (at approximately 2,250 veh/ln) The downstream capacity is further reduced to 1324 veh/hr/ln and th e relationship between T.T. and demand for different le ngths of the entry segment is presented in Figure 4-29. As shown, there is significant difference in the T.T. per mile between each of the lengths of the entry segment. Therefore length of the entry segmen t is an important variable in the estimation of T.T. when there is a downstream bottleneck. As shown in the Figure 4-29, once demand reaches downstream capacity, T.T. starts to linearly increase with de mand and then the relationship flattens out to a maximum value of T.T. (at approximately 2,000 veh/ln). To find the impact of the number of vehicles in the is a downstream bottleneck on the T.T. of the downstream bottleneck, a particular co mbination of demand and downstream segment capacity values are chosen such that a queue is formed after the simulation is run for a while. As shown in the Figure 4-30, the T.T. per of the dow nstream bottleneck closely follows the trend of the number of vehicles in the downstream bottleneck. Therefore the number of vehicles in the downstream bottleneck is found to be an important variable in the estimati on of T.T. within the downstream bottleneck when ther e is a downstream bottleneck. As shown in the Figure 4-30,

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50 once downstream bottleneck gets saturated with traffic, T.T. starts to flatten out to a maximum value of T.T. To find the impact of the number of vehicles in the is a upstream se gment on the T.T. of the upstream segment, a particular combina tion of demand and downs tream segment capacity values are chosen such that a queue is formed af ter the simulation is run for a while. As shown in the Figure 4-31, the T.T. per of the upstream segm ent closely follows the trend of the number of vehicles in the downstream bottleneck. Therefore the number of vehicles in the upstream segment is found to be an important variable in the estimation of T.T. within the upstream segment when there is a upstream segment. As shown in the Figure 4-31, once upstream segment gets saturated with traffic, T.T. starts to flatten out to a maximum value of T.T. Summary: Based on the investigation made from the plots (Figure 4-17 to Figure 4-40) describing the variation of T.T. with several factors, the following observations were made: 1) The variation of T.T. with demand has a st ep curve (Figure 4-17) as opposed to the popular exponentially in creasing curve (as in BPR or MT C models). The step curve can be characterized by two points; (1) when de mand equals downstream segment, until this point the T.T. remains relatively constant and after this point the T.T. suddenly starts to increase at an exponential rate (2) when the exponentially increasing T.T. suddenly starts to flatten and reaches a maximum T.T. A lthough the shape of the T.T. plot against demand is relatively similar when the demand is less than the capacity, the shape differs significantly in the congested region. While the traditional models predict exponentially increasing T.T.s once the demand exceeds capac ity, the analysis conducted in this study suggests that the T.T. curve flat tens after a part icular point. 2) Capacity of the downstream se gment plays a key role in the prediction of T.T. The variation of T.T. with demand varies si gnificantly depending on whether the demand is greater than or less than the downstream capac ity (Figure 4-18). Thus the impact of all other variables is broken-down into 3 cases : (1) when there is a downstream bottleneck (2) when there is no downstream bottleneck. 3) FFS shows up significant variat ion in T.T. when there is no downstream bottleneck (Figure 4-19). However if there is a downstream bottleneck, it is found that as the FFS increases, the T.T. per mile increases until the demand reaches downstream segment capacity. Once demand reaches downstream segment capacity, congestion starts to occur and vehicles can no longer travel at free flow conditions. Thus the FFS no longer impacts the T.T. (Figure 4-20 & Figure 4-21).

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51 4) On-ramp demand doesnt show up significant variation in T.T. when there is no downstream bottleneck (Figure 4-22). However if there is a downstream bottleneck, it is observed that T.T. per mile at a given demand is different for different values of on-ramp demand (Figure 4-23 & Figure 4-24). Moreover it is also observed that this difference in T.T. (for different values of on ramp demand) keeps increasing with demand until the demand reaches downstream capacity. Once the demand reaches the downstream capacity the difference in T.T. per mile (for different values of on-ramp demand) remains fixed with demand. It is also observed that th e T.T. per mile is higher for higher on-ramp demand. 5) Length of the entry segment doesnt show up si gnificant variation in T.T. per mile when there is no downstream bottleneck (Figure 4-28). However, it is found that the length of the entry segment is an important variable when there is no downstream bottleneck, as shown in Figure 4-29 and Figure 4-30. It is observed from Figure 4.29 that the T.T. per mile decreases with increase in length of the segment. This phenomenon can be explained as follows: when the segment length is large the queuing of vehicles is mostly concentrated at the downstream end of the se gment, leaving the upstream segment at free flow conditions. As the segment length increase s, the section with free flow conditions increase, thus the average speed of the segm ent increases and in-turn the T.T. decreases as shown in Figure 4-29 and Figure 4-30 6) The number of lanes does not have a significan t impact on T.T. neither when there is no downstream bottleneck nor when there is a downstream bottl eneck (Figure 4-10, Figure 4-11, & Figure 4-12) From the simulation analysis in this section, it is observed that vari ation of T.T. with demand primarily depends on whether or not demand exceeds the downstream segment capacity. It is also observed that the im pact of any variable (with the exception of downstream segment capacity) on T.T. of any freeway segment de pends on the downstream segment capacity. 4.2.3 Diverge Segment A sketch of a diverge freeway segm ent is shown in Figure 4-31. The diverge segment network consists of four freeway links and an o ff-ramp link. The first link is the entry link which spans from the beginning of the diverge segment to the start of deceleration lane, as shown in Figure 4-31. The second link is the diverging section, it spans al ong the length of the deceleration lane. The third link is immediately downstream of the diverging section till the exit point of the diverge segment. The fourth and fi nal link is the downstream section, which starts from the exit point of diverge segment and span s for a fixed length (2000 ft). This downstream

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52 segment is used in this study to control the numbe r of vehicles that can move out of the diverge segment, in other words the downstream capacity. This is achieved in the simulation by varying the geometry, traffic control, a nd driver behavior characteristics of the downstream segment. The picture of the diverge freeway segment considered is shown in Figure 4-31. In order to generate the s cenarios for a diverge segment the following values for each variable were chosen. The picture of the Diverg e freeway segment considered is shown in Figure 4-31 A brief description of the va riables considered to devel op scenarios is given below. Demand per lane: Number of vehicles attempting to enter the subject segment. If the demand exceeds capacity then a queue is formed upstream of the entrance of the subject segment. In this case the number of vehicles ac tually entering the segment could be lower than the demand. Eight different values of demand are used, ranging from 1000 veh/hr/ln to 9999 veh/hr/ln. Downstream capacity: The maximum number of vehicl es exiting from the downstream section. Although there is no standa rd procedure to design the dow nstream segment, so that it reaches a particular capacity, five different road configurations were de veloped such that the throughput varies uniformly over a large range of values. FFS: The average speed on a section when there is very low demand. Four different speeds were tested; 55 mph, 60 mph, 65 mph, and 70 mph. Off-Ramp exit %: The fraction of vehicles exiting to o ff ramp at the diverge point. In this study for diverge segment, three different valu es of off-ramp exit % are used: 100, 300, and 500 veh/hr/ln.

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53 Number of lanes: The number of through lanes in each direction. This study tested 2 lane segments, 3 lane segments, and 4 lane segments. Length of the entry segment: The length of freeway secti on located between the entry point of the merge segment to th e beginning of the acceleration lane. The complete set of values tested is in Table 4-9, and scenarios are developed for each combination of these for a diverge segment. The complete set of values tested is shown in Table 4-9, and scenarios are developed for each combination of these for a diverge segment. 6,075 different scenarios were created for merge freeway segment. Each of these scenarios is simulated 10 times and the average travel time density, and number of vehicles exiting the system are computed. The run time for simu lating all of these 6,075 scenarios 10 times was about 150 hrs on a .39 Ghz core 2 duo CPU with 3 GB memory. Preliminary analysis was conducted to evaluate the impacts of each of these variables on the T.T. per mile. It was found that the impact of demand per lane is very significant when the downstream segment has reduced capacity. Figure 4-33 shows that the T.T. remains relatively constant until demand reaches downstream capacity. Once demand reaches downstream capacity, T.T. starts to linearly increase with demand and then th e relationship flattens out to a maximum value of T.T. (at approximately 2,000 veh/ln). To find the impact of downstream capacity on T.T., the downstream capacity is varied from no capacity reduction (2137 veh/hr/ln) to very low capacity (1323 veh/hr/ln). Figure 4-34 presents the relationship between downstream capac ity and T.T. As shown in the previous figure, the T.T. plots consist of three pa rts. In the first part, when demand is lower than the downstream capacity, the relationship between T.T. and demand is relatively flat. In the second part, when

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54 demand exceeds downstream segment, T.T. suddenl y starts increasing linearly with demand. In the third and final part, when demand starts approaching 2250 veh/hr/ln, the linearly increasing T.T. curve flattens out and tends to a constant T.T. As illustrated in Figure 4-34 the downstream capacity has a very significant impact on T.T. Because of the high impact of the reduced dow nstream capacity, the impact of the remaining variables on T.T. is presented in two cases; a) when there is no reduction in capacity of the downstream section and b) when there is redu ction in capacity of th e downstream section. To find the impact of free-flow speed on T.T ., the free-flow speed is varied from 50 mph to 70 mph and the relationship between T.T. a nd demand for each of the free-flow speeds is observed. Figure 4-35 presents the relationship be tween T.T. and demand for different free-flow speeds when there is no downstream bottleneck. As shown there is significant difference in the T.T. per mile between each of the FFS. Therefore FFS is an important vari able in the estimation of T.T. when there is no downstream bottleneck. As the speed increases, the T.T. per mile decreases. When there is no reduction in downstream segment capacity, with higher FFS the vehicles can travel faster and the T.T. decrease s. The relationship between T.T. and demand is a set of parallel lines, one for each speed. The T. T. linearly increases, by a very minimal value, with increase in demand. To find the impact of free-flow speed on T.T. when there is a downstream bottleneck, the free-flow speed is varied from 50 mph to 70 mph and the relationship between T.T. per mile and demand is observed for each of these FFS. Figure 4-36 presents the relationship between T.T. and demand for different free-flow speeds when the downstream segment has reduced capacity equal to 1689 veh/hr/ln. As shown, the FFS increase s, the difference in T.T. per mile between each of the FFS decreases until the demand r eaches the downstream segment capacity. Once

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55 demand reaches downstream segment capacity, conge stion starts to occur and vehicles can no longer travel at free flow conditions Thus there is no change in T. T. with increase in FFS. As shown in the Figure 4-36, once demand reaches do wnstream capacity, T.T. starts to linearly increase with demand and then the relationship flattens out to a maximum value of T.T. (at approximately 2,000 veh/ln). The downstream capacity is further reduced to 1324 veh/hr/ln and th e relationship between T.T. and demand for different free-flow speeds is presented in Figure 4-37. As shown, once demand reaches downstream segment capacity, conge stion starts to occur and vehicles can no longer travel at free-flow conditions In these cases there is no change in T.T. with increase in free-flow speed. As shown in the Figure 4-37, once demand reaches downstream capacity, T.T. starts to linearly increase with demand and then the relationship flattens out to a maximum value of T.T. To find the impact of percentage of vehicles exiting through off ramp on T.T., the exit percentage is varied from 5 % to 20 % and the relationship between T.T. and demand for each of the exit percentages is observed. Figure 4-38 pr esents the relationship between T.T. and demand for different exit percentages when there is no downstream bottleneck. As shown, there is no significant difference in the T.T. per mile betw een each of the exit percentages. Therefore exit percentage is not an important variable in the estimation of T.T. when there is no downstream bottleneck. As shown in the Figure 4-38, the T.T. remains relatively constant with increasing demand, when there is no reduction in downstream capacity. To find the impact of percentage of vehicles exiting through off ramp on T.T. when there is a downstream bottleneck, the exit percentage is varied from 5 % to 20 % and the relationship between T.T. and demand for each of the exit pe rcentages is observed. Figure 4-39 presents the

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56 relationship between T.T. and demand for diffe rent exit percentages, when the downstream segment has reduced capacity equal to 1689 veh/hr/ln. As shown, as the exit percentage increases, the difference in T.T. per mile between each of the exit percentages decreases until the demand reaches the downstream segment capacity. As shown in the Figure 4-39, once demand reaches downstream capacity, T.T. starts to linearly increase with demand and then the relationship flattens out to a maximum valu e of T.T. (at approximately 2,000 veh/ln). The downstream capacity is further reduced to 1324 veh/hr/ln and th e relationship between T.T. and demand for different exit percentages is presented in Figure 4-40. As shown, there is no change in T.T. with increas e in exit percentage. As shown in the Figure 4-40, once demand exceeds downstream capacity, T.T. curve flat tens out to a maximum value of T.T. To find the impact of length of entry segment on T.T., the length of entry segment is varied from 500 ft to 10,000 ft and the relationship between T.T. and demand for each of the length of entry segment is observed. Figure 4-41 presents the relationship between T.T. and demand for different lengths of entry segments when there is no downstream bottleneck. As shown there is no significant difference in the T.T. per mile between each of the length of entry segment. Therefore length of entry segment is not an impor tant variable in the es timation of T.T. when there is no downstream bottleneck. The relationship between T.T. and demand is a set of parallel lines, one for each length of entry segment. The T.T. linearly increases, by a very minimal value, with increase in demand. To find the impact of the length of the entry segment on T.T. when there is a downstream bottleneck, the length of the entry segment is vari ed from 500 ft to 10,000 ft and the relationship between T.T. per mile and demand is observed for each of these lengths of the entry segment. Figure 4-42 presents the relationship between T.T. and demand for different lengths of entry

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57 segment when the downstream segment has reduced capacity equal to 1689 veh/hr/ln. As shown, there is significant difference in the T.T. per m ile between each of th e lengths of the entry segment. Therefore the length of the entry segment is an importan t variable in the estimation of T.T. when there is a downstream bottleneck. As shown in the Figure 4-42, the T.T. per mile decreases with increasing length of the segment. When the segment is very long the queuing of vehicles is mostly concentrated at the downstream end of the segment, with the upstream part operating at free flow conditions. As the segment length increases, the section with free flow conditions increase, thus the average speed of the segment increases and in-turn the T.T. decreases as shown in Figure 4-42. As shown in the Figure 4-42, once demand reaches downstream capacity, T.T. starts to linearly increase with de mand and then the relationship flattens out to a maximum value of T.T. (at approximately 2,000 veh/ln). The downstream capacity is further reduced to 1324 veh/hr/ln and th e relationship between T.T. and demand for different le ngths of the entry segment is presented in Figure 4-43. As shown, there is significant difference in the T.T. per mile between each of the lengths of the entry segment. Therefore length of the entry segmen t is an important variable in the estimation of T.T. when there is a downstream bottleneck. As shown in the Figure 4-43, once demand reaches downstream capacity, T.T. starts to linearly increase with de mand and then the relationship flattens out to a maximum value of T.T. (at approximately 2,000 veh/ln). To find the impact of number of lanes on T.T. when there is no downstream bottleneck, the number of lanes is varied from 2 lanes to 4 lanes and the relationship between T.T. and demand for each of the number of lanes is observed. Figu re 4-44 presents the relationship between T.T. and demand for different number of lanes when there is no downstream bottleneck. As shown, there is no significant difference in the T.T. pe r mile between each of the number of lane

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58 configurations. Therefore number of lanes segment is not an importa nt variable in the estimation of T.T. when there is no downstream bottleneck. As shown in the Figure 4-44, the T.T. remains relatively constant with incr easing demand, when there is no reduction in downstream capacity. It should be noted that the demand here and everywhere else in the document refers to vehicles that are attempting to use the facility on a per lane basis. Thus, while testing the impact of number of lanes, demand refers to demand per lane and not the total demand. To find the impact of number of lanes on T.T. when there is a downstream bottleneck, the number of lanes is varied from 2 lanes to 4 lanes and the relationship between T.T. and demand for each of the number of lanes is observed. Figu re 4-45 presents the relationship between T.T. and demand for different number of lanes when there is a downstream bottleneck. As shown, there is no significant difference in the T.T. pe r mile between each of the number of lane configurations. Therefore number of lanes segment is not an importa nt variable in the estimation of T.T. when there is a downstream bottlenec k. As shown in the Figure 4-45, the T.T. remains relatively constant with increas ing demand, when there is redu ction in downstream capacity. To find the impact of the number of vehicles in the is a downstream bottleneck on the T.T. of the downstream bottleneck, a particular co mbination of demand and downstream segment capacity values are chosen such that a queue is formed after the simulation is run for a while. As shown in the Figure 4-46, the T.T. per of the dow nstream bottleneck closely follows the trend of the number of vehicles in the downstream bottleneck. Therefore the number of vehicles in the downstream bottleneck is found to be an important variable in the estimati on of T.T. within the downstream bottleneck when ther e is a downstream bottleneck. As shown in the Figure 4-46, once downstream bottleneck gets saturated with traffic, T.T. starts to flatten out to a maximum value of T.T.

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59 To find the impact of the number of vehicles in the is a upstream se gment on the T.T. of the upstream segment, a particular combina tion of demand and downs tream segment capacity values are chosen such that a queue is formed af ter the simulation is run for a while. As shown in the Figure 4-47, the T.T. per of the upstream segm ent closely follows the trend of the number of vehicles in the downstream bottleneck. Therefore the number of vehicles in the upstream segment is found to be an important variable in the estimation of T.T. within the upstream segment when there is a upstream segment. As shown in the Figure 4-47, once upstream segment gets saturated with traffic, T.T. starts to flatten out to a maximum value of T.T. Summary: Based on the investigation made from the plots (Figure 4-32 to Figure 4-47) describing the variation of T.T. with several factors, the following observations were made: 1) The variation of T.T. with demand has a st ep curve (Figure 4-33) as opposed to the popular exponentially in creasing curve (as in BPR or MT C models). The step curve can be characterized by two points; (1) when de mand equals downstream segment, until this point the T.T. remains relatively constant and after this point the T.T. suddenly starts to increase at an exponential rate (2) when the exponentially increasing T.T. suddenly starts to flatten and reaches a maximum T.T. A lthough the shape of the T.T. plot against demand is relatively similar when the demand is less than the capacity, the shape differs significantly in the congested region. While the traditional models predict exponentially increasing T.T.s once the demand exceeds capac ity, the analysis conducted in this study suggests that the T.T. curve flat tens after a part icular point. 2) Capacity of the downstream segment plays a key role in the prediction of T.T. The variation of T.T. with demand varies sign ificantly depending on whether the demand is greater than or less than the downstream cap acity (Figure 4-34). Thus the impact of all other variables is broken-down into 3 cases: (1) when there is no downstream bottleneck (2) when there is a downstream bottleneck. 3) FFS shows up significant variation in T.T. when there is no reduction in capacity of the downstream segment (Figure 4-35). However if there is a downstream bottleneck, it is found that as the FFS increases, the T.T. pe r mile increases until the demand reaches downstream segment capacity, as sh own in Figure 4-36 & Figure 4-37. 4) Off-ramp exit % shows up no signi ficant variation in T.T. wh en there is no downstream bottleneck (Figure 4-38). Thus off-ramp ex it % is not an important variable in the estimation of T.T. when there is no downst ream bottleneck. However when there is a downstream bottleneck, it is observ ed that T.T. per mile at a given demand is different for different values of off-ramp exit %. Moreover it is also observed that this difference in T.T. (for different values of off-ramp exit %) keeps increasing with demand until the

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60 demand reaches downstream capacity. Once the demand reaches the downstream capacity the difference in T.T. per mile (for di fferent values of off -ramp exit %) starts to decrease until it reaches the cap acity of the diverge segment and then remains fixed with demand. It is also observed that the T.T. per mile is higher for lower off-ramp exit %. When the downstream segment has full reduction in capacity, it is f ound that for a given off-ramp exit %, there is no change in T.T. per mile with main line demand, as shown in Figure 4-40. Moreover at any given main line demand value the value of T.T. per mile is lower for higher off-ramp exit %. 5) Length of the entry segment doesnt show up si gnificant variation in T.T. when there is no downstream bottleneck (Figure 4-41). However if when there is a downstream bottleneck, it is found th at the length of the entry segment is an important variable when the downstream segment has reduced capacity as shown in Figure 4-42 and Figure 4-43. It is observed from Figure 4-43 th at the T.T. per mile decreases with increase in length of the segment. This phenomenon can be explained as follows: when the segment length is large the queuing of vehicles is mostly concentrated at the downstream end of the segment, leaving the upstream segment at free flow conditions. As the segment length increases, the section with fr ee flow conditions in creases, thus the av erage speed of the segment increases and in-turn the T.T. per mile decreases as shown in Figure 4-42. 6) The number of lanes shows no significant imp act on T.T. independent of the downstream bottleneck (Figure 4-44, & Figure 4-45) 4.2.4 Weaving segment The weaving segm ent network developed for tes ting consists of four freeway links and two ramp links. The first link is the entry link, that spans from the beginning of the weaving segment to the point where the ramp meets the freeway, as shown in Figure 4-47. The second link is the weaving section, where weaving takes place. Th e third link is immediately downstream of the weaving section till the exit point of the weav ing segment. The fourth and final link is the downstream section, which starts from the exit po int of weaving segment and extends for a fixed length (2000 ft). This downstream segment is used in this study to control the number of vehicles that can move out of the diverge segment, in other words the downstream capacity. This is achieved in the simulation by varying the geomet ry, traffic control, and driver behavior characteristics of the downstream segment.

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61 A brief description of the va riables considered to devel op scenarios is given below. Demand per lane: Number of vehicles attempting to enter the subject segment. If the demand exceeds capacity then a queue is formed upstream of the entrance of the subject segment. In this case the number of vehicles ac tually entering the segment could be lower than the demand. Eight different values of demand are used, ranging from 1000 veh/hr/ln to 9999 veh/hr/ln. Downstream capacity: The maximum number of vehicl es exiting from the downstream section. Although there is no standa rd procedure to design the dow nstream segment, so that it reaches a particular capacity, five different road configurations were de veloped such that the throughput varies uniformly over a large range of values. FFS: The average speed on a section when there is very low demand. Four different speeds were tested; 55 mph, 60 mph, 65 mph, and 70 mph. Off-Ramp exit %: The fraction of vehicles exiting to o ff ramp at the diverge point. In this study for diverge segment, three different valu es of off-ramp exit % are used: 100, 300, and 500 veh/hr/ln. Number of lanes: The number of through lanes in each direction. This study tested 2 lane segments, 3 lane segments, and 4 lane segments. Length of the entry segment: The length of freeway secti on located between the entry points of the merge segment to th e beginning of the acceleration lane. The complete set of values tested is in Table 4-11, and scenarios are developed for each combination of these for a weaving segment. The complete set of values tested is shown in Table 4-11, and scenarios are developed for each combination of these for a weaving segment. In order to generate th e scenarios for weaving

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62 segment the following values for each variable were chosen.30,375 different scenarios were created for weaving freeway segment. Each of these scenarios is simulated 10 times and the average travel time, density, and number of vehi cles exiting the system are computed. The run time for simulating all of these 30,375 scenarios 10 times was about 400 hrs on a .39 Ghz core 2 duo CPU with 3 GB memory. Preliminary analysis was conducted to evaluate the impacts of each of these variables on the T.T. per mile. It was found that the impact of demand per lane is very significant when the downstream segment has reduced capacity. Figure 4-48 shows that the T.T. remains relatively constant until demand reaches downstream capacity. Once demand reaches downstream capacity, T.T. starts to linearly increase with demand and then th e relationship flattens out to a maximum value of T.T. (at approximately 2,000 veh/ln). To find the impact of downstream capacity on T.T., the downstream capacity is varied from no capacity reduction (2209 veh/hr/ln) to very low capacity (1326 veh/hr/ln). Figure 4-49 presents the relationship between downstream capac ity and T.T. As shown in the previous figure, the T.T. plots consist of three pa rts. In the first part, when demand is lower than the downstream capacity, the relationship between T.T. and demand is relatively flat. In the second part, when demand exceeds downstream segment, T.T. suddenl y starts increasing linearly with demand. In the third and final part, when demand starts approaching 2250 veh/hr/ln, the linearly increasing T.T. curve flattens out and tends to a constant T.T. As illustrated in Figure 4-49 the downstream capacity has a very significant impact on T.T. Because of the high impact of the reduced dow nstream capacity, the impact of the remaining variables on T.T. is presented in two cases; a) when there is no reduction in capacity of the downstream section and b) when there is redu ction in capacity of th e downstream section.

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63 To find the impact of free-flow speed on T.T., th e free-flow speed is varied from 50 mph to 70 mph and the relationship between T.T. and demand for each of the free-flow speeds is observed. Figure 4-50 presents the relationship be tween T.T. and demand for different free-flow speeds when there is no downstream bottleneck. As shown there is significant difference in the T.T. per mile between each of the FFS. Therefore FFS is an important vari able in the estimation of T.T. when there is no downstream bottleneck. As the speed increases, the T.T. per mile decreases. When there is no reduction in downstream segment capacity, with higher FFS the vehicles can travel faster and the T.T. decrease s. The relationship between T.T. and demand is a set of parallel lines, one for each speed. The T. T. linearly increases, by a very minimal value, with increase in demand. To find the impact of free-flow speed on T.T. when there is a downstream bottleneck, the free-flow speed is varied from 50 mph to 70 mph and the relationship between T.T. per mile and demand is observed for each of these FFS. Figure 4-51 presents the relationship between T.T. and demand for different free-flow speeds when the downstream segment has reduced capacity equal to 1696 veh/hr/ln. As shown, the FFS increase s, the difference in T.T. per mile between each of the FFS decreases until the demand r eaches the downstream segment capacity. Once demand reaches downstream segment capacity, conge stion starts to occur and vehicles can no longer travel at free flow conditions Thus there is no change in T. T. with increase in FFS. As shown in the Figure 4-51, once demand reaches do wnstream capacity, T.T. starts to linearly increase with demand and then the relationship flattens out to a maximum value of T.T. (at approximately 2,000 veh/ln) The downstream capacity is further reduced to 1326 veh/hr/ln and th e relationship between T.T. and demand for different free-flow speeds is presented in Figure 4-52. As shown, once

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64 demand reaches downstream segment capacity, conge stion starts to occur and vehicles can no longer travel at free-flow conditions In these cases there is no change in T.T. with increase in free-flow speed. As shown in the Figure 4-52, once demand reaches downstream capacity, T.T. starts to linearly increase with demand and then the relationship flattens out to a maximum value of T.T. To find the impact of percentage of vehicles exiting through off ramp on T.T., the exit percentage is varied from 5 % to 15 % and the re lationship between T.T. and demand for each of the exit percentages is observed. Figure 4-53 pr esents the relationship between T.T. and demand for different exit percentages when there is no downstream bottleneck. As shown, there is no significant difference in the T.T. per mile betw een each of the exit percentages. Therefore exit percentage is not an important variable in the estimation of T.T. when there is no downstream bottleneck. As shown in the Figure 4-53, the T.T. remains relatively constant with increasing demand, when there is no reduction in downstream capacity. To find the impact of percentage of vehicles exiting through off ramp on T.T. when there is a downstream bottleneck, the exit percentage is varied from 5 % to 15 % and the relationship between T.T. and demand for each of the exit pe rcentages is observed. Figure 4-54 presents the relationship between T.T. and demand for diffe rent exit percentages, when the downstream segment has reduced capacity equal to 1696 veh/hr/ln. As shown in Figure 4-54, there is no significant impact of exit percentage on travel time per mile until demand reaches downstream segment capacity. Once demand exceeds downstr eam segment capacity, exit percentage has significant impact on travel time per mile. As shown in Figure 4-54, once demand reaches downstream capacity, T.T. starts to linearly increase with de mand and then the relationship flattens out to a maximum value of T.T. (at approximately 2,000 veh/ln).

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65 The downstream capacity is further reduced to 1326 veh/hr/ln and th e relationship between T.T. and demand for different exit percentages is presented in Figure 4-55. As shown in Figure 4-55, there is no significant impact of exit percentage on travel time per mile until demand reaches downstream segment capacity. Once de mand exceeds downstream segment capacity, exit percentage has significant impact on travel time per mile. As shown in Figure 4-55, once demand exceeds downstream capacity, T.T. starts to linearly increase with demand and then the relationship flattens out to a maximum valu e of T.T. (at approximately 2,000 veh/ln). To find the impact of length of entry segment on T.T., the length of entry segment is varied from 500 ft to 10,000 ft and the relationship between T.T. and demand for each of the length of entry segment is observed. Figure 4-56 presents the relationship between T.T. and demand for different lengths of entry segments when there is no downstream bottleneck. As shown in Figure 4-56, there is no significant difference in the T.T. per mile between each of the length of entry segment. Therefore length of entry segment is not an important variable in the estimation of T.T. when there is no downstream bottleneck. The relationship between T.T. and demand is a set of parallel lines, one for each length of entry segment. The T.T. linearly increases, by a very minimal value, with increase in demand. To find the impact of the length of the entry segment on T.T. when there is a downstream bottleneck, the length of the entry segment is vari ed from 500 ft to 10,000 ft and the relationship between T.T. per mile and demand is observed for each of these lengths of the entry segment. Figure 4-57 presents the relationship between T.T. and demand for different lengths of entry segment when the downstream segment has reduced capacity equal to 1696 veh/hr/ln. As shown in Figure 4-57, there is no significa nt impact of lengths of the entry segment on travel time per mile until demand reaches downstream segment capacity. Once demand exceeds downstream

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66 segment capacity, length of the entry segment has significant impact on travel time per mile. Therefore the length of the entry segment is an im portant variable in the estimation of T.T. when there is a downstream bottleneck. As shown in th e Figure 4-57, the T.T. per mile decreases with increasing length of the segment. When the segm ent is very long the queuing of vehicles is mostly concentrated at the downstream end of th e segment, with the upstream part operating at free flow conditions. As the segment length increa ses, the section with free flow conditions increase, thus the average speed of the segment increases and in-turn the T.T. decreases as shown in Figure 4-57. As shown in the Figure 4-57, once demand reaches downstream capacity, T.T. starts to linearly increase with demand and then the relationship flattens out to a maximum value of T.T. (at approximately 2,000 veh/ln). The downstream capacity is further reduced to 1326 veh/hr/ln and th e relationship between T.T. and demand for different le ngths of the entry segment is presented in Figure 4-58. As shown, there is significant difference in the T.T. per mile between each of the lengths of the entry segment. Therefore length of the entry segmen t is an important variable in the estimation of T.T. when there is a downstream bottleneck. As shown in the Figure 4-58, once demand reaches downstream capacity, T.T. starts to linearly increase with de mand and then the relationship flattens out to a maximum value of T.T. (at approximately 2,000 veh/ln). To find the impact of number of lanes on T.T. when there is no downstream bottleneck, the number of lanes is varied from 2 lanes to 4 lanes and the relationship between T.T. and demand for each of the number of lanes is observed. Figu re 4-59 presents the relationship between T.T. and demand for different number of lanes when there is no downstream bottleneck. As shown, there is no significant difference in the T.T. pe r mile between each of the number of lane configurations. Therefore number of lanes segment is not an importa nt variable in the estimation

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67 of T.T. when there is no downstream bottleneck. As shown in the Figure 4-59, the T.T. remains relatively constant with incr easing demand, when there is no reduction in downstream capacity. It should be noted that the demand here and everywhere else in the document refers to vehicles that are attempting to use the facility on a per lane basis. Thus, while testing the impact of number of lanes, demand refers to demand per lane and not the total demand. To find the impact of number of lanes on T.T. when there is a dow nstream bottleneck, the number of lanes is varied from 2 lanes to 4 lanes and the relationship between T.T. and demand for each of the number of lanes is observed. Figu re 4-60 presents the relationship between T.T. and demand for different number of lanes when there is a downstream bottleneck. As shown, there is no significant difference in the T.T. pe r mile between each of the number of lane configurations. Therefore number of lanes segment is not an importa nt variable in the estimation of T.T. when there is a downstream bottlenec k. As shown in the Figure 4-60, the T.T. remains relatively constant with increas ing demand, when there is redu ction in downstream capacity. To find the impact of on-ramp demand on T.T., the length ramp-demand is varied from 100 veh/hr/ln to 500 veh/hr/ln and the relationship between T.T. and demand for each value of on-ramp demand is observed. Figure 4-61 presents the relationship between T.T. and demand for different on-ramp demand when there is no downstream bottleneck. As shown, there is no significant difference in the T.T. per mile be tween each of the on-ramp demands. Therefore onramp demand is not an important variable in the estimation of T.T. when there is no downstream bottleneck. To find the impact of on-ramp demand on T.T. when there is a downstream bottleneck, the ramp-demand is varied from 100 veh/hr/ln to 500 veh/hr/ln and th e relationship between T.T. and demand for each value of on-ramp demand is observed. Figure 4-62 presents the relationship

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68 between T.T. and demand for different on-ramp demand when there is a downstream bottleneck. As shown, there is no significant difference in th e T.T. per mile between each of the on-ramp demands. Therefore on-ramp demand is not an impor tant variable in the estimation of T.T. when there is no downstream bottleneck. The downstream capacity is further reduced to 1324 veh/hr/ln and th e relationship between T.T. and demand for different on-ramp demands is presented in Figure 4-63. As shown, as the FFS increases, the difference in T.T. per mile between each of the on-ramp demand starts increasing after the demand reaches downstream se gment capacity. As shown in the Figure 4-63, once demand reaches downstream capacity, T.T. star ts to linearly increase with demand and then the relationship flattens out to a maximum va lue of T.T. (at approximately 2,000 veh/ln). To find the impact of the number of vehicles in the is a downstream bottleneck on the T.T. of the downstream bottleneck, a particular co mbination of demand and downstream segment capacity values are chosen such that a queue is formed after the simulation is run for a while. As shown in the Figure 4-64, the T.T. per of the dow nstream bottleneck closely follows the trend of the number of vehicles in the downstream bottleneck. Therefore the number of vehicles in the downstream bottleneck is found to be an important variable in the estimati on of T.T. within the downstream bottleneck when ther e is a downstream bottleneck. As shown in the Figure 4-64, once downstream bottleneck gets saturated with traffic, T.T. starts to flatten out to a maximum value of T.T. To find the impact of the number of vehicles in the is a upstream se gment on the T.T. of the upstream segment, a particular combina tion of demand and downs tream segment capacity values are chosen such that a queue is formed af ter the simulation is run for a while. As shown in the Figure 4-65, the T.T. per of the upstream segm ent closely follows the trend of the number of

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69 vehicles in the downstream bottleneck. Therefore the number of vehicles in the upstream segment is found to be an important variable in the estimation of T.T. within the upstream segment when there is a upstream segment. As shown in the Figure 4-65, once upstream segment gets saturated with traffic, T.T. starts to flatten out to a maximum value of T.T. Summary: Based on the investigation made from the plots (Figure 4-48 to Figure 4-65) describing the variation of T.T. with several factors, the following observations were made: 1) The variation of T.T. with demand has a st ep curve (Figure 4-48) as opposed to the popular exponentially in creasing curve (as in BPR or MT C models). The step curve can be characterized by two points; (1) when de mand equals downstream segment, until this point the T.T. remains relatively constant and after this point the T.T. suddenly starts to increase at an exponential rate (2) when the exponentially increasing T.T. suddenly starts to flatten and reaches a maximum T.T. A lthough the shape of the T.T. plot against demand is relatively similar when the demand is less than the capacity, the shape differs significantly in the congested region. While the traditional models predict exponentially increasing T.T.s once the demand exceeds capac ity, the analysis conducted in this study suggests that the T.T. curve flat tens after a part icular point. 2) Capacity of the downstream segment plays a key role in the prediction of T.T. The variation of T.T. with demand varies sign ificantly depending on whether the demand is greater than or less than the downstream cap acity (Figure 4-49). Thus the impact of all other variables is broken-down into 3 cases: (1) when there is no downstream bottleneck (2) when there is a downstream bottleneck. 3) FFS shows up significant variation in T.T. when there is no reduction in capacity of the downstream segment (Figure 4-50). However if there is a downstream bottleneck, it is found that as the FFS increases, the T.T. pe r mile increases until the demand reaches downstream segment capacity, as show n in Figure 4-51 and Figure 4-52. 4) Off-ramp exit % shows up no signi ficant variation in T.T. wh en there is no downstream bottleneck (Figure 4-53). Thus off-ramp ex it % is not an important variable in the estimation of T.T. when there is no downst ream bottleneck. However when there is a downstream bottleneck, it is observ ed that T.T. per mile at a given demand is different for different values of off-ramp exit %. Moreover it is also observed that this difference in T.T. (for different values of off-ramp exit %) keeps increasing with demand until the demand reaches downstream capacity. Once the demand reaches the downstream capacity the difference in T.T. per mile (for di fferent values of off -ramp exit %) starts to decrease until it reaches the cap acity of the diverge segment and then remains fixed with demand. It is also observed that the T.T. per mile is higher for lower off-ramp exit %. When the downstream segment has full reduction in capacity, it is f ound that for a given off-ramp exit %, there is no change in T.T. per mile with main line demand, as shown in

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70 Figure 4-54 and Figure 4-55. More over at any given main line demand value the value of T.T. per mile is lower for higher off-ramp exit %. 5) Length of the entry segment doesnt show up si gnificant variation in T.T. when there is no downstream bottleneck (Figure 4-56). However if when there is a downstream bottleneck, it is found th at the length of the entry segment is an important variable when the downstream segment has reduced capacity as shown in Figure 4-57 and Figure 4-58. It is observed from Figure 4-58 th at the T.T. per mile decreases with increase in length of the segment. This phenomenon can be explained as follows: when the segment length is large the queuing of vehicles is mostly concentrated at the downstream end of the segment, leaving the upstream segment at free flow conditions. As the segment length increases, the section with fr ee flow conditions in creases, thus the av erage speed of the segment increases and in-turn the T.T. per mile decreases as shown in Figure 4-58. 6) The number of lanes shows no significant imp act on T.T. independent of the downstream bottleneck (Figure 4-59, & Figure 4-60)

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71 Table 4-1. Range of values for each variable that may affect T.T. along basic freeway segments Variable Minimum value Maximum value Number of Lanes 2 4 Demand/lane on Main line 1000 9999 (veh/hr) Speed 55 70 (mph) Length of Segment 5000 (ft) 25,000 (ft) Capacity of Downstream Segment No blockage 1 Lane blocked and 95% rubber necking factor for rest of the lanes Table 4-2. Range of values for each variable that may affect T.T. along merge segment Variable Minimum value Maximum value Number of Lanes 2 5 Demand on Main line 1000 9999 (veh/hr) Demand on Ramp 100 500 (veh/hr) Speed 50 70 (mph) Distance from link start to the On-ramp location 1500 3000 Capacity of Downstream Segment No blockage 1 Lane blocked and 95% rubber necking factor for rest of the lanes Table 4-3. Range of values for each variable that may affect T.T. along diverge segment Variable Minimum value Maximum value Number of Lanes 2 5 Demand on Main line 1000 9999 (veh/hr) Speed 50 70 (mph) Percent of vehicles passing through 80 100 Distance from link start to the On-ramp location 1500 3000 Distance between On-ramp and Offramp 200 2000 (ft) Capacity of Downstream Segment No blockage 1 Lane blocked and 95% rubber necking factor for rest of the lanes Table 4-4. Range of values for each variable in weaving segment Variable Minimum value Maximum value Number of Lanes 2 4 Demand on Main line 1500 9999 (veh/hr) Demand on Ramp 100 500 (veh/hr) Speed 50 70 (mph) Percent of vehicles passing through 80 100 Distance from link start to the On-ramp location 1500 3000 Length of weaving section 500 2500 (ft) Capacity of Downstream Segment No blockage 1 Lane blocked and 99% rubber necking factor for rest of the lanes

PAGE 72

72 Table 4-5. Input values simulate d for basic freeway segments Demand per lane Downstream capacity FFS Length of the segment Number of lanes 1000 No Blockage 55 5000 2 1250 1 Lane Blocked 60 10000 3 1500 1 Lane Blocked and 90% rubber necking factor 65 15000 4 1750 1 Lane Blocked and 95% rubber necking factor 70 20000 2000 FFS of 25 mph 25000 2250 FFS of 15 mph 2500 9999 8 values 5 values 4 valu es 5 values 3 values # Scenarios = 8*5*4*5*3 = 2400 scenarios Table 4-6. Impact of study variables on T.T. of BFS Variable Unrestricted downstream segment capacity Restricted downstream segment capacity FFS Significant Not significant length of BFS Not significant Significant # Lanes Not significant Not significant Demand Significant Significant Downstream Capacity N/A N/A Table 4-7. Input values simulated for a merge segment Freeway demand per lane Downstream Capacity Demand per lane (Ramp) FFS # Lanes Length of the entry section 1000 No Blockage 100 50 2 500 1200 1 Lane Blocked 300 60 3 1000 1400 1 Lane Blocked and 90% rubber necking factor 500 70 4 1500 1500 FFS of 20 mph 2500 1600 FFS of 10 mph 5000 1800 2000 2500 3000 9 values 5 values 3 values 3 values 3 values 5 values Scenarios = 9*5*3*3*3*5 = 6075 scenarios

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73 Table 4-8. Impact of study variab les on T.T. of merge segment Variable Unrestricted downstream segment capacity Restricted downstream segment capacity Demand per lane (Ramp) Not significant Significant FFS Significant Not significant # Lanes Not significant Not significant Length of the entry section Not significant Significant Demand Significant Significant Downstream Capacity N/A N/A Table 4-9. Input values simu lated for a diverge segment Demand per Lane (main line) (veh/hr/ln) Downstream Capacity (veh/hr/ln) Speed (mph) Off-ramp Exit % # Lanes Length of Entry Segment (ft) 1000 No Blockage 50 5 2 500 1200 1 Lane Blocked 60 10 3 1,000 1400 1 Lane Blocked and 90% rubber necking factor 70 20 4 1,500 1500 FFS of 25 mph 2,500 1600 FFS of 15 mph 5,000 1800 2000 2500 3000 9 values 5 values 3 values 3 values 3 values 5 values # Scenarios = 9*5*3*3*3*5 = 6,075 scenarios Table 4-10. Impact of study variab les on T.T. of diverge segment Variable Unrestricted downstream segment capacity Restricted downstream segment capacity FFS Significant Not significant Off-ramp Exit % Not significant Significant # Lanes Not significant Not significant Length of Entry Segment (ft) Not significant Significant Demand Significant Significant Downstream Capacity N/A N/A

PAGE 74

74 Table 4-11. Variable values for weaving segment Demand/Lane (main line) Demand (Ramp) Off Ramp Demand Length of weaving section Speed # Lanes Length of entry segment 1000 100 85 1000 50 2 500 1200 300 90 1500 60 3 1000 1400 500 95 2000 70 4 1500 1500 750 2500 2500 1600 1000 3000 5000 1800 2000 2500 3000 9 values 5 values 3 values 5 valu es 3 values 3 values 5 values Total Scenarios = 9*5*3*5*3*3*5 = 30,375 scenarios Table 4-12. Impact of study variab les on T.T. of weaving segment Variable Unrestricted downstream segment capacity Restricted downstream segment capacity FFS Significant Not significant Off-ramp Demand Not significant Significant On-ramp Demand Not significant Significant # Lanes Not significant Not significant Length of Entry Segment (ft) Not significant Significant Demand Significant Significant Downstream Capacity N/A N/A Figure 4-1. Picture of a basic freeway segment.

PAGE 75

75 Figure 4-2. Variation of TT per mile with dema nd (lanes = 2, FFS = 50 mph, length of basic freeway segment = 5000 ft, and downs tream capacity = 1515 veh/hr/lane) Figure 4-3. Variation of TT per mile with dema nd for various values of downstream capacity (lanes = 2, length of basic freeway segment = 5000 ft and FFS is 55 mph) 0 50 100 150 200 250 300 350 400 10001250150017502000225025009999TT/mile (sec/mi)Demand per lane (veh/hr/lane) 0 100 200 300 400 500 600 700 800 900 1000 10001250150017502000225025009999TT/mile (sec/mi)Demand per lane (veh/hr/lane) Downstream Capacity 2138 2008 1515 1112 848

PAGE 76

76 Figure 4-4. Variation of TT per mile with demand for different values of speed (Lanes = 2, length of basic freeway Segment = 5000 ft, and downstream capacity = 2250 veh/hr/lane) Figure 4-5. Variation of TT per mile with different values of speed (lanes = 2, length of basic freeway segment = 5000 ft and dow nstream capacity = 1324 veh/hr/lane) 0 10 20 30 40 50 60 70 80 10001250150017502000225025009999TT/mile (sec/mi)Demand per lane (veh/hr/lane) 55 mph 60 mph 65 mph 70 mph 0 100 200 300 400 500 600 10001250150017502000225025009999TT/mile (sec/mi)Demand per lane (veh/hr/lane) 55 mph 60 mph 65 mph 70 mph

PAGE 77

77 Figure 4-6. Variation of TT per mile with different values of speed (lanes = 2, length of basic freeway segment = 5000 ft and downstream capacity = 849 veh/hr/lane) Figure 4-7. Variation of TT per mile with demand for different lengths of the BFS (lanes = 2, length of basic freeway segment = 5000 ft and downstream capacity = 2250 veh/hr/lane)

PAGE 78

78 Figure 4-8. Variation of TT per mile with demand for different lengths of the BFS (lanes = 2, FFS = 55 mph, and downstream cap acity = 1324 veh/hr/lane) Figure 4-9. Variation of TT per mile with demand for various lengths of the BFS (lanes = 2, FFS = 55 mph, and downstream capacity = 849 veh/hr/lane) 0 100 200 300 400 500 600 10001250150017502000225025004999TT/mile (sec/mi)Demand per lane (veh/hr/lane) Length of BFS = 5000 ft 10000 ft 15000 ft 20000 ft 25000 ft 0 200 400 600 800 1000 1200 10001250150017502000225025004999TT/mile (sec/mi)Demand per lane (veh/hr/lane) Length of BFS = 5000 ft 10000 ft 15000 ft 20000 ft 25000 ft

PAGE 79

79 Figure 4-10. Variation of TT per mile with demand for various values of number of lanes of the BFS (FFS = 55 mph, length of basic freew ay segment = 5000 ft and downstream capacity = 2250 veh/hr/lane) Figure 4-11. Variation of TT per mile with demand for various values of number of lanes of the BFS (FFS = 55 mph, length of basic freew ay segment = 5000 ft and downstream capacity = 850 veh/hr/ane) 0 10 20 30 40 50 60 70 80 10001250150017502000225025009999TT/mile (sec/mi)Demand per lane (veh/hr/lane) 2 Lanes 3 lanes 4 Lanes 0 200 400 600 800 1000 1200 10001250150017502000225025009999TT/mile (sec/mi)Demand per lane (veh/hr/lane) 2 Lanes 3 lanes 4 Lanes

PAGE 80

80 Figure 4-12. Variation of TT per mile with dema nd for the downstream segment with (number of lanes = 2, FFS = 55 mph) Figure 4-13. Variation of TT per mile with dema nd for the downstream segment with (number of lanes = 2, FFS = 55 mph) 0.00 100.00 200.00 300.00 400.00 500.00 600.00 700.00 800.00 900.00 848168821532240TT/mile (sec/mi)Downstream Capacity(veh/hr/lane) 1000 1250 1500 1750 2000 2250 2500 3333 0 100 200 300 400 500 600 700 800 900 10001250150017502000225025004999.5TT/mile (sec/mi)Demand per lane (veh/hr/lane) 2240 2153 1688 848

PAGE 81

81 Figure 4-14. Time series plot between TT per m ile of the downstream bottleneck and the number of vehicles in the downstream bottleneck Figure 4-15. Time series plot between TT per m ile of the upstream segment and the number of vehicles in the upstream segment 0 50 100 150 200 250 300 350 400 450 500 0 100 200 300 400 500 600 700 800 900 1357911131517192123252729313335373941434547495153555759T.T. per mile# minutes since start of simulation TT BK/mi Veh BK 0 200 400 600 800 1000 1200 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 010203040506070T.T. per mile# since start of simulation Veh SS TT SS/mi

PAGE 82

82 Figure 4-16. Sketch of a merge freeway segment. Figure 4-17. Variation of TT per mile with de mand (lanes = 2, FFS = 50 mph, length of entry section = 500 ft, ramp demand = 100 ve h/hr/ln, and downstream capacity = 1689 veh/hr/lane) 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 100012001400150016001800200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane)

PAGE 83

83 Figure 4-18. Variation of TT per mile with de mand (lanes = 2, FFS = 50 mph, length of entry section = 500 ft, and ramp demand = 100 veh/hr/ln) Figure 4-19. Variation of TT per mile with demand for different values of speed (lanes = 2, FFS = 50 mph, length of entry section = 500 ft, and ramp demand = 100 veh/hr/ln, and downstream capacity = 2400 veh/hr/lane) 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00 500.00 100012001400150016001800200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) Downstream Segment Capacity 1324 1689 2155 2481 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100012001400150016001700200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) FFS 50 mph 60 mph 70 mph

PAGE 84

84 Figure 4-20. Variation of TT per mile with demand for different values of speed (lanes = 2, FFS = 50 mph, length of entry section = 500 ft, and ramp demand = 100 veh/hr/ln, and downstream capacity = 1689 veh/hr/lane) Figure 4-21. Variation of TT per mile with demand for different values of speed (lanes = 2, FFS = 50 mph, length of entry section = 500 ft, and ramp demand = 100 veh/hr/ln, and downstream capacity = 1324 veh/hr/ln) 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 100012001400150016001700200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) FFS 50 mph 60 mph 70 mph 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00 500.00 100012001400150016001700200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) FFS 50 mph 60 mph 70 mph

PAGE 85

85 Figure 4-22. Variation of TT per mile with demand for different values of ramp demand (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 2491 veh/hr/ln) Figure 4-23. Variation of TT per mile with demand for different values of ramp demand (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 1689 veh/hr/lane) 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100012001400150016001700200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) Ramp Demand 100 veh/hr/ln 300 veh/hr/ln 500 veh/hr/ln 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00 100012001400150016001700200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) Ramp Demand 100 veh/hr/ln 300 veh/hr/ln 500 veh/hr/ln

PAGE 86

86 Figure 4-24. Variation of TT per mile with demand for different values of ramp demand (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 1324 veh/hr/lane) Figure 4-25. Variation of TT per mile with demand for different values of # lanes (length of entry section = 500 ft, and FFS = 50 mi/hr, ramp demand = 100 veh/hr/ln, and downstream capacity = 2400 veh/hr/lane) 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00 500.00 100012001400150016001700200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) Ramp Demand 100 veh/hr/ln 300 veh/hr/ln 500 veh/hr/ln 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100012001400150016001700200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) # Lanes 2 3 4

PAGE 87

87 Figure 4-26. Variation of TT per mile with demand for different values of # lanes (length of entry section = 500 ft, and FFS = 50 mi/hr, ramp demand = 100 veh/hr/ln, and downstream capacity = 1685 veh/hr/lane) Figure 4-27. Variation of TT per mile with demand for different values of length of entry section (# Lanes = 2, FFS = 50 mi/hr, ramp demand = 100 veh/hr/ln, and downstream capacity = 2400 veh/hr/lane) 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 100012001400150016001700200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) # Lanes 2 3 4 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100012001400150016001700200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) Length of collectors segment 500 ft 2,500 ft 5,000 ft 10,000 ft

PAGE 88

88 Figure 4-28. Variation of TT per mile with demand for different values of length of entry section (# lanes = 2, FFS = 50 mi/hr, ramp dema nd = 100 veh/hr/ln, and downstream capacity = 1689 veh/hr/lane) Figure 4-29. Variation of TT per mile with demand for different values of length of entry section (# lanes = 2, FFS = 50 mi/hr, ramp dema nd = 100 veh/hr/ln, and downstream capacity = 1324 veh/hr/lane) 0.00 100.00 200.00 300.00 400.00 500.00 600.00 100012001400150016001700200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) Length of collectors segment 500 ft 2,500 ft 5,000 ft 10,000 ft

PAGE 89

89 Figure 4-30. Time series plot between TT per m ile of the downstream bottleneck and the number of vehicles in the downstream bottleneck Figure 4-31. Time series plot between TT per m ile of the upstream segment and the number of vehicles in the upstream segment 0 20 40 60 80 100 120 140 160 180 0 50 100 150 200 250 300 350 1357911131517192123252729313335373941434547495153555759T.T. per mile# minutes from start of simulation TT BK/mi Veh BK 0 50 100 150 200 250 300 350 400 450 0 50 100 150 200 250 300 010203040506070T.T. per mile# Minutes from start of simulation Veh SS TT SS/mi

PAGE 90

90 Figure 4-32. Sketch of a diverge freeway segment. Figure 4-33. Variation of TT per mile with demand (lanes = 2, FFS = 50 mph, length of entry section = 500 ft, ramp Exit % = 5, a nd downstream capacity = 1515 veh/hr/lane) 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00 100012001400150016001800200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) Entry Segment

PAGE 91

91 Figure 4-34. Variation of TT per mile with demand for different values of downstream segment capacity (lanes = 2, FFS = 50 mph, length of entry section = 500 ft, and ramp exit % = 5) Figure 4-35. Variation of TT per mile with demand for different values of speed (lanes = 2, FFS = 50 mph, length of entry section = 500 ft, and ramp exit % = 5, and downstream capacity = 2137 veh/hr/lane) 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00 100012001400150016001800200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) Downstream Segment Capacity 1326 1697 2153 2136 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100012001400150016001700200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) FFS 50 mph 60 mph 70 mph

PAGE 92

92 Figure 4-36. Variation of TT per mile with demand for different values of speed (lanes = 2, FFS = 50 mph, length of entry section = 500 ft, and ramp exit % = 5, and downstream capacity = 1689 veh/hr/lane) Figure 4-37. Variation of TT per mile with demand for different values of speed (lanes = 2, FFS = 50 mph, length of entry section = 500 ft, and ramp exit % = 5, and downstream capacity = 1324 veh/hr/lane) 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 100012001400150016001700200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) FFS 50 mph 60 mph 70 mph 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00 100012001400150016001700200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) FFS 50 mph 60 mph 70 mph

PAGE 93

93 Figure 4-38. Variation of TT per mile with demand for different values of off-ramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 2136 veh/hr/ln) Figure 4-39. Variation of TT per mile with demand for different values of off-ramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 1689 veh/hr/ln) 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100012001400150016001700200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) % Exit 5 % 10% 20% 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 100012001400150016001700200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) % Exit 5 % 10% 20%

PAGE 94

94 Figure 4-40. Variation of TT per mile with demand for different values of off-ramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 1324 veh/hr/ln) Figure 4-41. Variation of TT per mile with demand for different values of length of entry section (# lanes = 2, FFS = 50 mi/hr, ramp dema nd = 100 veh/hr/ln, and downstream capacity = 2136 veh/hr/lane) 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00 100012001400150016001700200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) % Exit 5 % 10% 20% 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100012001400150016001700200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) Length of collectors segment 500 ft 2,500 ft 5,000 ft 10,000 ft

PAGE 95

95 Figure 4-42. Variation of TT per mile with demand for different values of length of entry section (# lanes = 2, FFS = 50 mi/hr, ramp dema nd = 100 veh/hr/ln, and downstream capacity = 1689 veh/hr/lane) Figure 4-43. Variation of TT per mile with demand for different values of length of entry section (# lanes = 2, FFS = 50 mi/hr, ramp dema nd = 100 veh/hr/ln, and downstream capacity = 1324 veh/hr/lane) 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 100012001400150016001700200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) Length of collectors segment 500 ft 2,500 ft 5,000 ft 10,000 ft 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00 500.00 100012001400150016001700200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) Length of collectors segment 500 ft 2,500 ft 5,000 ft 10,000 ft

PAGE 96

96 Figure 4-44. Variation of TT per mile with demand for different values of # lanes (length of entry section = 500 ft, and FFS = 50 mi/hr, off-ramp exit % = 5, and downstream capacity = 2136 veh/hr/lane) Figure 4-45. Variation of TT per mile with demand for different values of # lanes (length of entry section = 500 ft, and FFS = 50 mi/hr, off-ramp exit % = 5, and downstream capacity = 1689 veh/hr/lane) 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100012001400150016001700200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) 2 Lanes 3 Lanes 4 Lanes 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 100012001400150016001700200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) 2 Lanes 3 Lanes 4 Lanes

PAGE 97

97 Figure 4-46. Time series plot between TT per m ile of the downstream bottleneck and the number of vehicles in the downstream bottleneck Figure 4-47. Time series plot between TT per m ile of the upstream segment and the number of vehicles in the upstream segment 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 010203040506070T.T. per mile# minutes since start of simulation Veh SS TT SS/mi 0 20 40 60 80 100 120 140 160 180 0 50 100 150 200 250 300 350 1357911131517192123252729313335373941434547495153555759T.T. per mile# minutes since start of simulation TT BK/mi Veh BK

PAGE 98

98 Figure 4-48. Sketch of a weaving freeway segment. Figure 4-49. Variation of TT per mile with de mand (# lanes = 2, FFS = 50 mph, length of entry section = 500 ft, ramp exit % = 5, an d downstream capacity = 1696 veh/hr/lane) 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 100012001400150016001800200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane)

PAGE 99

99 Figure 4-50. Variation of TT per mile with demand for different values of downstream segment capacity (lanes = 2, FFS = 50 mph, length of entry section = 500 ft, and ramp exit % = 5) Figure 4-51. Variation of TT per mile with demand for different values of speed (lanes = 2, FFS = 50 mph, length of entry section = 500 ft, and ramp exit % = 5, and downstream capacity = 2209 veh/hr/lane) 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00 500.00 100012001400150016001800200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) Downstream Segment Capacity 1326 1696.00 2153 2209 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100012001400150016001800200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) FFS 50 mph 60 mph 70 mph

PAGE 100

100 Figure 4-52. Variation of TT per mile with demand for different values of speed (lanes = 2, FFS = 50 mph, length of entry section = 500 ft, and ramp exit % = 5, and downstream capacity = 1696 veh/hr/lane) Figure 4-53. Variation of TT per mile with demand for different values of speed (lanes = 2, FFS = 50 mph, length of entry section = 500 ft, and ramp exit % = 5, and downstream capacity = 1326 veh/hr/lane) 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 100012001400150016001800200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) FFS 50 mph 60 mph 70 mph 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00 500.00 100012001400150016001800200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) FFS 50 mph 60 mph 70 mph

PAGE 101

101 Figure 4-54. Variation of TT per mile with demand for different values of off-ramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 2209 veh/hr/ln) Figure 4-55. Variation of TT per mile with demand for different values of off-ramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 1696 veh/hr/ln) 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100012001400150016001800200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) % Exit 5 % 10% 15% 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 100012001400150016001800200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) % Exit 5 % 10% 15%

PAGE 102

102 Figure 4-56. Variation of TT per mile with demand for different values of off-ramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 1326 veh/hr/ln) Figure 4-57. Variation of TT per mile with demand for different values of length of entry section (# lanes = 2, FFS = 50 mi/hr, ramp dema nd = 100 veh/hr/ln, and downstream capacity = 2209 veh/hr/lane) 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00 100012001400150016001800200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) % Exit 5 % 10% 15% 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100012001400150016001800200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) Length of entry segment 500 ft 2,500 ft 5,000 ft 10,000 ft

PAGE 103

103 Figure 4-58. Variation of TT per mile with demand for different values of length of entry section (# lanes = 2, FFS = 50 mi/hr, ramp dema nd = 100 veh/hr/ln, and downstream capacity = 1696 veh/hr/lane) Figure 4-59. Variation of TT per mile with demand for different values of length of entry section (# lanes = 2, FFS = 50 mi/hr, ramp dema nd = 100 veh/hr/ln, and downstream capacity = 1326 veh/hr/lane) 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 100012001400150016001800200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) Length of entry segment 500 ft 2,500 ft 5,000 ft 10,000 ft 0.00 100.00 200.00 300.00 400.00 500.00 600.00 100012001400150016001800200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) Length of entry segment 500 ft 2,500 ft 5,000 ft 10,000 ft

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104 Figure 4-60. Variation of TT per mile with demand for different values of # lanes (length of entry section = 500 ft, and FFS = 50 mi/hr, off-ramp exit % = 5, and downstream capacity = 2209 veh/hr/lane) Figure 4-61. Variation of TT per mile with demand for different values of # lanes (length of entry section = 500 ft, and FFS = 50 mi/hr, off-ramp exit % = 5, and downstream capacity = 1696 veh/hr/lane) 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100012001400150016001800200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) # Lanes 2 3 4 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 100012001400150016001800200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) # Lanes 2 3 4

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105 Figure 4-62. Variation of TT per mile with demand for different values of ramp demand (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 2491 veh/hr/ln) Figure 4-63. Variation of TT per mile with demand for different values of ramp demand (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 1689 veh/hr/lane) 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100012001400150016001800200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) Ramp Demand 100 veh/hr/ln 300 veh/hr/ln 500 veh/hr/ln 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 100012001400150016001800200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) Ramp Demand 100 veh/hr/ln 300 veh/hr/ln 500 veh/hr/ln

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106 Figure 4-64. Variation of TT per mile with demand for different values of ramp demand (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 1324 veh/hr/lane) Figure 4-65. Time series plot between TT per m ile of the downstream bottleneck and the number of vehicles in the downstream bottleneck 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00 500.00 100012001400150016001800200025003000TT/mile (sec/mi)Demand per lane (veh/hr/lane) Ramp Demand 100 veh/hr/ln 300 veh/hr/ln 500 veh/hr/ln 0 20 40 60 80 100 120 140 0 50 100 150 200 250 300 350 1357911131517192123252729313335373941434547495153555759T.T. per mile# minutes since start of simulation TT BK/mi Veh BK

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107 Figure 4-66. Time series plot between TT per m ile of the upstream segment and the number of vehicles in the upstream segment 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 010203040506070T.T. per mile# minutes since start of simulation Veh SS TT SS/mi

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108 CHAPTER 5 ANALYTICAL MODELS Based on th e simulation results, analytical m odels are developed to predict T.T. as a function of the selected critical variables. The st ructure of the analytical models is described in Section 5.1. The analytical models for basic fre eway segments are pr esented in Section 5.2, while the models for merge segments and diverg e segments are presented in section 5.3 and Section 5.4. The models for weaving segments ar e presented in Section 5.5. The models for Bottleneck are presented in Section 5.6. 5.1 Model Structure T.T. for congested and uncongested conditions is m odeled separately and the variables that impact T.T. are also separately considered. The first set of models estimate the T.T. when the demand doesnt exceed downstream segment capac ity, while the second set of the models estimates the T.T. when the demand exceeds the downstream segment capacity. When the demand doesnt exceed downstream segment capacity, it is concluded that the relation between T.T., demand, and other variables is linear. Thus these set of conditions are modeled using simple multivariate regression models. On the other hand when the demand exceeds downstream segment capacity, it is foun d that the relation between T.T., demand, and other variables takes the shape of an S curve, as shown in Figure 5-1. As shown in Figure 5-1, the T.T. remains relatively constant until demand reaches downstream segment capacity. Once demand reaches downstream segment capacity, T.T. st arts to linearly increase with demand and then the relationship flattens out to a maximum value of T.T. The S curve can be characterized by two points; (1) when demand equals downstream segment, until this point the T.T. remains relatively constant and after this point the T.T. starts to increase at an exponential rate (2) when the expo nentially increasing T.T. starts to flatten and

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109 reaches a maximum value of T.T. This S curve can be modeled using either (a) three separate linear models (b) using a single logistic func tion (c) estimate only the maximum T.T. using simulated data and use a theore tically derived parameter that defines the location on the S curve. The first approach requires identification of the points where the T.T. starts to increase at an exponential rate and where th e exponentially increasi ng T.T. starts to flatten and reaches a maximum value of T.T. This task, of identifying the two characteristic points, is implicitly taken care while estimating the logistic model. Moreover, the logistic curve, as shown in Figure 5-2, is smoother at the characteristic points. However, use of logistic function eith er forces the relation between T.T. and other variable also to be logi stic or made the function very complicated and hard to read. The third approach; where the ma ximum T.T. is first estimated using simple multivariate regression models and then a para meter, which defines the location on the S curve, is theoretically derived as a function demand, capacity, and length of the segment alone. Thus, the third approach is used to model T.T. under congested conditions. The structure of the multivariate regression models used for uncongested conditions is described in section 5.1.1, similar regression func tions are used for congested conditions and are described in section 5.1.2. The two sets of models developed and their applications are presented in Section 5.1.3. 5.1.1 Models for Uncongested Conditions This section describ es the struct ure of models used to estimate T.T. when the demand does not exceed downstream segment capacity. The structure of simple multivariate regression model is as follows: Y1i = for i = 1, 2 ... n. (5-1) Where, Yi= Dependent variable (in this case travel time per mile)

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110 Explanatory factors or independent variables. = Constant term. Coefficients on the explanatory variables. These coefficients capture the marginal impact of the corre sponding explanatory variable. i= Error term, which captures the impact of unobserved factors (not accounted for by X1i, X2i,,XKi ) It should be noted that the a bove regression equation is very similar to that of the speedflow curve in HCM 2000. However, in HCM, the variation between speed and flow is studied and in this study, the variation between T.T. and demand is studied. Moreover, in HCM the analysis is done for only basic freeway segment. However, in this study, the analysis is done for all the four freeway segments. 5.1.2 Models for Congested Conditions This section describ es the stru cture of models used to estimate T.T. when the demand exceeds downstream capacity. Models for congested conditions are developed in two stages; first the maximum T.T. is estimated, and then a parameter alpha is estimated. Alpha parameter describes the location on the S curve. Y2i = (5-2) Where, Yi= Dependent variable (Travel time) Parameter describing the location on the S curv e. This parameter is derived theoretically.

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111 = = A simple multivariate regression model. Xi = {X1i, X2i,, XKi } = Explanatory factors or independent variables. = {1, 2,., K} = Coefficients on the explanatory vari ables. These coefficients capture the marginal impact of the co rresponding explan atory variable. The above two models can be combined into a single model which can be applied in all situations irrespective of the relative va lues of demand and downstream capacity. 5.1.3 Application This section presents the com bined model, which combines models from both the parts described above. The following constr uct is used to achieve this combination, which is described below: Yi = (5-3) Where, Yi = Dependent variable (Travel time) Xi = = Explanatory factors or independent variables. = {1, 2,., K} = Coefficients on the explanatory vari ables. These coefficients capture the marginal impact of the co rresponding explan atory variable. 0, = Constant. = A simple multivariate regression model.

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112 = ; yields 1 if demand exceeds downstr eam capacity. Thus, when demand exceeds downstream capacity, the first part of the model produces ma x T.T. for uncongested conditions. D = Demand. Cd = Capacity of downstream segment. A special case of this combination, when th e demand is less than the downstream segment capacity, yields us the model from the first part Another special case, when the demand exceeds the downstream capacity, yields the model from part two. Using the model structure shown above in Equa tion-3, five separate models are estimated one each for basic freeway segment, merge segmen t, diverge segment, and weaving segment and the fifth for bottleneck. 5.2. Travel Time Models for BFS When de mand is less than the downstream segm ent capacity, free flow speed is found to be the only variable that impact s travel time. T.T. model for unc ongested conditions is presented below: V = Free flow speed D = Demand Cd = Capacity of downstream segment. The regression statistics for B FS is presented in Table 5-1 It should be noted that the above regression equation presented is very similar to that of the speed-flow curve in HCM 2000. However, in HCM, the variation between speed and flow is studied and in this study, the va riation between T.T. and demand is studied. Moreover, in HCM the analysis is done for only basic freeway segmen t. However, in this study, the analysis is done

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113 for all the four freeway segments. The T.T. predicted by the uncongested model is compared with the HCM speed flow graph and presented in Figure 5-3. In order to tie up the uncongested model with congested model, the uncongested model is modified such that when demand exceeds downstream segment capacity, the T.T. predicted by uncongested model becomes a constant T.T. This new structure is presented below: (5-4) It can be observed from equation-4 that the T.T. varies with demand until demand is less than downstream segment capacity. Once the demand reaches downstream segment capacity, T.T. does not vary with increase in demand, a nd it becomes a constant. Thus, the estimated model behaves consistently with the objective of the fi rst part of the model. The second part of the model corresponds to those scenarios where demand is greater than the downstream segment capacity. In this part of the model, demand, downstream capacity, and length of the basic freeway segment variables impact T.T. Thus, for this part of the models, demand, downstream segment capacity, and length of the basic freeway segment are considered as explanatory variable. The model for second part is estimated in two stages, first the range of the T.T. is modeled and then the shap e of the sigmoid curve is estimated. In order to estimate the range of T.T., a few plots were created between the range of T.T. and demand for a series of length of basic freeway segment. One of the plots is presented in Figure 5-4. As shown, for a given length of basic freeway segment, the range of T.T. varies similar to a parabolic curve with demand. It is also observed th at as the length of the basic freeway segment increases, the range of the T.T. decreases. As the final objective of this model estimation is to develop a combin ed model that will be used for all values of demand, the second model is modified such that it smoothly connects the model from first part at demand equals dow nstream capacity. This modification involves

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114 modeling range of T.T. minus T.T. from part one when demand equals capacity. The model for estimating range of T.T. minus T.T. from part one when demand equals capacity is shown below: (5-5) Where, = Range of travel time minus travel time from part one when demand equals capacity = Length of basic freeway segment = Capacity of downstream segment The congested T.T. range model stat istics are presented in Table 5-2. It can be observed from equation-5 that as the length of the basic freeway segment increases, the range of the T.T. decreases. Furthe r it can also be observed that as the downstream segment capacity increases the maximum T.T. expone ntially decreases. Thus it is found that the estimated model follows the observed logic in the model. The parameter is theoretically derived using simple queuing system. Consider a section of road, such as BFS shown in Figure 4-1, with a bottleneck of capacity at the downstream end of the section. When demand exceeds the downstream capacity, a moving queue starts forming inside the segment. As the queue length increases the T.T. per mile increases as shown in Figure 4-15. Once the m oving queue completely occupies the entire segment, the T.T. per mile reaches a maximum value. The parameter tries to capture the ratio of the average T.T. to the maximum T.T.. The parameter is calculated using the equation shown below. = T.T. avg/ T.T. max = + (1(5-6) Where L = Length of the section J = Jam density

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115 D = Freeway demand = Downstream capacity The combined model for basic freeway segment (BFS) is presented below: TT = + (5-7) 5.3 Travel Time Models for Merge Segment When de mand is less than the downstream segm ent capacity, free flow speed is found to be the only variable (besides demand and downstr eam capacity) that impacts travel time. T.T. model for uncongested conditi ons is presented below: (5-8) V = Free flow speed D = Freeway demand = On-ramp demand Cd = Capacity of downstream segment The summary of uncongested model for merg e segment is presen ted in Table 5-2. In order to tie up this model with model from second part, (5-9) It can be observed from equation-6 that the T.T. varies with demand until demand is less than downstream segment capacity. Once the demand reaches downstream segment capacity, T.T. does not vary with increase in demand, a nd it becomes a constant. Thus, the estimated model behaves consistently with the objective of the first part of the model. The second part of the model corresponds to those scenarios where demand exceeds the downstream segment capacity. Under these c onditions, demand, downstream capacity, and

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116 length of the basic freeway segment variables were found to impact T.T. and are used as explanatory variable. The congested model is estimated in two stages: first the range of the T.T. is modeled and then the shape of the sigmoid curve is estimated. As the final objective of this model estimation is to develop a combin ed model that will be used for all values of demand, the second model is modified such that it smoothly connects the model from first part at demand equals dow nstream capacity. This modification involves modeling range of T.T. minus T.T. from part one when demand equals capacity. The model for estimating range of T.T. minus T.T. from part one when demand equals capacity is shown below: (5-10) Where, = Range of travel time minus travel time from part one when demand equals capacity = Length of basic freeway segment = Capacity of downstream segment The congested T.T. range model stat istics are presented in Table 5-4. It can be observed from equation-5 that as the length of the basic freeway segment increases, the range of the T.T. decreases. Furthe r it can also be observed that as the downstream segment capacity increases the maximum T.T. expone ntially decreases. Thus it is found that the estimated model follows the observed logic in the model. The combined model for basic freeway segment (BFS) is presented below: TT = + (5-11)

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117 Where is derived similarly to the way it is derived for basic fr eeway segment, but the demand now includes freeway demand and the on-ramp demand. 5.4 Travel Time Models for Diverge Segment When de mand is less than the downstream segment capacity, free flow speed was found to be the only variable that impacts travel time. T.T. for uncongested conditions is presented below: (5-12) Where, V = Free flow speed D = Demand Cd = Capacity of downstream segment. The summary of uncongested model for BFS is presented in Table 5-5. In order to tie up this model with model from second part, (5-13) It can be observed from equation-4 that the T.T. varies with demand until demand is less than downstream segment capacity. Once the demand reaches downstream segment capacity, T.T. does not vary with increase in demand, a nd it becomes a constant. Thus, the estimated model behaves consistently with the objective of the fi rst part of the model. The second part of the model corresponds to those scenarios where demand exceeds the downstream segment capacity. Under these c onditions, demand, downstream capacity, and length of the entry segment variables were found to impact T.T. and are used as explanatory variable. The congested model is estimated in two stages : first the range of the T.T. is modeled and then the shape of the sigmoid curve is estimated. As the final objective of this model estimation is to develop a combin ed model that will be used for all values of demand, the second model is modified such that it smoothly connects the

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118 model from first part at demand equals dow nstream capacity. This modification involves modeling range of T.T. minus T.T. from part one when demand equals capacity. The model for estimating range of T.T. minus T.T. from part one when demand equals capacity is shown below: (5-13) Where, = Range of travel time minus travel time from part one when demand equals capacity = Length of entry segment = Capacity of downstream segment = Off-ramp demand/exit percentage The congested T.T. range model stat istics are presented in Table 5-6. It can be observed from equation-5 that as the length of the basic freeway segment increases, the range of the T.T. decreases. Furthe r it can also be observed that as the downstream segment capacity increases the maximum T.T. expone ntially decreases. Thus it is found that the estimated model follows the observed logic in the model. The combined model for basic freeway segment (BFS) is presented below: T.T. = + (5-14) Where is derived similarly to the way it was derived for basic freeway segment, but the demand now includes freeway dema nd and the off-ramp demand.

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119 5.5 Travel Time Models for Weaving Segment When de mand is less than the downstream segment capacity, free flow speed was found to be the only variable that impacts travel time. T.T. m odel for uncongested conditions is presented below: (5-15) Where, V = Free flow speed D = Demand Cd = Capacity of downstream segment The summary of uncongested model for weavi ng segment is presented in Table 5-7. In order to tie up this model with model from second part, (5-16) It can be observed from equation-4 that the T.T. varies with demand (sum of freeway demand and ramp demand) until demand equals downstream segment capacity. Once the demand reaches downstream segment capacity, T.T. does not vary with increase in demand, and it becomes a constant. Thus, the estimated model be haves consistently with the objective of the first part of the model. The second part of the model corresponds to those scenarios where demand exceeds the downstream segment capacity. Under these condi tions, demand, downstream capacity, and the length of the entry segment variables were found to impact T.T. and are used as explanatory variable. The congested model is estimated in two stages : first the range of the T.T. is modeled and then the shape of the sigmoid curve is estimated. As the final objective of this model estimation is to develop a combin ed model that will be used for all values of demand, the second model is modified such that it smoothly connects the

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120 model from first part at demand equals dow nstream capacity. This modification involves modeling range of T.T. minus T.T. from part one when demand equals capacity. The model for estimating range of T.T. minus T.T. from part one when demand equals capacity is shown below: (5-17) Where, = Range of travel time minus travel time from part one when demand equals capacity = Length of entry segment = Capacity of downstream segment = Off-ramp demand/exit percentage The congested T.T. range model stat istics are presented in Table 5-8. It can be observed from equation-5 that as the length of the basic freeway segment increases, the range of the T.T. decreases. Furthe r it can also be observed that as the downstream segment capacity increases the maximum T.T. expone ntially decreases. Thus it is found that the estimated model follows the observed logic in the model. The combined model for weaving segment is presented below: + (5-18) Where is derived similarly to the way it was derived for basic freeway segment, but the demand now includes freeway demand, on -ramp demand, and off-ramp demand. 5.6 Travel Time Models for Bottleneck In this study a bottleneck is always assum ed to be a basic freeway segment. T.T. models for a bottleneck are developed only under conge sted conditions. When the bottleneck is

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121 uncongested, the T.T. models developed for ba sic freeway segment are used assuming the downstream segment of the bottlene ck has unrestricted capacity. Th is section presents the T.T. models for bottleneck under congested conditions. It was found that demand and capacity are th e only variables that impacts T.T. for congested conditions. The impact of demand on T.T. for various capacity values is shown in Figure 5-6. As shown in Figure 5-6, for a given capacity the impact of demand on T.T. is insignificant. The impact of capacity on T.T. for various va lues of demand is shown in Figure 5-7. As shown in Figure 5-7, for a given demand the impact of capacity on T.T. is significant and the impact of demand on T.T. is insignificant. As shown in Figure 5-7, the variation of T.T. with capacity is in the shape of a parabola with the transition point near 2400. Thus, a parabolic function is used to model the relationship between T.T. and capacity. The model for estimating T.T. of the bottleneck is shown below: (5-19) Where, = Range of travel time minus travel time from part one when demand equals capacity = Capacity of downstream segment The congested travel time range model st atistics are presented in Table 5-9.

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122 Table 5-1. BFS uncongested model statistics Explanatory variables CoefficientsStandard Errort Stat P-value Intercept 120.86860.634767190.4141 0 -1.006320.009373-107.361 0 4.6546770.33310613.97355 0 Goodness of fit measures R2 0.975288 Adjusted R2 0.975122 Number of cases 300 Table 5-2. BFS congested T.T. range model summary Explanatory variables Coefficients Standard Error t Stat P-value Intercept 0 N/A N/A N/A 4.561 0.130 35.040 0.000 -0.524 0.041 -12.827 0.000 Goodness of fit measures R2 0.889 Adjusted R2 0.886 Number of cases 400 Table 5-3. Merge uncongested model summary Explanatory variables CoefficientsStandard Errort Stat P-value Intercept 126.8311.128112.4090.000 Speed -1.0900.011-95.4400.000 ((D+Dr)/Cd) 5.6780.6368.9230.000 DS Capacity -0.0010.000-2.0870.037 Goodness of fit measures R2 0.92 Adjusted R2 0.92 Number of cases 844 Table 5-4. Merge congested T.T. ra nge model statistics and estimates Explanatory variables Coefficients Standard Error t Stat P-value Intercept 14.763.274.52 0.00 3.350.0654.42 0.00 0.100.052.08 0.04 192.1017.9110.73 0.00

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123 Table 5-5. Diverge uncongested model summary Explanatory variables CoefficientsStandard Errort Stat P-value Intercept 132.810 1.4094.710.00 Speed -1.038 0.01-69.410.00 D/C 8.634 0.7012.410.00 DS-Capacity -0.006 0.00-13.710.00 Goodness of fit measures R2 0.82 Adjusted R2 0.82 Number of cases 1152 Table 5-6. Diverge congested T.T. range model summary Explanatory variables CoefficientsStandard Errort Stat P-value Intercept 0N/A N/A N/A 4.8680.08159.818 0.000 0.2400.0693.458 0.001 % Exit -10.4120.553-18.845 0.000 Goodness of fit measures R2 0.93 Adjusted R2 0.93 Number of cases 720 Table 5-7. Weaving segment uncongested model summary Explanatory variables CoefficientsStandard Errort Stat P-value Intercept 115.18 1.3883.510.00 Speed -1.0496 0.01-79.190.00 12.83460.5822.030.00 DS-Capacity 0.0012 0.002.720.01 Goodness of fit measures R2 0.65 Adjusted R2 0.65 Number of cases 3615

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124 Table 5-8. Weaving segment congest ed T.T. range model summary Explanatory variables CoefficientsStandard Errort Stat P-value Intercept 34.83962.119316.4392 0.0000 3.40970.0282120.8524 0.0000 -0.05680.0218-2.6077 0.0092 % Exit -4.41840.1836-24.0636 0.0000 Goodness of fit measures R2 0.94 Adjusted R2 0.94 Number of cases 1728 Table 5-9. Bottleneck T.T. model summary Explanatory variables CoefficientsStandard Errort Stat P-value Intercept 114.049 4.316 26.4270.000 1.723 0.037 46.2210.000 Goodness of fit measures R2 0.49 Adjusted R2 0.49 Number of cases 2232

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125 Figure 5-1. Variation of TT per mile with dema nd (lanes = 2, FFS = 50 mph, length of basic freeway segment = 5000 ft, and downs tream capacity = 1515 veh/hr/lane) Figure 5-2. Sigmoid curve 0 50 100 150 200 250 300 350 400 10001250150017502000225025009999 Demand Per lane (veh/lane/hr)Travel time per mile (sec/mile) Travel time per mile

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126 Figure 5-3. Comparison of averag e HCM speed and model speed Figure 5-4. Variation of maximum T.T. with de mand for a series of length of basic freeway segment 54 56 58 60 62 64 66 68 70 72 1000120014001600180020002200Speed (mph)Demand veh/hr/ln HCM Speed Model Speed 0.00 100.00 200.00 300.00 400.00 500.00 600.00 700.00 800.00 900.00 1000.00 02505007501000125015001750200022502500Travel time per mile (sec)Capacity of downstream segment (ft) Length of BFS 5000 ft 10,000 ft 15,000 ft 20,000 ft 25,000 ft

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127 Figure 5-5. Variation of travel time with time interval Figure 5-6. Variation of TT per mile with dema nd for various values of downstream capacity (lanes = 2, length of basic freeway segment = 5000 ft and FFS is 55 mph) 0 100 200 300 400 500 600 700 800 900 10001250150017502000225025004999.5TT/mile (sec/mi)Demand per lane (veh/hr/lane) 2240 2153 1688 848 T.T. T.T. max T.T. avg 1 hr Time t

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128 Figure 5-7. Variation of TT per mile with capac ity for various values of demand (lanes = 2, length of basic freeway segment = 5000 ft and FFS is 55 mph) 0.00 100.00 200.00 300.00 400.00 500.00 600.00 700.00 800.00 900.00 848168821532240TT/mile (sec/mi)Downstream Capacity(veh/hr/lane) 1000 1250 1500 1750 2000 2250 2500 3333

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129 CHAPTER 6 COMPARISION WITH OTHER ANALYTICAL MODELS This section com pares the estimated T.T. from analytical models and other existing planning T.T. models. As the BPR and MTC mode ls are macroscopic and focus mainly on the planning applications, reasonable comparisons cannot be made between them and Akceliks model nor with the analytical models developed in this study. The analytical models developed in this study are comparable with Akceliks model only, and these comparisons are presented below. The analytical T.T. models are compared w ith the existing models such as: BPR, MTC, and Akcelik. Based on these comparisons, the methodology of using simulation for estimating T.T. can be compared against existing models. It can be observed that both Akceliks model a nd analytical models developed in this study make similar predictions under uncongested cond itions i.e., when demand is less than the downstream capacity. However, when dema nd exceeds downstream segment capacity, the analytical models Akceliks model and devel oped in this study do not make similar predictions.While the Akceliks model shows linear change in travel time between congested and un-congested conditions. The analytical model howev er predicts that the travel time increases exponentially and then flattens out af ter the study segmen t is saturated.

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130 Figure 6-1. Variation of upstream segment T.T. with demand for several an alytical models with capacity at 1515 veh/hr/ln 0 500 1000 1500 2000 2500 1000125015001750200022502500TT/mile (sec/mi)Demand per lane (veh/hr/lane) Study Model BPR MTC Akcelik's Model

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131 CHAPTER 7 CONCLUSIONS & RECOMMENDATIONS This chapter summarizes the m ain findings from the research work carried out as part of this thesis. Based on these findings, furt her research recommendations are made. 7.1 Summary Liter ature was reviewed to identify variables th at might impact T.T.. Using these variables, scenarios were developed and simulated to identify the most important vari ables that may affect T.T. in the simulator. Using these important variables, a set of scenarios were developed and simulated to obtain a database for analytical model development. Analytical models were developed using this database. The analytical mode ls developed in this thesis were compared to other T.T. estimation models. 7.2 Conclusions Analytical T .T. models using demand have been developed, and are applicable for both under-saturated and oversaturated conditions. At high levels of demand or congestion these models are not consistent with each other and have not been compared with field data. Further, some of the existing models, such as BPR, consider flows greater than capacity, which is unrealistic. Thus there is a need for further a dvancement in the T.T. estimation models which make accurate predictions at both saturated and un saturated congestion leve ls. Moreover most of the existing models (BPR and MTC) do not c onsider the queuing pheno menon explicitly. Thus analytical models which consider formation a nd dissipation of queues and also consider the delay associated with these queues in estimatio n of T.T. is required. Towards this end, the present study developed analytical models for estimating T.T., using simulation data. A preliminary list of variables that may affect the T.T. are considered. These variables are used for simulation, and significant variables are selected for furthe r consideration. Not all of the

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132 freeway segments require the same set of inputs to estimate T.T., therefore each segment type is considered separately. The models developed in this study can be used in various freeway applications, listed in Section 7.3 to estimate freeway corridor T.T. These models can be used to estimate freeway T.T. easily and quickly compared to a fullscale simulation of the corridor. Further, the m odels developed in this study are much more accurate and represent field c onditions better than the BPR and MTC models, which do not consider capacity restrictions on li nks i.e. allow more vehicles to be loaded onto th e link than the capacity of the link. Moreover, th e models developed in this st udy are applicable to all the freeway segment types are thus more versatil e that the BPR and MTC models which dont distinguish the different freeway segments. 7.3 Model Applications The m odels developed as part of this thesis can be applied to study freeway corridors under several situations as listed below: Freeway Work Zones o When there is a freeway work-zone, some of the lanes might be closed. This lane closure creates bottleneck, which affects the T.T. of all the upstream segments. The T.T. of the work-zone bottleneck and the upstream segments can be obtained fr om the models developed in this thesis. Freeway corridors with lane drops o When there is a lane drop, bottleneck is created. This bottleneck affects the T.T. of all the upstream segments. The T.T. of the lane drop bottleneck and the upstream segments can be obta ined from the models developed in this thesis. Freeway Incidents o When there is a freeway incident, a bottleneck is created. This bottleneck affects the T.T. of all the upstream segments. The T.T. of the lane drop

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133 bottleneck and the upstream segments can be obtained from the models developed in this thesis. 7.4 Further Research This study used CORSIM m icro-simulation so ftware package for simulating scenarios, which are later used for devel opment of the analytical models Several other micro-simulation software packages are available, including AIMSUN, PARAMICS, and VISSIM that suit the general requirements of this study. The algorit hms used in these micro-simulation software packages are different. The impact of other micr o-simulation software packages on the analysis conducted in this study can be carried out. Driver population factor and per centage of trucks were not c onsidered in this study, to contain the number of scenarios within a reasonable range. Future research might consider these variables in addition to the variable already considered in this study. Instead of using simulation to generate the da ta for estimating models, the possibility of using flow-density curves to estimate uncongested and congested T.T.s should be explored. Instead of using a queuing system to model the transition from uncongested conditions to congested conditions, the possibi lity of using shockwave an alysis should be explored.

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134 REFERENCES Abdelwahab W M., (1998), Elasticities of Mode C hoice Probabilities and Market Elasticities of Demand: Evid ence from a Simultaneous Mode Choice/Shipment size Freight Transport Model, Transport Research E, Vol 34, No. 4, pp. 257-266 Ando N., and E. Taniguchi (2006), Travel Time Reliability in Vehicle Routing and Scheduling with Time Windows Netrks and Spatial Economics Vol 6, num 3-4, pp. 293311 Balke, K., Ullm an, G., McCasla nd, W., Mountain, C., Dudek, C., 1995. Benefits of real-time travel information in Houston, Texas Southwest Region University Transportation Center, Texas Transportation Institute, College Station, TX. Bertini R. L., M. Lasky, C. M. Monsere (2005), Validating Predicted Rural Corridor Travel Times from an Automated License Plate Recognition System Submitted to the IEEE Transactions on Intelligen t Transportation Systems. Bertini R. L., Z. Horwitz, K. Tufte, S. Matthews (2006), Techniques for Mining Truck Data to Improve Freight Op erations and Planning, TransNow University Transportation Center, PI. Beuthe M., B. Jourquin, J. F. Geerts, and H. N Koul (2001), Michel Freight Transportation Demand Elasticities: A Geographic Mul timodal Transportation Network Analysis Transportation Research Part E, Vol 37, pp. 253-266 Bhat, C.R., (1995) A Heteroscedastic Extreme Value Model of Interc ity Mode Choice Transportation Research Part B Vol. 29, No. 6, pp. 471-483, 1995. Bureau of Public Roads (1964). Traffic Assignment Manual. U.S. Dept. of Commerce, Urban Planning Division, Washington D.C. R-L. Cheu, X. Jin, K-C. Ng, Y-L. Ng, and D. Srinivasan (1998) Calibration of FRESIM for Singapore Expressway Using Genetic Algorithm Journal of Trans portation Engineering, ASCE, vol. 124(6), pp. 526-535. Coifman B. and Cassidy, M. (2002) Vehicle Reidentification and Travel Time Measurement on Congested Freeways, Transportation Research: Part A vol 36, no 10, pp. 899-917. Coifman B., Vehicle reidentification and travel time measurement using loop detector speed traps Ph.D. dissertation, Univ. California, Berkeley, 1998. Durbin, J., and Watson, G. S., Testing for Serial Correlation in Least Squares Regression I." Biometrika 37 (1950): 409-428. Fan Y., and Y. Nie (2006), Optimal Routing for Maximizing the Travel Time Reliability Networks and Spatial Economics Vol 6, num 3-4, pp. 333-344

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135 Fan Y. Y., R. E. Kalaba, and J. E. Moore (2005), Arriving on Time Journal of Optimization Theory and Applications Vol 127, no 3, pp. 497-513 Jones C., D. Murray, J. Short (2005), Methods of Travel Time Measurement in FreightSignificant Corridors paper presented at the 76th annual TRB meeting, Transportation Research Board. Kanayama k., Y. Fujikawa, K. Fujimoto, M. Horino (1991), Development of vehicle-license number recogniti system using real-time image processing and its application to traveltime measurement in IEEE Veh. Technol. pp. 798. Li Y., and M. McDonald (2002 ), Link Travel Time Estimation Using Single GPS Equipped Probe Vehicle. Proceedings of The IEEE 5th Inte rnational Conference on Intelligent Transportation Systems, IEEE, Singapore, 932-937, September 2002. Liu X. X., H. Rachel, T. Yang, B. Ran, A Literature and Best Pr actices Scan: ITS Data Management and Archiving University of Wisconsin at Madison, submitted to the Wisconsin DOT, May 2002. Michandani, O., Syal, R. and Lucas, D. Traffic Assignment Using Iterated Route-based Simulation Proc. Of 82nd Annual Meeting of the Transportation Research Board, 2003. Palen, J., 1997. The need for surveillance in intelligent transportation systems Intellimotion, Vol. 6(1), University of California PATH, Berkeley, CA, pp. 1 Singh, R. Beyond the BPR Curve: Updating Speed-Flow and Speed-Capacity Relationships in Traffic Assignment. Presented at 5th Conference on Transportation Planning Methods Applications, Seattle, Washington, April 1995 Spiess, H., 1990. Conical Volume Delay Functions Transportation Science, Volume 24, Number 2, pp. 153-158. Taniguchi E., and R. G. Thompson (2002), Modelling City Logistics Transportation Research Record, num 1790, pp. 45-51 Taniguchi E., and R. G. Thompson (2003), Innovations in Freight Transport. WIT, Southampton Taniguchi E., and R. G. Thompson (2004), Logistics Systems for Sustainable Cities Elsevier, Oxford Taniguchi E., and R. G. Thompson and T. Yamada (2001), City Logistics. Network Modeling and Intelligent Transport Systems Pergamon, Oxford Taniguchi E., and R. G. Thom pson and T. Yamada (2001), Predicting the Effects of City Logistics. Transport Review, Vol 23, num 4, pp. 489-515

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136 Taniguchi E., T. Yamada, and D. Tamagawa (2000), Probabilisitc Routing and Scheduling of Urban Pickup or Delivery Trucks with Variable Travel Times. Reliability of transport Networks, pp 73-89 Turner S. M., (1995) Advanced Techniques for Travel Time Da ta Collection IEEE Turner S. M., and J. H. Douglas (1995), Probe Vehicle Sample Sizes for Real-Time Information: The Houston Experience Proceedings of the Sixth International Conference on Vehicle navigation and Information Systems, Seattle, Washington. Washburn S. S., N. L. Nihan (1999) Estimating Link Travel Time With The Mobiliser Video Image Tracking System Journal of Transportation E ngineering, Vol. 125, No. 1, January/February, 1999. Witlox F., and E. Vandaele (2005), Determinig the Monetary Valu e of Quality Attributes in Freight Transportation Using a Stated Preference Approach Transport planning and Technology, Vol 28, No 2, pp. 77-92 J. Hourdakis, P. G. Michalopoulos and J. Kottommannil (2003) Practial Procedure for Calibrating Microscopic Tr affic Simulation Models. Transportation Research Record,No. 1852, pp. 130-139, 2003.

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137 BIOGRAPHICAL SKETCH Ra makrishna Yennamani was born in India, in 1984. He received his bachelors degree in civil engineering from the Indian Institute of Technology Madras, Chennai, India in 2006, also receiving a minor degree in operations research. Mr. Ramakrishna is a research assistant in the Transportation Research Center, at the University of Florida, Department of Civil and Coastal Engineering, and he received his Master of Science degree in December 2008.