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PAGE 1 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 PAGE 2 2 2008 Ramakrishna Yennamani PAGE 3 3 To my parents PAGE 4 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. PAGE 5 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 RealTime 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 PAGE 6 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 PAGE 7 7 LIST OF TABLES Table page 41 Range of values for each variable that m ay affect T.T. along basic freeway segments .... 7142 Range of values for each variable th at may affect T.T. along merge segment .................. 7143 Range of values for each variable th at may affect T.T. along diverge segment ................ 7144 Range of values for each variable in weaving segment ..................................................... 7145 Input values simulated for basic freeway segments ...........................................................7246 Impact of study vari ables on T.T. of BFS .......................................................................... 7247 Input values simulated for a merge segment ...................................................................... 7248 Impact of study variable s on T.T. of merge segment ........................................................ 7349 Input values simulated for a diverge segment .................................................................... 73410 Impact of study variables on T.T. of diverge segment ...................................................... 73411 Variable values for weaving segment ................................................................................ 74412 Impact of study variables on T.T. of weaving segment ..................................................... 7451 BFS uncongested model statistics .................................................................................... 12252 BFS congested T.T. range model summary ..................................................................... 12253 Merge uncongested model summary ............................................................................... 12254 Merge congested T.T. range model statistics and estimates ............................................ 12255 Diverge uncongested model summary ............................................................................. 12356 Diverge congested T.T. range model summary ............................................................... 12357 Weaving segment uncongested model summary ............................................................. 12358 Weaving segment congested T.T. range model summary ............................................... 12459 Bottleneck T.T. model summary ..................................................................................... 124 PAGE 8 8 LIST OF FIGURES Figure page 21 Comparison of BPR, MTC, Akcelik and 1994 HCM T.T. functions for q/c<1.5 (source: Rupinder Singh, 1999) ......................................................................................... 2822 Comparison of BPR, MTC, Akcelik and 1994 HCM T.T. functions for q/c <2 (source: Rupinder Singh, 1999) ......................................................................................... 2831 Methodology flow chart .....................................................................................................3341 Picture of a basic freeway segment. ................................................................................... 7442 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) ..................... 7543 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) ...................... 7544 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) .................................................................................................................. ......7645 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) ...................... 7646 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) ........................ 7747 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) .................................................................................................................. ......7748 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) ......................................... 7849 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) ................................................... 78410 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) ..............................................................................................79411 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 PAGE 9 9 412 Variation of TT per mile with demand for the downstream segment with (number of lanes = 2, FFS = 55 mph) ................................................................................................... 80413 Variation of TT per mile with demand for the downstream segment with (number of lanes = 2, FFS = 55 mph) ................................................................................................... 80414 Time series plot between TT per mile of the downstream bottleneck and the number of vehicles in the downstream bottleneck .......................................................................... 81415 Time series plot between TT per mile of the upstream segment and the number of vehicles in the upstream segment ...................................................................................... 81416 Sketch of a merge freeway segment. ................................................................................. 82417 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) .................................................................................................................. ......82418 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) ......................................................... 83419 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) ......................................................................... 83420 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) ......................................................................... 84421 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) ............................................................................. 84422 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) ...................................................................................................................85423 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) ...............................................................................................................85424 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) ...............................................................................................................86425 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 PAGE 10 10 426 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) ..............................................................................................87427 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) ..............................................................................................87428 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) ..............................................................................................88429 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) ..............................................................................................88430 Time series plot between TT per mile of the downstream bottleneck and the number of vehicles in the downstream bottleneck .......................................................................... 89431 Time series plot between TT per mile of the upstream segment and the number of vehicles in the upstream segment ...................................................................................... 89432 Sketch of a diverge freeway segment. ............................................................................... 90433 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) .......... 90434 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) .....................................................................................................................................91435 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) ..............................................................................................91436 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) ..............................................................................................92437 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) ..............................................................................................92438 Variation of TT per mile with demand for different values of offramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 2136 veh/hr/ln) ...................................................................................................................93 PAGE 11 11 439 Variation of TT per mile with demand for different values of offramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 m i/hr, and downstream capacity = 1689 veh/hr/ln) ...................................................................................................................93440 Variation of TT per mile with demand for different values of offramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 1324 veh/hr/ln) ...................................................................................................................94441 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) ..............................................................................................94442 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) ..............................................................................................95443 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) ..............................................................................................95444 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) ............................................................................................................96445 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) ............................................................................................................96447 Time series plot between TT per mile of the upstream segment and the number of vehicles in the upstream segment ...................................................................................... 97449 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) .......... 98450 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) .....................................................................................................................................99451 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) ..............................................................................................99452 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 PAGE 12 12 453 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) ............................................................................................100454 Variation of TT per mile with demand for different values of offramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 2209 veh/hr/ln) .................................................................................................................101455 Variation of TT per mile with demand for different values of offramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 1696 veh/hr/ln) .................................................................................................................101456 Variation of TT per mile with demand for different values of offramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 1326 veh/hr/ln) .................................................................................................................102457 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) ............................................................................................102458 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) ............................................................................................103459 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) ............................................................................................103460 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) ..........................................................................................................104461 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) ..........................................................................................................104462 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) .................................................................................................................105463 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) .............................................................................................................105464 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 PAGE 13 13 465 Time series plot between TT per mile of the downstream bottleneck and the number of vehicles in the downstream bottleneck ........................................................................ 106466 Time series plot between TT per mile of the upstream segment and the number of vehicles in the upstream segment .................................................................................... 10751 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) ................... 12552 Sigmoid curve ............................................................................................................. .....12553 Comparison of average HCM speed and model speed .................................................... 12654 Variation of maximum T.T. with demand for a series of length of basic freeway segment ....................................................................................................................... .....12655 Variation of travel time with time interval ...................................................................... 12756 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) .................... 12757 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)......................................12861 Variation of upstream segment T.T. with demand for several anal ytical models with capacity at 1515 veh/hr/ln ................................................................................................130 PAGE 14 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 PAGE 15 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 undersaturated 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 PAGE 16 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 onramp demand and length of the entry segment for merge segment, with the addition of the offramp demand and length of the entry segment for diverge segment, with the addition of the onramp demand, offramp demand, and length of the en try segment for weave segment. PAGE 17 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 pretrip 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 shortterm 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 shortterm 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 undersaturated (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). PAGE 18 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. PAGE 19 19 CHAPTER 2 LITERATURE REVIEW This chapter reviews literature relevant to th e topic. First, the stateofthe art on T.T. models used in planning applications are review ed (Section 2.1). Next, th e stateofart 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): (21) Where, PAGE 20 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): PAGE 21 21 (22) 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 (23) Where, t= T.T. t0= free flow T.T. t = time period for which the specified demand persists q= flow C= capacity = Delay parameter PAGE 22 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 21 and Figure 22. It can be observed from Figure 21 and Figur e 22 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 nonlinearly 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 simulationbased 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, PAGE 23 23 intersection control, start up loss ti mes, vehicle headways, and pedestrian traffic. They used this simulationbased estimation of T.T., for their traffic assignment process. 2.2 Travel Time Estimation fo r RealTime 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 reidentified using its lengt h as its signature (Coifman 1998). By identifying the vehicle at both the upstream and downstream 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 downstream 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 PAGE 24 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, noninstrumented vehicle tracking, and passive probe technique. Microwave radar PAGE 25 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. PAGE 26 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 onramp: Higher the demand from onramp, 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 offramp: 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 onramp: Higher the demand from onramp 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 offramp: 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). PAGE 27 27 2.5 Summary and Conclusions Analytical T .T. models using demand have been developed, and are applicable for both undersaturated 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 PAGE 28 28 segment are also considered with the addition of the onramp demand and length of the entry segment for merge segments, with the addition of the offramp demand and length of the entry segment for diverge segments, with the addition of the onramp demand, offramp demand, and length of the entry segment for weave segments. Figure 21. Comparison of BPR, MTC, Akcelik and 1994 HCM T.T. functions for q/c<1.5 (source: Rupinder Singh, 1999) Figure 22. Comparison of BPR, MT C, Akcelik and 1994 HCM T.T. functions for q/c <2 (source: Rupinder Singh, 1999) PAGE 29 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 31. 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 icrosimulation 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 microsimulation 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 PAGE 30 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 onramp, 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 offramp, 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 onramp, demand on offramp, length of the entry segment, weaving Length. PAGE 31 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 PAGE 32 32 predicted T.T. using the analytic al models developed as part of this thesis along with other analytical models in literature. PAGE 33 33 Figure 31. 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 PAGE 34 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 41, Table 42, Table 43, and Table 44. 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. PAGE 35 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 onramps or offramps. A sketch of a basic freeway segment is shown in Figure 41. The basic freeway segment shown in Figure 41 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 PAGE 36 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. FreeFlow 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 2lane segments, 3lane segments, and 4lane 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 45, 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 42 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. PAGE 37 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 43 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 43, 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 freeflow speed on T.T., th e freeflow speed is varied from 55 mph to 70 mph and the relationship between T.T. and demand for each of the freeflow speeds is observed. Figure 44 presents the relationship be tween T.T. and demand for different freeflow 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 PAGE 38 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 freeflow speed on T.T. when there is a downstream bottleneck, the freeflow 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 freeflow 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 45, 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 freeflow speeds is presented in Figure 46. As shown in the Figure 46, 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 freeflow conditions, and there is no change in T.T. with increase in freeflow 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 47 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 PAGE 39 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 47, 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 48 presents the relationship between T.T. and demand for different freeflow 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 48, 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 48. As shown in the Figure 48, 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. PAGE 40 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 49. 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 49, 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 410 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 410, 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 411 presents the relationship between T.T. and demand as a function of nu mber of lanes when there is a downstream PAGE 41 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 411, 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 412 presents the relationship between downstream capacity and T.T per mile of the downstream segment. As shown in Figure 413, 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 413 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 414, 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 414, PAGE 42 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 415, 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 415, 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 42 to Figure 415) 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 42) 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 43). Thus the impact of all other variables is brokendown 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 44). However if there is a downstream bottleneck, the FFS does not impact the T.T. (Figure 45 & Figure 46). PAGE 43 43 4) The length of the basic freeway segment is no t significant when there is not bottleneck (Figure 47). However when there is a downstream bottleneck, the length of basic free flow segment becomes significant, under conge sted conditions (Figure 48 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 410 & 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 46 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 416). 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. PAGE 44 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 2lane segments, 3lane segments, and 4lane 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 47, 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. PAGE 45 45 Preliminary analysis was conducted to evaluate the impacts of each of these variables on the T.T. per mile. Figure 417 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 418 presents the relationship between downstr eam capacity and the T.T. As shown in Figure 418 the T.T. plot with demand has two char acteristic points similar to the basic freeway segment. As illustrated in Figure 418 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 freeflow speed on T.T., th e freeflow speed is varied from 50 mph to 70 mph and the relationship between T.T. and demand for each of the freeflow speeds is observed. Figure 419 presents the relationship be tween T.T. and demand for different freeflow 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 freeflow speed on T.T. when there is a downstream bottleneck, the freeflow 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 420 presents the relationship between T.T. PAGE 46 46 and demand for different freeflow 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 420, 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 freeflow speeds is presented in Figure 421. 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 421, 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 onramp demand on T.T., the length rampdemand is varied from 100 veh/hr/ln to 500 veh/hr/ln and the relationship between T.T. and demand for each value of onramp demand is observed. Figure 422 presents the relationship between T.T. and demand for different onramp 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 onramp demands. Therefore onramp demand is not an important variable in the estimation of T.T. when there is no downstream bottleneck. PAGE 47 47 To find the impact of onramp demand on T.T. when there is a downstream bottleneck, the rampdemand 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 onramp demand is observed. Figure 423 presents the relationship between T.T. and demand for different onramp 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 onramp demands. Therefore onramp demand is not an impor tant variable in the estimation of T.T. when there is no downstream bottleneck. To find the impact of freeflow speed on T.T. when there is a downstream bottleneck, the freeflow 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 423 presents the relationship between T.T. and demand for different freeflow 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 onramp demands is presented in Figure 424. As shown, as the FFS increases, the difference in T.T. per mile between each of the onramp demand starts increasing after the demand reaches downstream se gment capacity. As shown in the Figure 424, 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 425 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 PAGE 48 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 425, 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 426 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 426, 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 427. 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. PAGE 49 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 428, 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 428, 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 429. 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 429, 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 430, 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 430, PAGE 50 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 431, 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 431, 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 417 to Figure 440) 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 417) 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 418). Thus the impact of all other variables is brokendown 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 419). 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 420 & Figure 421). PAGE 51 51 4) Onramp demand doesnt show up significant variation in T.T. when there is no downstream bottleneck (Figure 422). 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 onramp demand (Figure 423 & Figure 424). 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 onramp demand) remains fixed with demand. It is also observed that th e T.T. per mile is higher for higher onramp 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 428). 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 429 and Figure 430. 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 inturn the T.T. decreases as shown in Figure 429 and Figure 430 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 410, Figure 411, & Figure 412) 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 431. The diverge segment network consists of four freeway links and an o fframp 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 431. 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 PAGE 52 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 431. 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 431 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. OffRamp 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 offramp exit % are used: 100, 300, and 500 veh/hr/ln. PAGE 53 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 49, and scenarios are developed for each combination of these for a diverge segment. The complete set of values tested is shown in Table 49, 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 433 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 434 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 PAGE 54 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 434 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 freeflow speed on T.T ., the freeflow speed is varied from 50 mph to 70 mph and the relationship between T.T. a nd demand for each of the freeflow speeds is observed. Figure 435 presents the relationship be tween T.T. and demand for different freeflow 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 freeflow speed on T.T. when there is a downstream bottleneck, the freeflow 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 436 presents the relationship between T.T. and demand for different freeflow 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 PAGE 55 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 436, 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 freeflow speeds is presented in Figure 437. As shown, once demand reaches downstream segment capacity, conge stion starts to occur and vehicles can no longer travel at freeflow conditions In these cases there is no change in T.T. with increase in freeflow speed. As shown in the Figure 437, 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 438 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 438, 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 439 presents the PAGE 56 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 439, 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 440. As shown, there is no change in T.T. with increas e in exit percentage. As shown in the Figure 440, 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 441 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 442 presents the relationship between T.T. and demand for different lengths of entry PAGE 57 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 442, 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 inturn the T.T. decreases as shown in Figure 442. As shown in the Figure 442, 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 443. 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 443, 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 444 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 PAGE 58 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 444, 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 445 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 445, 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 446, 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 446, once downstream bottleneck gets saturated with traffic, T.T. starts to flatten out to a maximum value of T.T. PAGE 59 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 447, 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 447, 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 432 to Figure 447) 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 433) 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 434). Thus the impact of all other variables is brokendown 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 435). 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 436 & Figure 437. 4) Offramp exit % shows up no signi ficant variation in T.T. wh en there is no downstream bottleneck (Figure 438). Thus offramp 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 offramp exit %. Moreover it is also observed that this difference in T.T. (for different values of offramp exit %) keeps increasing with demand until the PAGE 60 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 offramp exit %. When the downstream segment has full reduction in capacity, it is f ound that for a given offramp exit %, there is no change in T.T. per mile with main line demand, as shown in Figure 440. Moreover at any given main line demand value the value of T.T. per mile is lower for higher offramp exit %. 5) Length of the entry segment doesnt show up si gnificant variation in T.T. when there is no downstream bottleneck (Figure 441). 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 442 and Figure 443. It is observed from Figure 443 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 inturn the T.T. per mile decreases as shown in Figure 442. 6) The number of lanes shows no significant imp act on T.T. independent of the downstream bottleneck (Figure 444, & Figure 445) 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 447. 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. PAGE 61 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. OffRamp 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 offramp 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 411, and scenarios are developed for each combination of these for a weaving segment. The complete set of values tested is shown in Table 411, and scenarios are developed for each combination of these for a weaving segment. In order to generate th e scenarios for weaving PAGE 62 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 448 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 449 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 449 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. PAGE 63 63 To find the impact of freeflow speed on T.T., th e freeflow speed is varied from 50 mph to 70 mph and the relationship between T.T. and demand for each of the freeflow speeds is observed. Figure 450 presents the relationship be tween T.T. and demand for different freeflow 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 freeflow speed on T.T. when there is a downstream bottleneck, the freeflow 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 451 presents the relationship between T.T. and demand for different freeflow 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 451, 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 freeflow speeds is presented in Figure 452. As shown, once PAGE 64 64 demand reaches downstream segment capacity, conge stion starts to occur and vehicles can no longer travel at freeflow conditions In these cases there is no change in T.T. with increase in freeflow speed. As shown in the Figure 452, 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 453 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 453, 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 454 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 454, 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 454, 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). PAGE 65 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 455. As shown in Figure 455, 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 455, 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 456 presents the relationship between T.T. and demand for different lengths of entry segments when there is no downstream bottleneck. As shown in Figure 456, 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 457 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 457, 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 PAGE 66 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 457, 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 inturn the T.T. decreases as shown in Figure 457. As shown in the Figure 457, 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 458. 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 458, 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 459 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 PAGE 67 67 of T.T. when there is no downstream bottleneck. As shown in the Figure 459, 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 460 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 460, the T.T. remains relatively constant with increas ing demand, when there is redu ction in downstream capacity. To find the impact of onramp demand on T.T., the length rampdemand is varied from 100 veh/hr/ln to 500 veh/hr/ln and the relationship between T.T. and demand for each value of onramp demand is observed. Figure 461 presents the relationship between T.T. and demand for different onramp 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 onramp 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 onramp demand on T.T. when there is a downstream bottleneck, the rampdemand 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 onramp demand is observed. Figure 462 presents the relationship PAGE 68 68 between T.T. and demand for different onramp 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 onramp demands. Therefore onramp 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 onramp demands is presented in Figure 463. As shown, as the FFS increases, the difference in T.T. per mile between each of the onramp demand starts increasing after the demand reaches downstream se gment capacity. As shown in the Figure 463, 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 464, 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 464, 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 465, the T.T. per of the upstream segm ent closely follows the trend of the number of PAGE 69 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 465, 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 448 to Figure 465) 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 448) 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 449). Thus the impact of all other variables is brokendown 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 450). 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 451 and Figure 452. 4) Offramp exit % shows up no signi ficant variation in T.T. wh en there is no downstream bottleneck (Figure 453). Thus offramp 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 offramp exit %. Moreover it is also observed that this difference in T.T. (for different values of offramp 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 offramp exit %. When the downstream segment has full reduction in capacity, it is f ound that for a given offramp exit %, there is no change in T.T. per mile with main line demand, as shown in PAGE 70 70 Figure 454 and Figure 455. More over at any given main line demand value the value of T.T. per mile is lower for higher offramp exit %. 5) Length of the entry segment doesnt show up si gnificant variation in T.T. when there is no downstream bottleneck (Figure 456). 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 457 and Figure 458. It is observed from Figure 458 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 inturn the T.T. per mile decreases as shown in Figure 458. 6) The number of lanes shows no significant imp act on T.T. independent of the downstream bottleneck (Figure 459, & Figure 460) PAGE 71 71 Table 41. 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 42. 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 Onramp location 1500 3000 Capacity of Downstream Segment No blockage 1 Lane blocked and 95% rubber necking factor for rest of the lanes Table 43. 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 Onramp location 1500 3000 Distance between Onramp 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 44. 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 Onramp 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 45. 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 46. 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 47. 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 PAGE 73 73 Table 48. 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 49. Input values simu lated for a diverge segment Demand per Lane (main line) (veh/hr/ln) Downstream Capacity (veh/hr/ln) Speed (mph) Offramp 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 410. Impact of study variab les on T.T. of diverge segment Variable Unrestricted downstream segment capacity Restricted downstream segment capacity FFS Significant Not significant Offramp 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 411. 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 412. Impact of study variab les on T.T. of weaving segment Variable Unrestricted downstream segment capacity Restricted downstream segment capacity FFS Significant Not significant Offramp Demand Not significant Significant Onramp 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 41. Picture of a basic freeway segment. PAGE 75 75 Figure 42. 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 43. 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 44. 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 45. 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 46. 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 47. 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 48. 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 49. 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 410. 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 411. 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 412. Variation of TT per mile with dema nd for the downstream segment with (number of lanes = 2, FFS = 55 mph) Figure 413. 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 414. Time series plot between TT per m ile of the downstream bottleneck and the number of vehicles in the downstream bottleneck Figure 415. 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 416. Sketch of a merge freeway segment. Figure 417. 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 418. 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 419. 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 420. 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 421. 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 422. 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 423. 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 424. 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 425. 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 426. 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 427. 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 428. 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 429. 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 430. Time series plot between TT per m ile of the downstream bottleneck and the number of vehicles in the downstream bottleneck Figure 431. 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 432. Sketch of a diverge freeway segment. Figure 433. 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 434. 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 435. 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 436. 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 437. 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 438. Variation of TT per mile with demand for different values of offramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 2136 veh/hr/ln) Figure 439. Variation of TT per mile with demand for different values of offramp 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 440. Variation of TT per mile with demand for different values of offramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 1324 veh/hr/ln) Figure 441. 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 442. 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 443. 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 444. Variation of TT per mile with demand for different values of # lanes (length of entry section = 500 ft, and FFS = 50 mi/hr, offramp exit % = 5, and downstream capacity = 2136 veh/hr/lane) Figure 445. Variation of TT per mile with demand for different values of # lanes (length of entry section = 500 ft, and FFS = 50 mi/hr, offramp 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 446. Time series plot between TT per m ile of the downstream bottleneck and the number of vehicles in the downstream bottleneck Figure 447. 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 448. Sketch of a weaving freeway segment. Figure 449. 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 450. 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 451. 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 452. 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 453. 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 454. Variation of TT per mile with demand for different values of offramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 2209 veh/hr/ln) Figure 455. Variation of TT per mile with demand for different values of offramp 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 456. Variation of TT per mile with demand for different values of offramp exit % (lanes = 2, length of entry section = 500 ft, and FFS = 50 mi/hr, and downstream capacity = 1326 veh/hr/ln) Figure 457. 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 458. 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 459. 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 PAGE 104 104 Figure 460. Variation of TT per mile with demand for different values of # lanes (length of entry section = 500 ft, and FFS = 50 mi/hr, offramp exit % = 5, and downstream capacity = 2209 veh/hr/lane) Figure 461. Variation of TT per mile with demand for different values of # lanes (length of entry section = 500 ft, and FFS = 50 mi/hr, offramp 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 PAGE 105 105 Figure 462. 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 463. 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 PAGE 106 106 Figure 464. 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 465. 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 PAGE 107 107 Figure 466. 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 PAGE 108 108 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 51. As shown in Figure 51, 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 PAGE 109 109 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 52, 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. (51) Where, Yi= Dependent variable (in this case travel time per mile) PAGE 110 110 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 = (52) Where, Yi= Dependent variable (Travel time) Parameter describing the location on the S curv e. This parameter is derived theoretically. PAGE 111 111 = = 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 = (53) 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. PAGE 112 112 = ; 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 tion3, 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 51 It should be noted that the above regression equation presented 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 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 PAGE 113 113 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 53. 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: (54) It can be observed from equation4 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 54. 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 PAGE 114 114 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: (55) 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 52. It can be observed from equation5 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 41, 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 415. 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(56) Where L = Length of the section J = Jam density PAGE 115 115 D = Freeway demand = Downstream capacity The combined model for basic freeway segment (BFS) is presented below: TT = + (57) 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: (58) V = Free flow speed D = Freeway demand = Onramp demand Cd = Capacity of downstream segment The summary of uncongested model for merg e segment is presen ted in Table 52. In order to tie up this model with model from second part, (59) It can be observed from equation6 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 PAGE 116 116 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: (510) 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 54. It can be observed from equation5 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 = + (511) PAGE 117 117 Where is derived similarly to the way it is derived for basic fr eeway segment, but the demand now includes freeway demand and the onramp 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: (512) Where, V = Free flow speed D = Demand Cd = Capacity of downstream segment. The summary of uncongested model for BFS is presented in Table 55. In order to tie up this model with model from second part, (513) It can be observed from equation4 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 PAGE 118 118 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: (513) Where, = Range of travel time minus travel time from part one when demand equals capacity = Length of entry segment = Capacity of downstream segment = Offramp demand/exit percentage The congested T.T. range model stat istics are presented in Table 56. It can be observed from equation5 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. = + (514) Where is derived similarly to the way it was derived for basic freeway segment, but the demand now includes freeway dema nd and the offramp demand. PAGE 119 119 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: (515) 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 57. In order to tie up this model with model from second part, (516) It can be observed from equation4 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 PAGE 120 120 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: (517) Where, = Range of travel time minus travel time from part one when demand equals capacity = Length of entry segment = Capacity of downstream segment = Offramp demand/exit percentage The congested T.T. range model stat istics are presented in Table 58. It can be observed from equation5 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: + (518) 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 offramp 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 PAGE 121 121 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 56. As shown in Figure 56, 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 57. As shown in Figure 57, 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 57, 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: (519) 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 59. PAGE 122 122 Table 51. BFS uncongested model statistics Explanatory variables CoefficientsStandard Errort Stat Pvalue Intercept 120.86860.634767190.4141 0 1.006320.009373107.361 0 4.6546770.33310613.97355 0 Goodness of fit measures R2 0.975288 Adjusted R2 0.975122 Number of cases 300 Table 52. BFS congested T.T. range model summary Explanatory variables Coefficients Standard Error t Stat Pvalue 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 53. Merge uncongested model summary Explanatory variables CoefficientsStandard Errort Stat Pvalue Intercept 126.8311.128112.4090.000 Speed 1.0900.01195.4400.000 ((D+Dr)/Cd) 5.6780.6368.9230.000 DS Capacity 0.0010.0002.0870.037 Goodness of fit measures R2 0.92 Adjusted R2 0.92 Number of cases 844 Table 54. Merge congested T.T. ra nge model statistics and estimates Explanatory variables Coefficients Standard Error t Stat Pvalue 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 PAGE 123 123 Table 55. Diverge uncongested model summary Explanatory variables CoefficientsStandard Errort Stat Pvalue Intercept 132.810 1.4094.710.00 Speed 1.038 0.0169.410.00 D/C 8.634 0.7012.410.00 DSCapacity 0.006 0.0013.710.00 Goodness of fit measures R2 0.82 Adjusted R2 0.82 Number of cases 1152 Table 56. Diverge congested T.T. range model summary Explanatory variables CoefficientsStandard Errort Stat Pvalue Intercept 0N/A N/A N/A 4.8680.08159.818 0.000 0.2400.0693.458 0.001 % Exit 10.4120.55318.845 0.000 Goodness of fit measures R2 0.93 Adjusted R2 0.93 Number of cases 720 Table 57. Weaving segment uncongested model summary Explanatory variables CoefficientsStandard Errort Stat Pvalue Intercept 115.18 1.3883.510.00 Speed 1.0496 0.0179.190.00 12.83460.5822.030.00 DSCapacity 0.0012 0.002.720.01 Goodness of fit measures R2 0.65 Adjusted R2 0.65 Number of cases 3615 PAGE 124 124 Table 58. Weaving segment congest ed T.T. range model summary Explanatory variables CoefficientsStandard Errort Stat Pvalue Intercept 34.83962.119316.4392 0.0000 3.40970.0282120.8524 0.0000 0.05680.02182.6077 0.0092 % Exit 4.41840.183624.0636 0.0000 Goodness of fit measures R2 0.94 Adjusted R2 0.94 Number of cases 1728 Table 59. Bottleneck T.T. model summary Explanatory variables CoefficientsStandard Errort Stat Pvalue 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 PAGE 125 125 Figure 51. 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 52. 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 PAGE 126 126 Figure 53. Comparison of averag e HCM speed and model speed Figure 54. 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 PAGE 127 127 Figure 55. Variation of travel time with time interval Figure 56. 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 PAGE 128 128 Figure 57. 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 PAGE 129 129 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 uncongested 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. PAGE 130 130 Figure 61. 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 PAGE 131 131 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 undersaturated 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 PAGE 132 132 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 workzone, 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 workzone 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 PAGE 133 133 bottleneck and the upstream segments can be obtained from the models developed in this thesis. 7.4 Further Research This study used CORSIM m icrosimulation so ftware package for simulating scenarios, which are later used for devel opment of the analytical models Several other microsimulation software packages are available, including AIMSUN, PARAMICS, and VISSIM that suit the general requirements of this study. The algorit hms used in these microsimulation software packages are different. The impact of other micr osimulation 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 flowdensity 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. PAGE 134 134 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. 257266 Ando N., and E. Taniguchi (2006), Travel Time Reliability in Vehicle Routing and Scheduling with Time Windows Netrks and Spatial Economics Vol 6, num 34, pp. 293311 Balke, K., Ullm an, G., McCasla nd, W., Mountain, C., Dudek, C., 1995. Benefits of realtime 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. 253266 Bhat, C.R., (1995) A Heteroscedastic Extreme Value Model of Interc ity Mode Choice Transportation Research Part B Vol. 29, No. 6, pp. 471483, 1995. Bureau of Public Roads (1964). Traffic Assignment Manual. U.S. Dept. of Commerce, Urban Planning Division, Washington D.C. RL. Cheu, X. Jin, KC. Ng, YL. Ng, and D. Srinivasan (1998) Calibration of FRESIM for Singapore Expressway Using Genetic Algorithm Journal of Trans portation Engineering, ASCE, vol. 124(6), pp. 526535. Coifman B. and Cassidy, M. (2002) Vehicle Reidentification and Travel Time Measurement on Congested Freeways, Transportation Research: Part A vol 36, no 10, pp. 899917. 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): 409428. Fan Y., and Y. Nie (2006), Optimal Routing for Maximizing the Travel Time Reliability Networks and Spatial Economics Vol 6, num 34, pp. 333344 PAGE 135 135 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. 497513 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 vehiclelicense number recogniti system using realtime 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, 932937, 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 Routebased 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 SpeedFlow and SpeedCapacity 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. 153158. Taniguchi E., and R. G. Thompson (2002), Modelling City Logistics Transportation Research Record, num 1790, pp. 4551 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. 489515 PAGE 136 136 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 7389 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 RealTime 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. 7792 J. Hourdakis, P. G. Michalopoulos and J. Kottommannil (2003) Practial Procedure for Calibrating Microscopic Tr affic Simulation Models. Transportation Research Record,No. 1852, pp. 130139, 2003. PAGE 137 137 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. 