CONDITIONAL CELL TRANSMISSION MODEL FOR TWO-WAY ARTERIALS IN OVERSATURATED CONDITIONS PING WANG A DISSERTATION

Transcription

1 CONDITIONAL CELL TRANSMISSION MODEL FOR TWO-WAY ARTERIALS IN OVERSATURATED CONDITIONS by PING WANG A DISSERTATION Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Civil, Environmental, and Construction Engineering in the Graduate School of The University of Alabama TUSCALOOSA, ALABAMA 2010 ii

2 Copyright Ping Wang 2010 ALL RIGHTS RESERVED iii

3 ABSTRACT In 2007, congestion caused urban Americans to travel 4.2 billion hours more and to purchase an extra 2.8 billion gallons of fuel for a congestion cost of $87.2 billion - an increase of more than 50% over the previous decade. Urban arterials operating in oversaturated conditions are now very common and are expected to become even more prevalent. As a result, there is an urgent need to explicitly address oversaturation. Simulation of oversaturation plays an important role in addressing it. However, the previous research, including existing traffic simulation software and theoretical approaches, take full account of traffic flow on two way arterials in oversaturated conditions. Therefore, improvements of existing traffic flow model simulation techniques are necessary to adequate study such fully oversaturated arterials. The objective of this research is to develop a novel feature for traffic flow models, to simulate when traffic queues on two way arterials periodically extend until then block an upstream signal in oversaturated conditions. Such a model should be capable of delineating the dynamic of traffic flow created by the merging and diverging activities on two way arterials. In additional, it should have the capability of describing blockages, spillback and shock wave phenomena along the oversaturated arterials. The Cell Transmission model (CTM) is used in the dissertation, because it can accommodate all traffic conditions from light condition to oversaturated condition. However, it has limitations and has only recently been extended from one way two way arterials. Two way ii

4 arterials have more diverge and merge activities at intersections, which make the coding of CTM more complex and time-consuming. Second, a noticeable inaccuracy in prior CTM research is the failure to simulate the blockages at intersections. They typically estimate the delay occurring on segments and ignore the delay occurring at intersections. These limitations affect CTM s accuracy and limit its use. To enhance CTM, a conditional cell transmission model (CCTM) is developed with two improvements. First, CTM is expanded for two-way arterials by taking account of all diverge and merge activities at intersections. Second, a conditional cell is added to simulate periodic spillback and blockages at an intersection. The cell exists conditionally, depending on whether or not there is a spillback at an intersection. In other words, if spillback happens, the conditional cell exists and stores the vehicles which spill back into the intersection; if there is no spillback, the conditional cell will not exist. In CCTM, users may input the probability of a conditional cell (drivers breaking the driving rule) and probability of occurrence of useful location of a gap to match the characteristics of local drivers behavior. This is a unique contribution of CCTM. The CCTM traffic flow simulation was initially developed using evolutions of small model of six cell mode. It included (a segment cell, a diverge cell, a cell in front of an intersection, a cell in a left turn lane, a cell in the minor street and a conditional cell). They were loaded with light duty traffic, moderate duty traffic and heavy duty traffic respectively. To test the overall performance of CCTM, a series of experiments are designed and performed for a multilane, two-way, three-signal sample network. Experiments were conducted to give sensitivity analyses to four user-defined parameters including traffic demand, traffic signal timing, possibility of occurrence of a useful gap and possibility of a conditional cell. The iii

5 results demonstrate that CCTM can accommodate various traffic demands and CCTM s accurate representation of traffic flow. Finally, to validate CCTM, it is compared with HCS (Highway Capacity Software 2000). Three scenarios of traffic demand are inputted into HCS and the results of travel speeds are compared with those of CCTM. The consistency between HCS 2000 and CCTM shows that CCTM is a reliable methodology of modeling traffic flow in oversaturated condition. iv

6 DEDICATION This dissertation and my life are dedicated to my son, Ethan Will Yang. v

7 LIST OF ABBREVIATIONS f k x t The traffic flow The density The space variable The time variable k jam Jam density Q V W Inflow capacity Free flow speed The speed of backward shock wave n i - ( ) The number of vehicles in cell i 1at time t 1 t n i (t) The number of vehicles in cell i at time t d Control delay (t) Q i The inflow capacity of cell i at timet N i (t) Vehicle holding capacity of cell i L i The length of cell Cell i f i (t) The actual flow into cell i at time t f i «( ) The actual flow into cell i + 1 at time t 1 t h s Saturation headway Saturation flow rate vi

8 DE i j Vehicles leave the network is denoted as The row number of a cell The column number of a cell vii

9 ACKNOWLEDGMENTS I am pleased to have this opportunity to thank the many colleagues, friends, and faculty members who have helped me with this research project. I am most indebted to Dr. Steven L. Jones, the chairman of my dissertation committee, for sharing his research expertise and wisdom regarding motivational theory. I would also like to thank all of my committee members, Dr. Daniel S. Turner, Dr. Jay K. Lindly, Dr. Daniel J. Fonseca and Dr. Keith A. Woodbury for their invaluable input, inspiring questions, and support of both the dissertation and my academic progress. I would like to thank my dear friends Dr. Norton, Mrs. Harris, Ayse, Saravanan, Moses, Elsa, Menasse and Mary for their kind help. Appreciation is also extended to my husband, my parents, and my sister for their strong support and inspiration. Finally I thank all of the kind people at The University of Alabama. viii

10 CONTENTS ABSTRACT... ii DEDICATION... v LIST OF ABBREVIATIONS... vi ACKNOWLEDGMENTS... viii LIST OF TABLES... xiv LIST OF FIGURES... xvii 1 INTRODUCTION... 1 Background... 1 Research Objective REVIEW OF RELATED LITERATURE... 5 Modeling Oversaturated Traffic Conditions... 5 Cell Transmission Model FORMULATION OF CONDITIONAL CELL TRANSMISSION MODEL Improvements to Cell Transmission Model (CTM) Modeling Two-way Flow Using CCTM Diverge Formulation ix

11 Merge Formulation Adding Conditional Cell to Simulate Spillback and Blockages at an Intersection Simulating the Spillback at an Intersection Judging the Availability of an Acceptable Gap Coding in CCTM PARAMETERS IN CCTM Built-in Parameters The Length of Cells The Holding Capacity of Cells The Flow Capacity of Cells User-Defined Parameters Traffic Demand Signal Timing The Possibility of the Conditional Cell The Possibility of the Occurrence of a Useful Gap ILLUSTRATIONS OF EVOLUTIONS OF EXAMPLE CELLS The Sample Network Evolution of Example Cells Example 1: A Cell in a Segment Cell (2, 3, 3) Example 2: A Diverge Cell Cell (2, 3, 6) x

12 Example 3: A Cell in Front on an Intersection Cell (2, 3, 7) Example 4: A Cell in the Left-Turn Lane Cell (2, 3, 7L) Example 5: A Cell in a Minor Street Cell (6, 2, 1) SENSITIVITY ANALYSES OF USER-DEFINED PARAMETERS OF CCTM Design of Experiments The Baseline Experiment Experiment 1: Traffic Demand versus Delay Experiment 2: Signal Timing versus Delay Experiment 3: The Possibility of the Occurrence of a Useful Gap Experiment 4: The Possibility of a Conditional Cell versus Delay (CTM vs. CCTM) VALIDATION OF CCTM Input Data to HCS-arterials File Results of Analysis CONCLUSIONS AND RECOMMENDATIONS Conclusions Development of CTM-based Theory Results of Experiments Contributions of CCTM Recommendations Recommendations for Future Research to Further Develop CCTM xi

13 Recommended of Future Applications of CCTM Summary REFERENCES APPENDIX A APPENDIX B xii

14 LIST OF TABLES Table 5-1. Evolutions of Cells from Time Step 1 to Time Step Table 6-1. Traffic Demand of Baseline Experiment Table 6-2. Phase Diagram of Baseline Experiment Table 6-3. Traffic Demand of Experiment 1a Table 6-4. Traffic Demand of Experiment 1b Table 6-5. Traffic Demand of Experiment 1c Table 6-6. Phase Diagram of Experiment 1c Table 6-7. Delay of Experiment 1c Percentage of Left Turns (Seconds) Table 6-8. Phase Diagram of Experiment 2a Table 6-9. Delay of Westbound and Eastbound on the Major Street (Seconds) Table Phase Diagram of Experiment 2b Table Delays on the Major Street and the Minor Street (Seconds) Table Phase Diagram of Experiment 2c Table Delay of Experiment 2c Using Lag Left Turns (Seconds) Table Phase Diagram of Experiment 2d Table Delay of the Major Street and Entire Network of Experiment 2d (Seconds) Table Delay of Experiment 3 Probability of Occurrence of a Useful Gap (Seconds) Table Comparisons of Delays between CTM and CCTM (Seconds) Table 7-1. Data Input into HCS-arterials xiii

15 Table 7-2. Geometry and Volume Parameters Table 7-3. Operation Parameters Table 7-4. Saturation Flow Adjustment Table 7-5. Comparison between CCTM and the HCS in Terms of Travel Speed Table A1. Evolution of Cells for Heavy Duty Traffic xiv

16 LIST OF FIGURES Figure 3-1. The relationship between CTM and CCTM Figure 3-2. Traffic flow movements at a typical two-way intersection Figure 3-3. Diverge in one-way flow Figure 3-4. Diverge in two-way flow Figure 3-5. Diverge points at a typical two-way intersection (Roess et al., 2004) Figure 3-7. Merge in two-way flow Figure 3-8. Merge points at a typical two-way intersection (Roess et al., 2004) Figure 3-9. Westbound left turn blocked by a spillback of eastbound through vehicles Figure Adding a conditional cell to hold spillback vehicles at an intersection Figure Procedure for adding a conditional cell Figure Left turn is blocked by a queue spillback Figure Concept of an acceptable gap Figure A gap is not wide enough Figure A useful gap occurs Figure A useful gap occurs Figure A location of a gap that is not suitable Figure A screenshot of Excel coding Figure 4-1. A screenshot depicting inputting traffic demand xv

17 Figure 17. A screenshot depicting inputting traffic signal timing Figure 4-3. A screenshot depicting inputting possibility of a conditional cell Figure 5-1. Layout of two-way, three-signal arterial network Figure 5-2. A section of an arterial network Figure 5-3. Evolutions of cells in Time Step 1 and Time Step Figure 5-4. Evolutions of example cells in light conditions Figure 5-5. Evolutions of example cells in moderate conditions Figure 5-6. Evolutions of example cells in heavy conditions Figure 5-7. Overflow of left turns blocks through-lane entrance Figure 6-1. Designs of experiments to test the performance of CCTM Figure 6-2. Initialization time Figure 6-3. Network delay of baseline experiment Figure 6-4. Delay on the major street of baseline experiment Figure 6-5. Delay in each direction of the major street of baseline experiment Figure 6-6. Network delay of experiment 1a Figure 6-7. Delay in each direction of the major street of experiment 1b Figure 6-8. Through flow blocks left turn bay Figure 6-9. Left turn flow blocks the through lane Figure A screenshot depicting forward waves in CCTM Figure A screenshot depicting backward waves in CCTM Figure Spillback at an intersection Figure Westbound left turn blocked by the spillback in the conditional cell Figure 7-1. The geometry and volume at Intersections A, B and C xvi

18 Figure B1. A Screenshot depicting HCS results for arterial analysis in light duty traffic Figure B2. A Screenshot depicting HCS results for arterial analysis in moderate duty traffic Figure B3. A Screenshot depicting HCS results for arterial analysis in heavy duty traffic xvii

19 CHAPTER 1 INTRODUCTION Background Traffic congestion continues to be a daily problem for millions of motorists in the United States and elsewhere in the world. In 2007, congestion caused urban Americans to travel 4.2 billion hours more and to purchase an extra 2.8 billion gallons of fuel for a congestion cost of $87.2 billion an increase of more than 50% over the previous decade (Schrank and Lomax, 2009). Urban arterials operating in oversaturated conditions are now very common and are expected to become even more prevalent. Consequently, there is an urgent need to investigate ways to relieve oversaturated conditions. Kim (1990) defines an oversaturation as a condition that occurs when queues of vehicles fill entire blocks and interfere with the performance of adjacent upstream intersections. In Pignataro (1978), oversaturation is defined as the condition when vehicles are prevented from moving forward freely. Oversaturation occurs either because of the presence of an excessive demand of vehicles in the intersection itself or because of queue backs up into any of the exit links of an intersection. In Park (1999), oversaturation occurs when queues that develop at intersections during a green time cannot be eliminated in one signal cycle and are carried over to the next green. So a spillback grows and reduces the mobility of traffic near oversaturated intersections. 1

20 In order to develop traffic control solutions to reduce congestion and mitigate its impacts congested traffic conditions must be studied using analytical traffic engineering techniques. Traffic simulation is an important tool for analyzing traffic engineering problems and potential solutions. Simulation of congested, oversaturated conditions, however, has proven difficult and many available tools do not adequately model such conditions. Therefore, improvements of existing traffic flow model simulation techniques are necessary to adequate study such fully oversaturated arterials. This research aims to develop a traffic flow feature to improve the modeling of two-way arterials so that they are capable of modeling oversaturated conditions. The cell transmission model (CTM) is a potential simulation tool because it can accommodate all traffic conditions from light condition to oversaturated condition. CTM-based traffic simulations rely on global consequences of local vehicle interactions in the traffic stream In the past decade, CTM has emerged as an alternative tool for investigating traffic flow phenomenon, which uses discrete space and time scales which make it simple to understand and fast to simulate (Girianna and Benekohal, 2002). Validation studies of CTM using field data suggest that it is capable of modeling various traffic conditions on both freeways and arterials (Lin and Ahanotu, 1995; Smilowitz and Daganzo, 1999). An advantage of CTM is that it is applicable over a full range of traffic conditions as it is based on the entire fundamental relationship between traffic flow and density (Lo, 1999). Capacity is reached when the product of density and speed results in the maximum flow rate. Any flow rate other than capacity can occur under two different conditions, one with a high speed and low density and the other with high density and low speed (FHWA, 2000). The high- 2

21 density, low speed point represents oversaturated flow. Hence, CTM is able to model both normal conditions and oversaturated conditions. 3

22 Research Objective The objective of this research is to propose, develop, and test an improvement to CTM to improve its ability to model oversaturated traffic flow on a two-way arterial. Specifically, the research presents a new feature, the Conditional Cell, to model traffic flow dynamics created by the merging and diverging activities on two way arterials and capture the blockages, spillback and shock wave phenomena attributable to the oversaturated arterial operations. This study is an extension of a larger research effort Project #06121: Traffic Signals for Oversaturated Arterials conducted by the University Transportation Center for Alabama (UTCA). 4

23 CHAPTER 2 REVIEW OF RELATED LITERATURE Modeling Oversaturated Traffic Conditions During the past four decades, many traffic simulation software programs have been developed to address oversaturation. Basically, these simulation programs can be classified into two broad categories: (a) microscopic or (b) macroscopic. Microscopic simulation models focus on one individual vehicle as it follows another vehicle. Popular microscopic simulation programs in use today include SimTraffic, AIMSUN, CORSIM, and VISSIM. These programs record discrete traffic events at fixed-time intervals. Essentially, microscopic simulation programs provide great detail about various traffic scenarios such as the behaviors of drivers and pedestrians, but they are unable to provide a global view of these scenarios. This detail-oriented approach makes these models unsuitable for simulating oversaturated conditions in two-way arterials. SimTraffic was developed by Trafficware Inc., a California-based company (Trafficware, 2006). It is a versatile and easy-to-use program. To explain the variability of traffic flow, SimTraffic uses the percentile delay method, which assumes that vehicle arrivals follow a Poisson distribution. The delay output is the average of the 10th, 30th, 50th, 70th and 90th percentile scenarios weighted by the percentile flow rates. According to the user s manual, the percentile delay method and Webster s formula would yield similar results in most cases. However, these formulae are frequently inaccurate in congested conditions (Yin et al., 2007). 5

24 AIMSUN (Advanced Interactive Micro-Simulation for Urban and Non-Urban Networks) is a full function microscopic simulation tool with a broad range of simulation capabilities (TSS, 2006). Like SimTraffic and CORSIM, it can simulate a variety of traffic scenarios on minor streets, arterials, and entire networks (Jones et al., 2004). AIMSUN also has features that SimTraffic and CORSIM do not. For examples, it can model dynamic traffic assignment and produce 3-D animations. CORSIM is used for modeling traffic in urban networks and is based on a discrete event simulation approach and uses a periodic scan with a time interval of one second (FHWA, 2005). Also, driver behavior and pedestrian movement can be simulated in CORSIM (Ahn, 1997). CORSIM also offers optional simulations such as the capability to estimate fuel consumption and vehicle emissions (Paksarsawan and Montgomery, 1992). It performs reasonably well in uncongested conditions but not congested conditions. Developed at the University of Karlsruhe (Germany) during the early 1970s, VISSIM can model transit and traffic flow in urban areas and their connecting roadways on a microscopic level (PTV, 2005). Traffic engineers, transit operators, and city planners like this multipurpose simulator, because it enables them to assess the effects of new vehicle technologies on congestion (Enrique, 2006). VISSIM is used on congested arterials, and it produced results consistent with those of CORSIM (Bloomberg, 1999). In contrast, macroscopic simulation models are able to provide a global view of various traffic scenarios by representing traffic flow in aggregate measures (Lonnie and Ming, 1998). Popular macroscopic simulation programs in use today include TRANSYT-7F and PASSER. TRANSYT was developed in the United Kingdom and later adapted by the Federal Highway Administration (FHWA, 2009). TRANSYT-7F release 8 is capable of modeling 6

25 oversaturated conditions. However, TRANSYT does not include traffic density as a user-defined parameter and ignores the dynamic nature of traffic, thus making it difficult to accurately model oversaturated conditions (Chow and Lo, 2007). It still is not an ideal method to handle the oversaturated condition although it is good for low or moderate conditions. PASSER, developed by the Texas Transportation Institute, has been used by transportation engineers for almost 30 years (TTI, 2006). It has been used mainly to develop signal timings for a number of traffic signal installations. PASSER has also been used to analyze improvements of intersection-related geometry and traffic management, and estimate delay (Yin et al., 2007). Even though it has been enhanced many times since its development, PASSER is designed for uncongested conditions (Yin et al., 2007). 7

26 Cell Transmission Model Overview One macroscopic simulation model that addresses a variety of traffic conditions in the Cell Transmission Model (CTM). In the past decade CTM has emerged as a useful tool for investigating traffic flow phenomenon. The research on CTM started from the Lighthill and Whitham (1955) and Richards (1956) (LWR) model, which describe the relationship among the traffic flow volume, density, time, and space for the full range of the fundamental diagram (Lo, 2004). It explicitly takes into account the macroscopic variables of flow and density. It has non-convergence problem in that it has multiple solutions but only one that is physically relevant. Hence, the difficulty in solving the model limits its wide use in the traffic signal control area. Daganzo (1994) reached a new approach in the development of CTM. He explored the use of the LWR Model by adopting a simplified fundamental diagram, which he called the Cell Transmission Model. The fundamental flow-density diagram describes the relationship between traffic flow and density, both in normal flow conditions and in oversaturated flow conditions. It is no needed to switch or recalibrate the model when moving to different traffic conditions (Lo, 2007). CTM can capture traffic flow phenomena such as queue formation and dissipation. It is a potential platform for modeling oversaturated traffic flow. Theoretical results need validation from practical evidence. As mentioned previously, studies by Lin and Ahanotu (1995) and Smilowitz and Daganzo (1999) validated CTM for freeway and arterial traffic. Lin and Ahanotu (1995) developed CTM as a discrete version of the hydrodynamic theory of traffic flow. It is capable of automatically tracking shock waves, 8

27 acceleration waves, and propagation and dissipation of queues. Their report examined the performance of the basic CTM in congested and uncongested traffic on a single freeway segment of I-880 in California. Smilowitz (1999) presented a traffic model that could be used in predicting traffic congestion on a rural road. In his study, traffic data from a congested rural road were used to show that traffic delays and vehicle accumulations between any two generic drivers located inside a road section can be predicted from the traffic counts measured at the extremes of the section. This traffic model does not require recalibration on the day of the experiment (Lo, 1999). Lo (1999) reached another milestone in the development of CTM. His first simulation model was limited to one-way streets without any turning movements. It took advantage of a convergent numerical approximation to the hydrodynamic model to simulate dynamic traffic flow. In his case study, a small simple network was given to demonstrate the properties of the model and to verify its performance at light, moderate and heavy condition respectively. Lo noted that a longer horizon was needed to study the timing plans performance. Lo (2001) added turning movements to CTM to accommodate its use in more general networks. The study developed a traffic control formulation designed as a dynamic intersection signal control optimization (DISCO). Traffic in DISCO is modeled after CTM. Field data was used to investigate the performance of DISCO in extreme traffic conditions. This study was still limited to one-way streets. In summary, the literature review shows limited research on traffic modeling for oversaturated conditions. Many researchers have indicated that controlling oversaturation is a complex, challenging task. CTM offers promise in accomplishing this task, because it could be 9

28 enhanced to handle oversaturated conditions. However, three issues remain as core problems in modeling traffic flow during oversaturation conditions. Most research on CTM has been limited to non-saturated, one-way roads. Only recently have models emerged for two-way flow. Current CTM models do not capture spillback and blockages at intersections in oversaturated conditions. Most models do not estimate measures of effectiveness (MOEs) (e.g., delay) of a traffic network. Basic Theory of the Cell Transmission Model The Lighthill, Whitham (1955) and Richard (1956) (LWR) Model can be stated by the following two conditions: f k + x t = 0 and f = F( k, x, t) (2-1) Where f = the traffic flow; k = the density; x= the space variable; t = the time variable; and F = the function relating f and k. Daganzo (1994) simplified the solution by adopting the following relationship between traffic flow f, and densityk, which he called CTM. 10

29 f = min {, Q, W ( k k) } Vk jam (2-2) Where k = density; k jam = jam density; Q = inflow capacity; V = free flow speed; and W = the speed of backward shock wave. CTM assumes that the network can be divided into a set of equal length cells. The length of each cell is equal to the distance a single vehicle travels in one time step at the free flow speed (Lo, 2001). When there is no congestion, a vehicle travels from one cell to another at each time step. If there is congestion, a vehicle cannot travel to the next cell; thus, it will stay in the same cell, and delay will occur. In each time step the number of vehicles traveling into cell i at time t is the minimum among the number of vehicles waiting to enter cell i, the maximum number of vehicles that can enter cell i in a given time step, and the available space in cell i (Lo, 1999). The equation is as follows: { n ( t), Q ( t), W / V[ N ( t) n ( )]} f ( t) = min 1 t (2-3) i i i i i Where f i (t) = the number of vehicles traveling into cell i at time t; n i - ( ) = the number of vehicles in cell i 1at time t; 1 t n i (t) = the number of vehicles in cell i at timet; Q i (t) = the inflow capacity of cell i at time t ; 11

30 W = shock wave speed; V = free flow speed; and N i (t) = vehicle holding capacity of celli. N i (t) is the vehicle holding capacity of cell i as determined by the following equation: Ni ( t) = k jam L (2-4) Where k jam = the jam density (veh/km) and L = the length of cell (km). L is the product of free flow speed and the length of the time step. L = V t (2-5) The equation inherently accommodates different traffic conditions from light flow to oversaturation. This is an advantage of CTM. In light traffic, the flow is equal to the number of vehicles in cell i 1 at timet. In bottleneck traffic, the flow is equal to the saturation flow rate, and in oversaturated traffic, the flow is equal to an available space in at time cell i at time t (Lo, 2001). In Lo (2001), it is formulated as follows: { ( )} n i light traffic 1 t f i (t) = { Q i (t)} bottleneck between cells (2-6) { W / V[ N ( t) n ( t) ]} i i oversaturated traffic 12

31 The network can be updated at every time step. n ( t + 1) = n ( t ) + f ( t ) f 1( t ) i i i i+ (2-7) Where i = Cell i ; n i (t) = the number of vehicles in cell i at time t; f i (t) = the actual flow into cell i at time t; and f t i ) = the actual flow into cell i + 1 at time t. ( +1 The equation states that the number of vehicles in a cell at time t + 1 is equal to the number of vehicles in that cell at the prior time t, plus the number of vehicles that entered, and minus the number of vehicles that exited (Lo, 2001). Estimation of Delay As mentioned above, when there is no congestion, a vehicle travels from one cell to another at each time step. If a vehicle cannot travel to the next cell and it stays at the same cell, a delay of one time step will occur. Delay here is defined as the additional time beyond the normal time when a vehicle travels at free flow speed, and it is determined by the following equation (Lo, 2004): d ( t ) = n ( t ) f 1( t ) (2-8) i i i+ This equation states that the delay of cell i at time t is equal to the number of vehicles in it minus the number of vehicles flowing into the next cell i + 1. The delay of the whole network is obtained by aggregating all cells during the time horizon (Lo, 2001). 13

32 Delay = t i d ( t) (2-9) i Effect of Signal Timing The effect of the signal timing on traffic flow can be represented via the inflow capacity Q i (t). If time tfalls in a green time period, the inflow capacity of the cell is set to the saturation flow rate. If time tfalls in a red time period, the inflow capacity of the cell is set to zero (Lo, 2007). Mathematically, this can be written as: s t green time Q i (t) = (2-10) 0 t red time 14

33 CHAPTER 3 FORMULATION OF CONDITIONAL CELL TRANSMISSION MODEL Improvements to Cell Transmission Model (CTM) Even though CTM is able to accommodate all traffic conditions, it has limitations. First, until recently, CTM-based studies have been limited to one-way arterials. Two-way arterials have more diverge and merge activities at intersections, which makes coding of CTM more complex and time-consuming. Second, currently formulations of CTM do not simulate blockages at intersections. So they do not capture the delay originating at oversaturated intersections, its effects on all movements at the intersection or those upstream. Therefore, two improvements of CTM are needed to adequately study two-way arterials in oversaturated conditions. The purpose of this study is to develop a novel feature for macroscopic traffic flow models that is capable of simulating oversaturated conditions in twoway arterials. This new model, proposed as Conditional Cell Transmission Model (CCTM), reflects two improvements to CTM. Figure 3-1 shows the relationship between the existing CTM and the new CCTM. CCTM has been developed for use in two-way arterials to delineate the dynamic of traffic flow created by the merging and diverging activities in these situations. CCTM includes the addition of a conditional cell at an intersection to simulate spillback and blockages. 15

34 Problems in CTM Improvements to CTM CCTM CTM is limited to one-way arterials. CTM fails to simulate blockages at intersections. All diverge and merge activities are considered. Conditional cells are added at oversaturated intersections. CCTM is able to simulate two-way arterials. CCTM is able to describe traffic flow with increased accuracy. Figure 3-1. The relationship between CTM and CCTM. 16

35 Modeling Two-way Flow Using CCTM To model two-way flow, all possible turning movements must be considered including the turns from minor streets to the two-way major arterial and turns from the two-way major arterial to minor streets at a two-way intersection. Figure 3-2 shows these turning movements generate many diverge and merge activities at a typical two-way intersection (Roess et al., 2004). A major reason that CTM has not been developed for two-way arterials is that traffic flow is much more complex than that on one-way arterials. The complexity lies in two aspects: (a) There are more diverge and merge activities at a two-way intersection. (b) There are only two flows that diverge from a cell in one-way flow; whereas, there could be three flows diverge from a cell in two-way flow. Formulations of both merge and diverge in two-way flow are discussed in the following paragraphs. Diverge Merge Figure 3-2. Traffic flow movements at a typical two-way intersection (Roess et al., 2004). 17

36 Diverge Formulation At the intersection, some vehicles go through while other vehicles make left or right turns. In oversaturated conditions, two blockages involving left turns could occur. One is that the overflow of left turns blocks the through-lane entrance. The other is that the overflow of through vehicles blocks the left-turn entrance (Kikuchi et al., 2007). For both situations, all flow is restricted if either the left-turn lane or through lane is unable to accommodate desired traffic flow (Lo, 2001). A vehicle that cannot exit its current cell will prevent the movement of all vehicles following it. In CCTM, this is captured by using cells which represent homogeneous segments of the traffic network. CCTM can capture such a phenomenon using the diverge formulation. Diverge for One-way Flow In Figure 3-3, Cell a is a cell where vehicles diverge, Cell b is for left turns and Cell c is for through vehicles. The outflow from Cell a is blocked if either though vehicles in cell b and left turn vehicles in cell c are full due to the holding space (Lo, 2001). This is exactly what happens in an oversaturation condition in the real world. The proportions of Cell a outflow going to Cell b and Cell c are equal to α and β, respectively. In this research, α is assumed to be 0.3 initially, which means the percentage of left-turn flow at intersections is 30%. A sensitivity analysis about this parameter is presented later in Chapter 6. a f b+c b c Figure 3-3. Diverge in one-way flow. 18

37 Then, inflow into Cell b and Cell c is as follows (Lo, 2001): f b+ c na ( t) Qa ( t) ( t) = min { [ ] } { [ ] } Min Qb ( t), N b ( t) nb ( t) / α Min Qc ( t), N c ( t) nc ( t) / β (3-1) Additionally, the inflow into Cell b and Cell c is as follows: f b =α f b + c (3-2) f c =β f b + c (3-3) Diverge for Two-way Flow The difference between diverge activities of one-way flow and that of two-way flow is that there are only two flows that diverge from a cell in one-way flow, and there could be three flows that diverge from a cell in two-way flow, as shown in Figure 3-4. b a f b+c+d c d Figure 3-4. Diverge in two-way flow. 19

38 In Figure3-4, Cell a is a diverge cell, Cell b is for left turns, Cell c is for through vehicles, and Cell d is for right vehicles. The proportions of Cell a outflow going to Cell b, Cell c and Cell d are equal to α, β andγ respectively. Then, inflow into Cell b, Cell c and Cell d is as follows: f b+ c+ d na ( t) Qa ( t) ( t) = min Min{ Qb ( t), [ Nb( t) nb ( t) ] }/ α Min{ Qc ( t), [ Nc ( t) nc ( t) ] }/ β { [ ] } Min Qd ( t), N d ( t) nd ( t) / γ (3-4) Thus, the inflow into Cell b, Cell c and Cell d is as follows: f b f b + c+ d =α (3-5) f c f b + c+ d =β (3-6) f d f b + c+ d =γ (3-7) At a typical two-way intersection, there are four diverge points as shown in Figure 3-5. Diverge formulations on these four points may be applied to model traffic flow at a two-way intersection. 20

39 Figure 3-5. Diverge points at a typical two-way intersection (Roess et al., 2004). Merge Formulation At an intersection, through vehicles and other left-turn and right-turn vehicles merge to a receiving lane. Turning movements are difficult to formulate because two cells flow into the same cell. As mentioned in the basic formulation of CTM, the flow between cells at time t is governed by the number of vehicles in the preceding cell t ), the inflow capacity (t), and the available space in the next cell Ni ( t) ni ( t) (Lo, 1999). n ( i -1 Q i Merge for One-way Flow In one-way flow case, three cells are involved. Figure 3-6 shows both Cell a and Cell b flowing into Cell c. a b f a (t) f b (t) c Figure 3-6. Merge in one-way flow. 21

40 In this study, all turning movements are protected, as opposed to permitted. Since the flows from Cell a and Cell b use different phases, they do not flow into Cell c at the same time. Thus, the flow from Cell a to Cell c can be formulated as follows (Lo, 2001): f a { n ( t), Q ( t), [ N ( t) n ( )]} ( t) = min t a a c c (3-8) Similarly, the flow from cell b to cell c can be formulated as follows: { n ( t), Q ( t), [ N ( t) n ( )]} f ( t) = min t b b b c c (3-9) Thus, the sum of outflows of Cell a to Cell b are as noted below (Lo, 2001). f a + b ( t) = f a ( t) + fb ( t) (3-10) Merge for Two-way Flow The difference between merge activities of a one-way flow and that of a two-way flow is straightforward. There are only two flows that merge to a cell in one-way flow; whereas, there could be three flows that merge to a cell in two-way flow, as shown in Figure

41 a b c f a (t) f b (t) f c (t) d Figure 3-7. Merge in two-way flow. The flow from Cell a to Cell d can be formulated as follows: { n ( t), Q ( t), [ N ( t) n ( )]} f ( t) = min t (3-11) a a a d d Similarly, the flow from cell b and cell c to cell d can be formulated as follows: { n ( t), Q ( t), [ N ( t) n ( )]} f ( t) = min t (3-12) b b b d d { n ( t), Q ( t), [ N ( t) n ( )]} f ( t) = min t (3-13) c c c d d Thus, the sum of outflows from Cell a, Cell b, and Cell c to Cell d are as noted below fa + b+ c( t) = fa( t) + fb( t) + fc( t) (3-14) 23

42 At a typical two-way intersection, there are four merge points as shown in Figure 3-8. Merge formulation on these four points may be applied to model traffic flow at a two-way intersection. Figure 3-8. Merge points at a typical two-way intersection (Roess et al., 2004). 24

43 Adding Conditional Cell to Simulate Spillback and Blockages at an Intersection The first improvement to CTM allowed CCTM to simulate the traffic flows on two-way arterials. The second improvement to CTM enabled CCTM to model blockages at intersections by adding the conditional cell to simulate spillback and blockages. Blockages are characteristics of oversaturated two-way arterials. They can occur in segments and at intersections. For example, left turns can be blocked by the oversaturated through traffic from the same direction or the spillback of through traffic from the opposite direction. The former is a blockage in a segment, and the later is a blockage at an intersection. Either blockage prohibits the desired movements and increases delay. Therefore, identifying and accounting for blockages is critical to estimating delay. By adding the conditional cell at intersections, CCTM is able to simulate blockages and spillbacks and thus estimate the corresponding delay. The following explains the methodology of the conditional cell in detail. DO NOT BLOCK THE INTERSECTION signs are used to mark the edges of an intersection area that are in close proximity to a signalized intersection, railroad crossing, or other nearby traffic control signal that might cause vehicles to stop within the intersection and impede other traffic entering the intersection (FHWA, 2009). Vehicles are not permitted to stop inside an intersection if there is not enough room for them to clear the far side of the intersection. Most drivers obey the rule; however, many do not. The traffic queues that form at signalized intersections may spillback and block access into or out of a minor street. For example, Figure 3-9 shows a westbound left turn blocked by the spillback of eastbound through vehicles. The eastbound through vehicles spillback into the intersection due to the oversaturation. The overflow vehicles occupy the space inside an intersection where the westbound left turn needs to 25

44 cross thus causing a blockage. (Note: This blockage does not occur in non-oversaturated conditions, since through vehicles are processed and do not stop inside the intersection.) Desired left turn Queue spillback Figure 3-9. Westbound left turn blocked by a spillback of eastbound through vehicles. CCTM allows for the possibility of an additional cell forming within an intersection to account for any vehicles that may caught there for some amount of time thereby incurring delay and potentially causing delay to conflicting movements. The cell exists conditionally, depending on whether or not there is a spillback at the intersection. In other words, if a spillback occurs, the conditional cell exists and stores the vehicles which accumulate inside the intersection. If a spillback does not occur, the conditional cell will not exist. CCTM uses two events to model this blockage. First, it uses a conditional cell to simulate the spillback at an intersection. Then, when the conditional cell appears, CCTM determines whether the cell is full or whether there is an acceptable gap inside the conditional cell to allow a left turn. 26

45 Simulating the Spillback at an Intersection In Figure 3-10, there is a conditional cell between cell a and cellb. It holds the spillback vehicles when cell b is fully occupied and cannot accommodate any more vehicles from cell a. a f 2 f 1 f 3 b A conditional cell Figure Adding a conditional cell to hold spillback vehicles at an intersection. The flow from cell a is controlled by several factors. The first controlling factor is the signal status. Cell a is close to the signalized intersection; therefore, the flow occurs during signal green time. The second controlling factor is the availability of space in cellb. If cell b is empty or has available space, the flow will go to cell b (shown as f 2 in Figure 3-10). If cell b is full, the flow will go to the conditional cell (shown as f 1 in Figure 3-10), causing a spillback queue at an intersection. The spillback vehicles wait in the conditional cell for the dissipation of the queue and then go to cell b (shown as f 3 in Figure 3-10). The procedure for adding a conditional cell is represented by a flowchart in Figure

46 NO YES NO YES NO YES Figure Procedure for adding a conditional cell. The calculations for f 1, f 2 and f 3 are described in the following paragraphs. The flow into the conditional cell is calculated by using the number of vehicles in cell a, the available space in the conditional cell and the flow capacity of the conditional cell. Mathematically, this is expressed as: f 1= Min ( n a, Q n, ( N con con n con )) (3-15) Where f = the flow from cell a into the conditional cell in Time Step t; 1 28

47 n a = the number of vehicles in cell a in Time Step t; Q con = the flow capacity of the conditional cell in Time Step t; n con = the number of vehicles in the conditional cell in Time Step t; and N con= vehicle holding capacity of the conditional cell. The flow into cell b is calculated by using the number of vehicles in cell a, the available space in cellb, and the flow capacity of cell b. Mathematically, this is expressed as: f 2 = Min ( n a, Q b, ( N b n b )); (3-16) Where f 2 = the flow from cell a into cell b in Time Step t; n a = the number of vehicles in cell a in Time Step t; Q b = the flow capacity of cell b in Time Step t; n b = the number of vehicles in cell b in Time Step t; and N b = vehicle holding capacity of cell b. The flow from the condition cell to cell b is calculated by using the number of vehicles in the conditional cell, the available space in cell b, and the flow capacity of cellb. Mathematically, this is expressed as: f 3 = Min ( n con, Q b, ( N b n b )); (3-17) 29

48 Where f 3 = the flow from the conditional cell into cell b in Time Step t; n con = the number of vehicles in the conditional cell in Time Step t; Q b = the flow capacity of cell b in Time Step t; n b = the number of vehicles in cell b in Time Step t; and N b = vehicle holding capacity of cell b. Judging the Availability of an Acceptable Gap When there is a green signal indication for the westbound left turn, these vehicles need to cross the conditional cell and go to the minor street. Before they make the left turn, they need to judge whether there is an acceptable gap in the conditional cell for them to cross. If the conditional cell is fully occupied by 13 spillback vehicles, then there is no gap and the vehicles are blocked (See Figure 3-12). If a gap exists in the conditional cell, the width and location of the gap determine whether it is an acceptable gap. First of all, the gap should be wide enough. Its width must be wider than one vehicle. Even if the gap is wide enough, if the gap s location is not suitable, vehicles still cannot cross it. If the location is suitable, vehicles will use the gap to make the desired movement. The location may be at the end the queue or may be in the middle of the queue. It depends on the characteristics of local drivers. Some drivers will leave a useful gap accessible to the minor street; others will not thus blocking access into or out of a minor street. 30

49 a b Figure Left turn is blocked by a queue spillback. Figure 3-13 explains the concept of an acceptable gap. The conditional cell holds some spillback vehicles and has a gap. Is the gap wide enough for vehicles making a left turn? Is the location of the gap accessible to the minor street? Figures 3-14, 3-15, 3-16, and 3-17 illustrate various situations of a gap. Desired Left Turn Cell a Conditional cell Cell b Is a gap wide enough? Spillback vehicles Is the location of a gap suitable? Figure Concept of an acceptable gap. 31

50 Figure A gap is not wide enough. Figure A useful gap occurs. 32

51 Figure A useful gap occurs. Figure A location of a gap that is not suitable. 33

52 Coding in CCTM Microsoft Excel was used in coding CCTM. In Excel, the rows stand for the position coordinatei, and the columns stand for the time coordinate t as shown in Figure For the position coordinatei, from left to right, each cell represents a section of arterials. The length of each section is equal to the distance a vehicle travels in a Time Step with free flow speed. The number in a cell is the number of vehicles section holds. The flow between cells (i.e., the number of vehicles traveling into cell i from the cell i+ 1at time t) is calculated by using Equation 2-3. As mentioned in Chapter 2, it is equal to the minimum of: the number of vehicles waiting to enter celli, n i - ( ), or the inflow capacity of celli in a given time step, (t), or the 1 t available space in celli, Ni( t) ni ( t) (Lo, 2001). The sample arterial network is two-way and has four lanes; therefore, four rows in Excel are used to represent four lanes in the real world. The first two rows (Lanes 1 and Lane 2) are for westbound traffic flow, and the later two rows (Lanes 3 and Lane 4) are for eastbound traffic flow. The last column of Lane 1 and Lane 2 and the first column of Lane 3 and Lane 4 have cells where vehicles enter the network, which is consistent with traffic operations in the real world. For the time coordinate t, the equation states that the number of vehicles in a cell at time step t + 1 is equal to the number of vehicles in that cell at the prior time step t, plus the number of vehicles that entered f i (t), and minus the number of vehicles that exited f i «( ) (Lo, 2004). The simulation horizon for the sample network is 15 minutes (90 time steps). Consequently, time coordinate tis from the 1st time step to the 90th time step. The number of 1 t Q i vehicles in each cell in the sample network is updated from time step t to time step t + 1, and then time step t+ 2 and so on. 34

53 Traffic signal timing is input to the column of signal status. Every movement at intersections is assigned a value of zero or one in the column of signal status. Zero represents red time (i.e., a movement does not have right of way); and one represents green time, (i.e., a movement is allowed to occur). Time Step Lane No. Traffic Demand Position 1 Position coordinatei Position 2 Link 1 Position 3 Position 4 Conditional Cell Position 1 Position 2 n f n f n f n f n f n f n Signal 0 is red Signal A Link 2 Signal is green Time coordinate t Figure A screenshot of Excel coding. 35

54 CHAPTER 4 PARAMETERS IN CCTM There are two categories of the parameters featured in CCTM. These categories are based on their uses. One category is the built-in parameters of CCTM, which represent the traffic characteristics of the network, and are default values in the model that will not change once the model is built. This category includes the length, the holding capacity, and the flow capacity of cells. The other category is the user-defined parameters, including traffic demands and traffic signal timing. The possibility of a conditional cell and the possibility of the occurrence of a useful gap are also added as additional parameters. 36

55 Built-in Parameters The Length of Cells The key idea of CTM and CCTM is to divide the network into homogenous cells. The length of the each cell is equal to the distance that a vehicle travels at the free-flow speed in a time step. Similar to Lo (2001), a time step of 10 seconds was adopted in this study. According to Highway Capacity Manual (National Research Council, 2000), the typical free flow speed for urban arterials is 48 km/h. Therefore, the length of each cell is calculated as follows: L = V T = 48 km/h 10 s = 133m (4-1) Where L = the length of cells, m; V = free flow speed, km/h; and T = The length of time step, s. The Holding Capacity of Cells The holding capacity in CCTM defines the maximum number of vehicles that a cell can accommodate. The holding capacity is the product of the jam density and the length of cells. Jam density refers to a situation in which all movements stop, and the vehicles are most-closely packed (Roess et al., 2004). The common value of jam density is 102 vehicles/km/lane (May, 1999). The holding capacity of each cell is calculated as follows: N = L k jam = 133 m 102 vehicles/km/lane = 13 vehicles (4-2) 37

56 Where N = the holding capacity of cells, vehicles; L = The length of cells, m; and k jam = The jam density, vehicles/ km/lane. The Flow Capacity of Cells The flow capacity of cell is the maximum number of vehicles that can flow into or out of a cell in a time step (Lo, 2001). It is the product of the saturation flow rate and the time step. The saturation flow rate is maximum number of vehicles per hour per lane when flow is saturated. According to Highway Capacity Manual (National Research Council, 2000), 1,800 vehicles/hour/lane is recommended as the saturation flow rate. The flow capacity of a cell is: Q = S T = 1,800 vehicles/hour 10 s = 5 vehicles / time step (4-3) Where Q = flow capacity of cells, vehicles/ time step; S = saturation flow rate, vehicles/hour; and T = time step, s; CTM assumes that all parameters, including saturation flow rate, are constant. However, this is not consistent with situations in the real world. Many factors can affect the traffic flow including vehicle characteristics, driver characteristics, the time of day, the location of the road, the effects of the weather, etc. (Alecsandru and Ishak, 2007). In CCTM, randomly-distributed saturation flow rates are used instead of constant saturation flow rates. This reflects the variations in the saturation flow rate and increases CCTM s accuracy and ability to realistically represent traffic flow. According to Alecsandru and Ishak (2007), the normal distribution is 38

57 chosen. The average saturation flow rate is five vehicles/time step/lane and the standard deviation is one vehicle/time step/lane. 39

58 User-Defined Parameters Traffic Demand Traffic demand is a major input parameter since the function of a traffic network is to serve traffic demand. The traffic demand is the number of vehicles that want to travel past a point during a specified period. It varies with time and space. For example, traffic is highest at peak hours, and traffic is much higher on a major street than on a minor street. In CCTM, traffic demand can be input to each lane of the network. Its range is from zero to five vehicles/time step/lane (saturation flow rate). In CCTM, three common scenarios of traffic demands are tested: (a) light 360 vehicles/hour/lane (one vehicle/time step/lane) with initial density of 0.4 jam density, (b) moderate 1,080 vehicles/hour/lane (three vehicles/time step/lane) with initial density of 0.75 jam density, and (c) heavy 1,800 vehicles/hour/lane (five vehicles/time step/lane) with initial density of jam density. As mentioned in Chapter 3, in a Microsoft Excel spreadsheet, traffic demands are input to origin cells, (i.e., the first cell in each lane). Figure 4-1 illustrates where traffic demand is input directly by the user. For example, an arrow shows five vehicles enter Lane 3 at time step 1. 40

59 Link 1 Time Lane Traffic Position Position Position Position step No. demand n f n f n f n f Input traffic demand (five vehicles/ time step lane) to Lane 3 at Time Step Figure 4-1. A screenshot depicting inputting traffic demand. Signal Timing Signal timing is a special inputting parameter because it is subjective. It is artificial and mirrors the policy of traffic management. Signal timing has a number of variables, including cycle length, split, yellow time, clearance intervals, phase plan, offset, and operational strategy. Cycle length is composed of the signal time to serve all of the signal phases. Longer cycles will accommodate more vehicles per hour but might also produce higher average delays. In this paper, cycle length is set to 60 seconds initially, which can be changed by users. It must be a multiple of the time step, because the evolution of cells is recorded at every time step interval. For example, it can be 70 seconds, 100 seconds, etc. Split requires that the effective green time in a given cycle must be divided between the various signal phases. In CCTM, green time for each phase must be a multiple of the time step, because the evolution of cells is recorded at every time step interval. 41

60 Yellow time allows a vehicle that is one safe stopping distance away from the STOP line when the green is withdrawn to continue at the approach speed and enter the intersection legally on yellow. Clearance interval refers to all red indications that mark the transition from green to red in each signal phase. The all red interval is a period during which all signal phases are red. (Note: In this study, yellow and clearance intervals set to the default values to simplify the formulation. Because yellow and clearance intervals contribute to lost time in a cycle, the percentage of the cycle made up of lost time also decreases.) Phase plan comprises the number of phases to be used and the sequence in which they are implemented. As a general guideline, in the exclusive left turn phase three phases are adopted in this paper. Phase plan can be inputted by assigning a value to a parameter of the signal status k. If the signal is green, the value is one, and a flow is allowed. If the signal is red, the value is zero, and a flow is prevented. Offset is the difference between the two green initialization times. In CCTM, the offset is a fixed time and is equal to the travel time between intersections. For example, if travel time between Intersection A and Intersection B is equal to 70 seconds (seven time steps), the offset should be equal to 70 seconds (i.e., if the green time starts in the first time step at intersection A, it should start in the eighth time step at intersection B). Since offset is a user-defined parameter, it will not affect the methodology of CCTM. Operation strategy is fixed (i.e., it is predetermined) in this study. In fact, CCTM can successfully work with actuated timing. Actuated timing works by installing detectors at the intersection which registers whether or not there is a need for assigning the right-of- 42

61 way to the desired movements. Again, since operational strategy is a user-defined parameter, it will not affect the methodology of CCTM. Traffic signal timing is input to the column of signal intersections. At Intersection A, there are six possible movements on the major arterial. Every movement should be assigned a value of zero or one at the column of the signal intersection. Zero represents red time (i.e., a movement does not has right of way). One represents green time (i.e., a movement is allowed to occur). Figure 4-2 illustrates how signal timing data are input directly by the user. The arrow shows the signal timing at Intersection A in Time Step 1. Three movements are assigned a value of one: (a) one is through movement in Lane 3, (b) one is left-turn movement in Lane 3, and (c) one is through movement in Lane 4. Input traffic signal timing at Intersection A in Time Step 1 Link 1 Link 2 Time step Lane No. Position 3 Position 4 Signal A Conditional Cell Position 1 Position 2 n f n f n f n f n Figure 4-2. A screenshot depicting inputting traffic signal timing. 43

62 The Possibility of the Conditional Cell DO NOT BLOCK THE INTERSECTION is a driving rule many drivers break. Consequently, there is a need to add a possibility parameter that allows drivers to occasionally break the rule, thereby blocking the intersection (i.e., backing up into the conditional cell). In CCTM, the conditional cell is represented by letter c. Users can select the suitable values ranging from 0% to 100%. For examples, (a) 0% indicates that no drivers will break the rule if there is no room for them in the far side of the intersection; (b) 100% means that drivers must back up at the intersection; and (c) 50% means that sometimes drivers will break the rule, while at other times they will not. In a certain time step, whether drivers break the driving rule or not is a function of the possibility parameter. Mathematically, this possibility parameter may be expressed as follows: 1 if drivers break the driving rule Function ( c ) = (4-4) 0 if drivers do not break the driving rule Where c = the possibility of conditional cell. For example, if c is equal to 50%, it means that during the simulation time (90 time steps), in random selected 45 time steps, Function ( c ) is equal to one, and drivers break the driving rule. In other 45 time steps, Function ( c ) is equal to zero, and drivers do not break the driving rule. The possibility of conditional cell is input at the top of the Microsoft Excel spreadsheet and should be specified by the user before running the model. Figure 4-3 shows where the value is input directly by the user. 44

63 Possiblity of conditional cell (c)= Possibility of occurrence of a useful gap(g)= Evolutions of cells Input possibility of a conditional cell here. Link 1 Link 2 Input possibility of the occurrence of a useful gap here. Time Lane Traffic Position Position Position Position Signal A Conditional Position Position step No. demand Cell 1 2 n f n f n f n f n f n f n Figure 4-3. A screenshot depicting inputting possibility of a conditional cell. The Possibility of the Occurrence of a Useful Gap As described earlier in this paper, the width and the location of a gap determine its usefulness. Hence, there is a need to add a possibility parameter that simulates the occurrence of a useful gap (i.e., whether a gap exists and whether it is accessible to a minor street). In CCTM, the possibility of the occurrence of a useful gap represented by letter g. Users can select a suitable value ranging from 0% to 100%. For examples, (a) 0% indicates the absence of a useful gap (i.e., vehicles are blocked by the spillback and cannot access a minor street; (b) 100% means that there is always a suitable gap in the spillback; and (c) 50% means that sometimes a gap is useful, and sometimes it is not. The probability of this last situation is 50%. Mathematically, this can be expressed as follows: 45

64 Function ( g ) = 0 if there is no useful gap in a conditional cell 1 if the location of a gap is useful 0 if the location of a gap is not useful, although there is a gap in conditional cell (4-5) Where g = the possibility of the occurrence of a useful gap. For example, if g is equal to 50%, it means that during the simulation time (90 time steps), in 45 time steps, Function ( g ) is equal to one, and the location of a gap is useful. In other 45 time steps, Function ( g ) is equal to zero, and the location of a gap is not useful. The possibility of occurrence of a useful gap is input at the top of Microsoft Excel spreadsheet. It should specified by the user before running the model. Figure 18 shows where the number is input directly by the user. In summary, there are four user-defined parameters in CCTM: (a) traffic demand, (b) signal timing, (c) the possibility of a conditional cell, and (d) the possibility of the occurrence of a useful gap. Traffic demand depends on the local traffic environment which is related to urban planning and local economic level. Traffic demand can be light, moderate, or heavy. Signal timing depends on the control policy of traffic management. The possibility of a conditional cell and the possibility of the occurrence of a useful gap reflect local drivers behaviors. 46

65 CHAPTER 5 ILLUSTRATIONS OF EVOLUTIONS OF EXAMPLE CELLS The Sample Network For illustration purposes, a three-signal, two-way arterial network was studied, although CCTM can be applied to a larger network. The sample network consists of three intersections. It has a two-way, four-lane major arterial which has four links labeled 1, 2, 3 and 4, and three minor links (minor streets) which are labeled 5, 6 and 7. Link 5 and Link 7 are one-way, one lane streets; and Link 6 is two-way, two-lane street. To simulate the traffic flow using CCTM, the transportation network is divided into homogeneous cells as shown in Figure 5-1. A cell in Figure 5-1 may be specified by the number of the link, the number of the lane, and the number of the position. For example, Cell (1, 2, 3) is in Link 1, Lane 2 and Position 3. Cells where vehicles enter the network are denoted as OR, and cells where vehicles leave the network are denoted as DE. 47

66 Position No. Position No. Position No. Position No. OR6 OR 4 Lane No. DE 3 DE 5 DE 1 OR 7 DE 2 OR 8 OR 1 DE 7 OR 2 DE 8 Link 1 Link 2 Link 3 Link 4 DE 4 DE 6 OR 5 OR 3 Link 5 Link 6 Link 7 N Figure 5-1. Layout of two-way, three-signal arterial network. 48

67 The data generated by CCTM is extensive. A sample of the data, shown in Table A1 in the Appendix A, can be used to observe the evolution of cells. In Table A1, Column 1 shows the number of time steps, and Column 2 shows the number of lanes. Columns 4, 6, 8, 10, 13, 15, 17, 19, 21, 23, 25, 27, 30, 32, 34, 36, 38,41,43,45, and 47 show the number of vehicles in each cell at each time step. Columns 5, 7, 9, 11, 14, 16, 18, 20, 22, 24, 26, 28, 31, 33, 35, 37, 39, 42, 44 and 46 show the number of inflowing vehicles at each time step. Columns 12, 29, and 40 show the status of the signal. The signal status of one represents a green time, and the signal status of zero represents a red time. To illustrate CCTM simulation procedure, a small part of the arterial network is extracted. Figure 5-2 contains sections of Lane 2 and Lane 3 on Link 2. DE 5 Lane 1 Lane 2 2,3,7L B Lane 3 2,3,3 2,3,6 2,3,7 Lane 4 C4 Link 2 DE 4 6,2,1 Figure 5-2. A section of an arterial network. Lane 2 is for the westbound traffic flow, and Lane 3 is for the eastbound traffic flow. Additionally, lane 3 has a left turn bay. Each lane has seven cells. The location of an individual cell is specified by the number of the link, the number of the lane, and the number of the cell position in the link. The name (link, lane, position coordinates) of each cell is shown in the Figure 5-2. For example, Cell (2, 2, 1) is on Link 2, Lane 2, and Position 1. Left-turn lanes are 49

68 designated by the use of the letter L as part of the position number. In Figure 5-2, the left-turn cell is named Cell (2, 3, 7L). The evolutions of these cells in Time Step 1 and Time Step 2 are shown in Figure 5-3. The evolutions of the cells can be easily tracked by following this series of figures. Figure 5-3a shows the number of vehicles in each cell at the beginning of Time Step 1. Figure 5-3b shows the flow that occurs during Time Step 1. Figure 5-3c shows the number of vehicles in each cell at the end of Time Step1, which is also the number at the beginning of Time Step 2. Figure 5-3d shows the flow that occurs during Time Step 2. Figure 5-3e shows the number of vehicles in each cell at the end of Time Step 2, which is also the number at the beginning of Time Step 3. 50

69 Ftep 2 Figure 5-3a The number of vehicles in each cell at the beginning of time step 1 Time step 1 fd ff fg fa fb fc fe Figure 5-3b The flows occur during time step1 Figure 5-3c The number of vehicles in each cell at the end of time step 1 Time step 2 Figure 5-3d The flows occur during time step 2 Figure 5-3e The number of vehicles in each cell at the end of time step 2 Figure 5-3. Evolutions of cells in Time Step 1 and Time Step 2. 51

70 Evolution of Example Cells To further understand CTM simulation procedure, six cells will be traced to observe their evolutions with time steps. Example 1: A Cell in a Segment Cell (2, 3, 3) At the beginning of Time Step 1, Cell (2, 3, 3) has 10 vehicles as do the other cells. During Time Step 1, three vehicles entered it, and three other vehicles exited it. Therefore, at the end of Time Step 1, this cell has = 10 vehicles. During Time Step 2, three vehicles exited it, and three other vehicles entered it. At the end of Time Step 2, this cell has = 10 vehicles. The procedure above involves two time steps. The calculation of Time Step 1 is shown below, which is similar to that of Time Step 2. Mathematically, ' n (2,3,3) = n(2,3,3 ) + f a f b (5-1) = = 10 Where f a = the flow from the previous Cell (2, 3, 2) to Cell (2, 3, 3) in Time Step 1; f b = the flow from Cell (2, 3, 3) to the next Cell (2, 3, 4) in Time Step 1; n (2,3,3) = the number of vehicles in Cell (2, 3, 3) at the beginning of Time Step 1; and ' n (2,3,3) = the number of vehicles in Cell (2, 3, 3) at the end of Time Step 1. The calculation of f a is shown below, which is similar to that of f b. 52

71 f = Min ( n (2,3,2), Q (2,3,3), ( N (2,3,3) n (2,3,3) )) (5-2) a = Min (10, 5, 13 10) = 3 Where n (2,3,2) = the number of vehicles in Cell (2, 3, 2) at the beginning of Time Step 1; Q (2,3,3) = the flow capacity of Cell (2, 3, 3) in Time Step 1; n (2,3,3) = the number of vehicles in Cell (2, 3, 3) at the beginning of Time Step 1; and N (2,3,3) = vehicle holding capacity of Cell (2, 3, 3). Example 2: A Diverge Cell Cell (2, 3, 6) At the start of Time Step 1, cell (2, 3, 6) has 10 vehicles. During Time Step 1, three vehicles entered it, and one left-turn vehicle and three through vehicles exited it. At the end of Time Step 1, this cell has = 9 vehicles. In Time Step 2, four vehicles entered the cell, and zero vehicles exited it. At the end of Time Step 2, this cell has = 13 vehicles. The procedure above involves two time steps. The calculation of Time Step 1 is shown below, which is similar to that of Time Step 2. ' n (2,3,6) = n(2,3,6 ) + f c f d f e (5-3) = = 9 53

72 Where, f c = the flow from Cell (2, 3, 5) to Cell (2, 3, 6) in Time Step 1; f d = the flow from Cell (2, 3, 6) to Cell (2, 3, 7L) in Time Step 1; f e = the flow from Cell (2, 3, 6) to Cell (2, 3, 7) in Time Step 1; n (2,3,6) = the number of vehicles in Cell (2, 3, 6) at the beginning of Time Step 1; and ' n (2,3,6) = the number of vehicles in Cell (2, 3, 6) at the end of Time Step 1; The calculation of f c, f d, fe is shown below. f = Min ( n (2,3,5), Q (2,3,6), ( N (2,3,6) n (2,3,6) )) (5-4) c = Min (10, 6, 13 10) = 3 Where n (2,3,5) = the number of vehicles in Cell (2, 3, 5) at the beginning of Time Step 1; Q (2,3,6) = the flow capacity of Cell (2, 3, 6) in Time Step 1; N (2,3,6) = vehicle holding capacity of Cell (2, 3, 6); n (2,3,6) = the number of vehicles in Cell (2, 3, 6) at the beginning of Time Step 1; f = Min ( n (2,3,6), (2,3,6) d Q, Min{ Q [ N ]} / α, [ N n ] ( 2,3,7), (2,3,7) n(2,3,7) Min{ Q( 2,3,7 L), (2,3,7 L) (2,3,7 L) }/ β ) β (5-5) = Min (10, 5, Min (5, (13 10))/0.7, Min (4, (13 10))/0.3) 0.3 = 1 54

73 f = Min ( n (2,3,6), (2,3,6) e Q, Min{ Q [ N ]} / α, [ N n ] ( 2,3,7), (2,3,7) n(2,3,7) Min{ Q( 2,3,7 L), (2,3,7 L) (2,3,7 L) }/ β ) α (5-6) = Min (10, 5, Min (5, (13 10))/0.7, Min (4, (13 10))/0.3) 0.7 = 3 Where α = the percentage of through vehicles in Cell (2, 3, 6), which is equal to 70%; β = the percentage of left turn vehicles in Cell (2, 3, 6), which is equal to 30%; n (2,3,6) = the number of vehicles in Cell (2, 3, 6) at the beginning of Time Step 1; n (2,3,7) = the number of vehicles in Cell (2, 3, 7) at the beginning of Time Step 1; n = the number of vehicles in Cell (2, 3, 7L) at the beginning of Time Step 1; ( 2,3,7 L) N (2,3,7) = vehicle holding capacity of Cell (2, 3, 7); N ( 2,3,7 L) = vehicle holding capacity of Cell (2, 3, 7L); Q (2,3,6) = the flow capacity of Cell (2, 3, 6) in Time Step 1; Q (2,3,7) = the flow capacity of Cell (2, 3, 7) in Time Step 1; and Q = the flow capacity of Cell (2, 3, 7L) in Time Step 1. ( 2,3,7 L) Example 3: A Cell in Front on an Intersection Cell (2, 3, 7) At the beginning of Time Step 1, Cell (2, 3, 7) has 10 vehicles as do all the other cells. During Time Step 1, three vehicles entered it, and zero vehicles exited it. Therefore, at the end of Time Step 1, this cell has = 13 vehicles. During Time Step 2, zero vehicles entered the cell, and six other vehicles exited it. At the end of Time Step 2, this cell has = 7 vehicles. 55

74 The procedure above involves two time steps. The calculation of Time Step 1 is shown below, which is similar to that of Time Step 2. Mathematically, ' n (2,3,7) = n(2,3,7 ) + f e f g (5-7) = = 13 Where f e = the flow from the previous Cell (2, 3, 6) to Cell (2, 3, 7) in Time Step 1; f g = the flow from Cell (2, 3, 7) to Cell (3, 3, 1) in Time Step 1; n (2,3,7) = the number of vehicles in Cell (2, 3, 7) at the beginning of Time Step 1; ' n (2,3,7) = the number of vehicles in Cell (2, 3, 7) at the end of Time Step 1; The calculation of fg is shown below. Note that fg is a flow occurring at an intersection and is controlled by the signal status. Here the letter k represents the status of the signal in equation. If the signal is green, then the value is one, and a flow occurs. If the signal is red, then the value is zero, and a flow does not occur. f g = Min ( n (2,3,7), Q (3,3,1), ( N (3,3,1) n (3,3,1) )) k (5-8) = Min (10, 6, 13 10) 0 = 0 Where k = the status of the signal; n (2,3,7) = the number of vehicles in Cell (2, 3, 7) at the beginning of Time Step 1; 56

75 Q (3,3,1) = the flow capacity of Cell (3, 3, 1) in Time Step 1; n (3,3,1) = the number of vehicles in Cell (3, 3, 1) at the beginning of Time Step 1; and N (3,3,1) = vehicle holding capacity of Cell (3, 3, 1). Example 4: A Cell in the Left-Turn Lane Cell (2, 3, 7L) At the beginning of Time Step 1, Cell (2, 3, 7L) has 10 vehicles as do all the other cells. During Time Step 1, one vehicle entered it, and five vehicles exited it. Therefore, at the end of Time Step 1, this cell has = 6 vehicles. During Time Step 2, zero vehicles exited the cell, and zero vehicles entered it. At the end of Time Step 2, this cell has = 6 vehicles. The procedure above involves two time steps. The calculation of Time Step 1 is shown below, which is similar to that of Time Step 2. Mathematically, n ' (2,3,7 L) = n(2,3,7 L) + f d f f (5-9) = = 6 Where f d = the flow from the previous Cell (2, 3, 6) to Cell (2, 3, 7L) in Time Step 1; f f = the flow from Cell (2, 3, 7L) to Cell (DE 5) in Time Step 1; n ( 2,3,7 L) = the number of vehicles in Cell (2, 3, 7L) at the beginning of Time Step 1; and ' n (2,3,7L) = the number of vehicles in Cell (2, 3, 7L) at the end of Time Step 1. 57

76 The calculation of f f is shown below. f = Min ( n ( 2,3,7 L), Q (DE5), ( N ( DE 5) n (DE 5) )) k Function ( g ) (5-10) f = Min (10, 5, ) 1 = 5 Where Function ( g ) = Possibility of the occurrence of a useful gap; n = the number of vehicles in Cell (2, 3, 7) at the beginning of Time Step 1; ( 2,3,7 L) Q (DE5) = the flow capacity of Cell (DE 5) in Time Step 1; n (DE 5) = the number of vehicles in Cell (DE 5) at the beginning of Time Step 1; N (DE 5) = vehicle holding capacity of Cell (DE 5); and k = the status of the signal. If the signal is green, then the value is one, and a flow occurs. If the signal is red, then the value is zero, and a flow does not occur. Example 5: A Cell in a Minor Street Cell (6, 2, 1) At the beginning of Time Step 1, Cell (6, 2, 1) has 10 vehicles as do all the other cells. During Time Step 1, three vehicles entered it, and zero vehicles exited it. Therefore, at the end of Time Step 1, this cell has = 13 vehicles. During Time Step 2, zero vehicles exited the cell, and zero vehicles entered it. At the end of Time Step 2, this cell has = 13 vehicles. 58

77 The procedure above involves two time steps. The calculation of Time Step 1 is shown below, which is similar to that of Time Step 2. Mathematically, ' n (6,2,1) = n(6,2,1 ) + f i f h (5-11) = = 13 Where f i = the flow from the previous Cell (6, 2, 2) to Cell (6, 2, 1) in Time Step 1; f h = the flow from Cell (6, 2, 1) to Cell (2, 2, 7), Cell (3, 4, 1) and Cell (DE5) in Time Step 1; n (6,2,1) = the number of vehicles in Cell (6, 2, 1) at the beginning of Time Step 1; and ' n (6,2,1) = the number of vehicles in Cell (6, 2, 1) at the end of Time Step 1; The calculation of fi is shown below. f = Min ( n (6,2,2), Q (6,2,1), ( N (6,2,1) n (6,2,1) )) (5-12) i = Min (10, 5, 13 10) = 3 Where n (6,2,2) = the number of vehicles in Cell (6, 2, 2) at the beginning of Time Step 1; Q (6,2,1) = the flow capacity of Cell (6, 2, 1) in Time Step 1; n (6,2,1) = the number of vehicles in Cell (6, 2, 1) at the beginning of Time Step 1; and 59

78 N (6,2,1) = vehicle holding capacity of Cell (6, 2, 1); The calculation of fh is shown below. f = Min ( n (6,2,1), Q (6,2,1), Min( Q (2,2,7), ( N (2,2,7) n (2,2,7) )/α ), h Min( (3,4,1) Q, ( N (3,4,1) (3,4,1) n )/β ), Min( Q (DE5), ( N ( DE 5) n (DE 5) )/γ )) k Function ( g ) (5-13) = Min (10, 5, Min (10, (13 10)/0.3), Min (10, (13 10)/0.2), = 0 Min (5, ( 10)/0.5)) 0 Where n (2,2,7) = the number of vehicles in Cell (2, 2, 7) at the beginning of Time Step 1; n (3,4,1) = the number of vehicles in Cell (3, 4, 1) at the beginning of Time Step 1; n (DE 5) = the number of vehicles in Cell (DE5) at the beginning of Time Step 1; Q (2,2,7) = the flow capacity of Cell (2, 2, 7) in Time Step 1; Q (3,4,1) = the flow capacity of Cell (3, 4, 1) in Time Step 1; Q (DE5) = the flow capacity of Cell (DE5) in Time Step 1; N (2,2,7) = vehicle holding capacity of Cell (2, 2, 7); N (3,4,1) = vehicle holding capacity of Cell (3, 4, 1); N (DE 5) = vehicle holding capacity of Cell (DE5); and Function ( g ) = the possibility of the occurrence of a useful gap. 60

79 To further understand the evolutions of example cells, three traffic demands of light, moderate and heavy are loaded into the network. The numbers of vehicles in example cells under each condition are recorded in Figures 5-4, 5-5, and 5-6. Light Conditions In light conditions, the number of vehicles in each cell changes with the signal cycle. When the signal is green, the number of vehicles decreases, because vehicles are released from the cell. When the signal is red, the number of vehicles increases, because vehicles are accumulated in it. As shown in Figure 5-2, Cell (2, 3, 7) is in front of a signal; therefore, its evolution responds to the signal status in time. The cell initially has five vehicles. The signal is red for it in Time Step 1, and the number of vehicles increases to seven. In Time Step 2, Time Step 3, and Time Step 4, the signal is green, and vehicles are released from the cell at a saturated flow rate. Consequently, the number of vehicles decreases continuously. In Time Step 5, the signal turns to red, and the number of vehicles continuously increases in Time Step 6, Time Step 7 and Time Step 8 until the signal turns to green in Time Step 9. The evolutions of Cell (2, 3, 3), Cell (2, 3, 6) and Cell (6, 2, 1) are similar to it; the number of vehicles change with the signal cycle. The number in Cell (2, 3, 7L) remains at a low value after Time Step 38, because an upstream diverge Cell (2, 3, 6) remains at a low value during the same time. As a result, there are few vehicles going from Cell (2, 3, 6) to Cell (2, 3, 7L). 61

80 Cell (2,3,3) A Cell in a Segment No. of vehicles Time (time step) Series1 Cell (2,3,6) A Diverge Cell 12 No. of Vehicles Time ( time step) Series1 No. of Vehicles Cell (2,3,7) A Cell in Front of an Intersection Series Time ( time step) No. of Vehicles Cell (2,3,7L) A Cell in the Left-turn Lane Series Time( time step) Cell (6,2,1) A Cell in a Side Street 12 No. of Vehicles Time ( time step) Series1 Figure 5-4. Evolutions of example cells in light conditions. 62

81 Moderate Conditions In moderate conditions, the evolution of cells still follows the signal cycle. From Figure 23 it is observed that the number of vehicles in Cell (2, 3, 7) decreases rapidly. This is because vehicles from Cell (2, 3, 7) have 30 seconds green time out of every 60-second cycle. Therefore, vehicles are released from it in a short time. Cell (6, 2, 1) appears to be frequently blocked in moderate conditions, because it has three movements including left turns, right turns and through flows. Blockage of any of these three movements causes the blockage of all three, since they share a lane. For example, in Time Step 12, during green time, a desired right-turn vehicle from Cell (6, 2, 1) is blocked due to the spillback on the major arterial. Then, it blocks all vehicles behind it on the same lane. Cell (2, 3, 7L) always has 13 vehicles because of its limited green time. So it is hard for vehicles to dissipate from it. Similar situations occur to other cells. 63

82 Cell(2,3,3) A Cell in a Segment No. of vehicles Time (time step) Series1 Cell(2,3,6) A Diverge Cell No. of vehicles Time (time step) Series1 Cell(2,3,7) A Cell in Front of an Intersection No. of vehicles Time (time step) Series1 Cell(2,3,7L) A Cell in the Left-turn No. of vehicles Time (time step) Series1 Cell(6,2,1) A Cell in a Side Street No. of vehicles Time (time step) Series1 Figure 5-5. Evolutions of example cells in moderate conditions. 64

83 Heavy Conditions In heavy conditions, the evolution of left-turn Cell (2, 3, 7L) is related to the flow and status of its neighbor cells. It is close to a signal. The cell is full (13 vehicles) in Time Step 6 and blocks the flows from upstream Cell (2, 3, 6). Cell (2, 3, 6) cannot release any vehicles until vehicles in Cell (2, 3, 7L) start to dissipate in Time Step 20. As it is observed in Figure 5-6, Cell (2, 3, 7) remains empty during the time period. 65

84 Cell(2,3,3) A Cell in a Segment No. of vehicles Time (time step) Series1 Cell(2,3,6) A Diverge Cell No. of vehicles Time (time step) Series1 Cell(2,3,7) A Cell in Front of an Intersection No. of vehicles Time (time step) Series1 Cell(2,3,7L) A Cell in a Left-turn Lane No. of vehicles Time (time step) Series1 Cell(6,2,1) A Cell in a Side Street No. of vehicles Time (time step) Figure 5-6. Evolutions of example cells in heavy conditions. 66 Series1

85 This is a common phenomenon in oversaturated condition, as shown in Figure 5-7. All flow is restricted if either the left turn lane or the through lane is unable to accommodate its allocation of flow to the extent that the waiting queue blocks the juncture of the through lane and left turn lane. In CCTM this is captured by using cells, which represent homogeneous segments of the traffic network. A vehicle that cannot exit its cell will prevent the movement of all vehicles behind it. CCTM is capable of capturing such phenomena. left-turn vehicles through vehicles Figure 5-7. Overflow of left turns blocks through-lane entrance. The above procedure may be expressed using a table, as shown in Table 5-1. Table headers indicate columns for time step, lane, link, and position. There are two kinds of information in the table: (a) the numbers of vehicles in cells and (b) the flows between cells. Additional, there is a column ( Signal B in Table 5-1) to show the status of signals at intersection B. For example, in Time Step 1, Link 2, Lane 3, Position 3 (the tail of downward pointing arrow n (2,3,3) begins in this cell), there is a number 10. This means there are 10 vehicles in Cell (2, 3, 3) in Time Step 1. The flows that occur to Cell (2, 3, 3) during Time Step 1 are pointed to by two arrows ( f a, f b ) in Table 1. This indicates that one flow is three vehicles, and the other flow is also three vehicles. Hence, there should be =10 vehicles in Time Step 2. Therefore, the number in Time Step 2, Link 2, Lane 3, Position 3, is 10 (as shown by 67

86 ' an arrow n (2,3,3) ). Using these same procedures, a complete table for the entire network can be generated. Table 5-1. Evolutions of Cells from Time Step 1 to Time Step 10 Link 2 Time Lane Position Position Position Position Position Position Position Signal step No B n f n f n f n f n f n f n f Lane Lane Lane Lane Lane f a f b n ' 0 3 (2,3,3) n (2,3,3) f c f d f e Lane Lane Lane Lane Lane Lane Lane Lane Lane Lane Lane Lane Lane Lane Lane Note: The letter n represents the number of vehicles in cells; the letter f represents the flow between cells. 68

87 CHAPTER 6 SENSITIVITY ANALYSES OF USER-DEFINED PARAMETERS IN CCTM Design of Experiments To ensure that CCTM performed as expected, a series of experiments is designed and conducted. The results indicated that CCTM can accommodate various traffic demands. Also, the experiments provided sensitivity analyses for traffic signal timing, the possibility of the occurrence of a useful gap, and the possibility of a conditional cell on the performance of CCTM. Several experiments were performed, as shown in Figure 6-1. First, a baseline experiment is conducted. Experiments awere then designed to investigate the relationship between each user-defined parameter (i.e., traffic demand, traffic signal timing, the possibility of the occurrence of a useful gap, and possibility of a conditional cell) and the performance of the model. The results of each experiment were compared to the results of the baseline experiment. The delay was chosen as the performance measure of the model since CCTM provides a convenient method to estimate the delay. 69

88 Figure 6-1. Designs of experiments to test the performance of CCTM. The initialization period or the warm-up of the simulation model is a period that the network needs to reach equilibrium. It is determined by the number of vehicles present on the network. Once the number of vehicles ceases to increase by a minimum specified amount, then the initialization period completes (FHWA, 2004). Some software programs can do this automatically. In CCTM, the warm-up period must be computed offline by the analyst. For a loading traffic demand of 360 vehicles/hour/lane, the increase in the number of vehicles present on the network is recorded in Figure

89 Figure 6-2. Initialization time. At Time Step 24, the incremental increase in the number of vehicles on the network was less than 5% for the first time (FHWA, 2004); therefore, initialization was set at 24 time steps (4 minutes). It is excluded from the reported data for system performance. After the initialization time, each experiment was run for 15 minutes, which is a typical analysis period as outlined in the HCM

90 The Baseline Experiment The purpose of the experiment is to build a baseline for further comparison, which will be compared with the results of other experiments. The input values, the results, and discussion of this experiment are described in the following paragraphs. Input Values Traffic demand: This is shown in Table 6-1. In the 15-minute experiment period, there was a demand of two vehicles/time step/lane (720 vehicles/hour/lane) on the major street and each of the minor streets. (Note: One vehicle/time step/lane is equivalent to 360 vehicles/hour/ lane; two vehicles/time step/lane is equivalent to 720 vehicles/hour/lane; and five vehicles/time step/lane (1,800 vehicles/ hour/lane) is the capacity.) Table 6-1. Traffic Demand of Baseline Experiment Time (minute) 1-15 Traffic Demand vehicles/time step/lane (vehicles/hour/lane) Major Street Minor Street 1 Minor Street 2 Minor Street 3 2 (720) 2 (720) 2 (720) 2 (720) Traffic signal timing: This is shown in Table 6-2. Possibility of conditional cell: 100% Possibility of occurrence of a useful gap: 10% 72

91 Table 6-2. Phase Diagram of Baseline Experiment Intersection Phases No. Movements Green split (Seconds) 1 20 A B C Results Delays in the entire network, on the major street, and in each direction (eastbound and westbound) of the major street are shown in Figure 6-3, Figure 6-4, and Figure 6-5, respectively Delay (Seconds) Time ( Minute) Figure 6-3. Network delay of baseline experiment. 73

92 6000 Delay (Seconds) Total Delay(Seconds) Time (Minute) Figure 6-4. Delay on the major street of baseline experiment Delay (Seconds) Series1 Series Time (Minute) Figure 6-5. Delay in each direction of the major street of baseline experiment. Discussion It was observed that delay increases with time. For example, in Figure 6-3, delay in the entire network appeared to level out about the ninth minute, and reached the peak at the end of the simulation period (15 minutes) with a value of 9,860 seconds. Delay on the major street had a similar pattern, leveling out about the ninth minute with a peak of 4,820 seconds at the 15 th minute as shown in Figure 6-4. It indicates that the network reaches steady constant rate at the ninth minute when the traffic demand and throughput are balanced. 74

93 Experiment 1: Traffic Demand versus Delay The purpose of Experiment 1 is to investigate the relationship between traffic demand and delay. Traffic demand in the baseline experiment is modified, and consequently, a change in the traffic demand results in a change in the performance of the model. Experiment 1a Traffic Demand Varies with Time The purpose of Experiment 1a is to investigate the trend in delay with time-varying traffic demand. When traffic demand increases, the delay should increase correspondingly; when traffic demand decreases, the delay should decrease correspondingly. In the baseline experiment, traffic demand is kept at 720 vehicles/hour/lane during the 15-minute simulation time. In Experiment 1a, traffic demand is maintained at 720 vehicles/hour/lane in the first and last five minutes, but was set to 360 vehicles/hour/lane from the sixth to the tenth minute. The input, the results, and the discussion of Experiment 1a are described in the following paragraphs. Input Values Possibility of conditional cell: 100% Possibility of occurrence of a useful gap: 10% Traffic demand: This is shown in Table 4. Time (minute) Table 6-3. Traffic Demand of Experiment 1a Traffic Demand vehicles/time step/lane (vehicles/hour/lane) Major Minor 1 Minor 2 Minor (720) 2 (720) 2 (720) 2 (720) (360) 1 (360) 1 (360) 1 (360) (720) 2 (720) 2 (720) 2 (720) 75

94 Traffic signal timing: This is the same as that in the baseline experiment. Results Figure 6-6 shows the trend of delay in the entire network during the 15 minutes simulation time. Delay (Seconds) Figure 6-6. Network delay of experiment 1a. Discussion In Figure 6-6, from the first to the fifth minute, the delay increases and reaches the peak at the fifth minute (8,910 seconds) when traffic demand is kept at 720 vehicles/hour/lane. Delay remains constant at that level between the fifth and sixth minutes but the delay decreases until the 10 th minute when traffic demand deceases to 360 vehicles/hour/lane. This occurs because demand drops (fewer vehicles enter the network, and more vehicles exit the network), but it takes one minute for the effect to appear in the system as the extra vehicles exit from signals). From the 11 th to the 15 th minute, the opposite occurs as delay increases again and reaches the peak at the 15 th minute (7,250 seconds) when traffic demand restores to 720 vehicles/hour/lane. Again, it takes about a minute for the system to change after the entering flow rate changes. For this experiment, the model performs in a logical and expected manner. 76

95 Experiment 1b Traffic demand Varies in Two Directions on the Major Street The purpose of Experiment 1b is to investigate the trend in delay if traffic demand varies with direction of flow. In the baseline experiment, traffic demand is 720 vehicles/hour/lane in both directions on the major street. In this experiment, traffic demand is maintained at 720 vehicles/hour/lane for westbound direction and increases to 1,080 vehicles/hour/lane for the eastbound direction. The input, results, and discussion of Experiment 1b are described in the following paragraphs. Input Values Possibility of conditional cell: 100% Possibility of occurrence of a useful gap: 10% Traffic demand: This is shown in Table 6-4. A demand of two vehicles/time step/lane (720 vehicles/hour/lane) in the westbound direction of the major street and each of the minor streets and a demand of three vehicles/time step/lane (1,080 vehicles/hour/lane) in the eastbound direction of the major street are used in this experiment. Time (minute) Table 6-4. Traffic Demand of Experiment 1b Traffic Demands vehicles/time step/lane (vehicles/hour/lane) Major street Minor 1 Minor 2 Minor 3 Eastbound Westbound (1,080) 2 (720) 2 (720) 2 (720) 2 (720) Traffic signal timing plan: This is the same as that in the baseline experiment. 77

96 Results Delays in each direction of the major street are recorded in Figure 6-7. Delay (Seconds) Figure 6-7. Delay in each direction of the major street of experiment 1b. Discussion Delay for each direction of flow in the baseline experiment were close (see Figure 30), because traffic demands of both directions were the same (720 vehicles/hour/lane). In Figure 32, it is seen that the delay in the eastbound direction of the major street are much higher than that in the westbound direction. This is because the eastbound traffic demand (1,080 vehicles/hour/ lane) was 50% higher than the westbound traffic demand during the 15 minute interval. This is the expected outcome, indicating that the model is responding to traffic flow volume. Experiment 1c Traffic Demand Varies with the Percentage of Left Turns The purpose of Experiment 1c is to investigate the effect of percentage of left turns on delay. In all other experiments, percentage of left turns is assumed to be 30%. For purposes of comparison, the percentage of left turns is selected to be 10% and 20% in this experiment. The input, results, and discussion of Experiment 1c are described in the following paragraph. 78

97 Input Values Possibility of conditional cell: 100% Possibility of occurrence of a useful gap: 10% Traffic demand: This is shown in Table 6-5. A demand of five vehicles/time step/lane (1,800 vehicles/hour/lane) on both the major street and the minor streets with initial jam density. Table 6-5. Traffic Demand of Experiment 1c Time (minute) Traffic Demands vehicles/time step/lane (vehicles/hour/lane) Major Street Minor 1 Minor 2 Minor ( 1,800) 5 (1,800) 5 (1,800) 5 (1,800) 5 (1,800) Traffic signal timing plan: This is shown in Table

98 Table 6-6. Phase Diagram of Experiment 1c Intersection Phases No. Movements 1 Green split (Seconds) 20 A B C Results Delays of left turn, major street and entire network at each percentage of left turns are recorded in Table 6-7. Table 6-7. Delay of Experiment 1c Percentage of Left Turns (Seconds) Percentage of Left Turns Left Turn Major Street Entire Network 10% 13, , ,060 20% 16, , ,480 30% 21, , ,860 Discussion Based on signal timing plan in Table 6-7, as the percentage of left turns increases, the delay of left turns increase (See Table 6-7). This result is reasonable, because more left turning vehicles are sharing the green time. Meanwhile, delays on the major street and the entire 80

99 network decrease. As through-traffic demand on the major street decreases from 90% to 80% and 70%, through vehicles are able to get through the signal more quickly. But at the same time vehicles turning left increase from 10% to 20% and 30%, and the increasing volumes translate to more delay for them. In other words, the delay decreases for a large volume of traffic (through vehicles) but increases for a smaller volume (left turns). The net result is less delay for the system. 81

100 Experiment 2: Signal Timing versus Delay Signal timing mirrors the policy of traffic management, and the effect of traffic signal timing on delay is somewhat complex. That is because signal timing has a number of variables, including cycle length, split times, yellow time, clearance interval, phase plan and offset. For example, it is difficult to draw general conclusions on the relationship between phase sequences and delay. However, given a constant cycle length and phase sequences, variation of splits among the phases mirrors the relationship between signal timing and delay. Experiment 2 is designed to investigate the relationship between signal timing and delay. Experiment 2a investigates the trend of delay of two directions on the major street when green time is shifted from one direction to the other direction. Experiment 2b investigates the trend of delay on the major street and the minor street when green time is shifted from the minor street to the major street. Experiment 2c investigates the effect of lead-left turns and lag-left turns on the delay. Experiment 2a Signal Timing Varies by Shifting of Green Time between Two Directions on the Major Street In experiment 2a, the signal timing in the baseline experiment is changed by shifting green time between two directions on the major street. The input, the results, and the discussion of Experiment 2a are described in the following paragraphs. Input Values Possibility of conditional cell: 100% Possibility of occurrence of a useful gap: 10% Traffic demand: This is the same that used in the baseline experiment. 82

101 Traffic signal timing: As shown in Table 6-8, 10 seconds of green time are shifted from eastbound through to westbound through on the major street at Intersections A and C, respectively. Table 6-8. Phase Diagram of Experiment 2a Intersection Phases No. Movements Green split (Seconds) 1 10 A B C Results Delays of westbound and eastbound on the major street are recorded in Table 6-9. Table 6-9. Delay of Westbound and Eastbound on the Major Street (Seconds) Experiment Westbound Major Eastbound Major Major Baseline 34,840 32,310 67,150 Experiment 2a 18,450 69,460 87,910 Discussion In the baseline experiment, the delay of westbound is 34,840 seconds, and the delay of eastbound is 32,310 seconds. After shifting 10 seconds green time from the eastbound to the westbound in Experiment 2a, the delay of westbound decreased to 18,450 seconds, and the delay of eastbound increased to 69,460 seconds. That was because the longer green time allowed more 83

102 westbound vehicles to cross the intersection. However, eastbound vehicles on the major street had to wait a longer time before the signal was green for them. This caused additional delay. This is the expected result and indicates that the model is responsive to changes in the tested green splits of the signal timing plan. Another conclusion may be drawn from this change. In the baseline delay is 67,150 seconds. After the change in green splits it rises to 87,910, an increase of 31%. So the arbitrary decision to change the splits produces a significant reduction in the effectiveness of the signal system. Experiment 2b Signal Timing Varies by Shifting of Green Time from the Minor Street to the Major Street In Experiment 2b, signal timing in the baseline experiment is changed by shifting green time from the minor street to the major street. The input, results, and discussion of Experiment 2b are described in the following paragraphs. Input Values Possibility of conditional cell: 100% Possibility of occurrence of a useful gap: 10% Traffic demand: This is the same as that used the baseline experiment. Traffic signal timing: As shown in Table 6-10, 10 seconds of green time are shifted from the minor street to the major street at Intersections A and C, respectively. 84

103 Table Phase Diagram of Experiment 2b Intersection Phases No. Movements 1 Green split (Seconds) 30 A B C Results Delays of the major street and the minor street are recorded in Table Table Delays on the Major Street and the Minor Street (Seconds) Experiment Major street Minor streets Baseline 67,150 72,780 Experiment 2b 35,880 81,600 Discussion Compared with the baseline experiment, the delay of the major street decreases, and the delay of the minor street increases after shifting 10 seconds of green time from the minor street to the major street. The reason is that the longer green time allows more vehicles on the major street to cross the intersection; whereas, vehicles on the minor street have to wait longer before the signal is green for them. Thus, the delay decreases for the largest share of vehicles (major 85

104 street) and increase for the minor share of vehicle (minor street), resulting in a net reduction in delay. This is the expected pattern and again infers the correct operational patter n for the model. Experiment 2c Signal Timing Varies by Using Lag-Left Turn Phase Instead of Lead-Left Turn Phase In Experiment 2c, signal timing in Experiment 1c is changed by using a lag-left turn phase instead of a lead-left turn phase. The input, results, and discussion of Experiment 2c are described in the following paragraphs. Input Values Possibility of conditional cell: 100% Possibility of occurrence of a useful gap: 10% Traffic demand: This is the same value used in Experiment 1c. Traffic signal timing: This is shown in Table

105 Table Phase Diagram of Experiment 2c Intersection Phases No. Movements Green split (Seconds) 1 20 A B C Results Delays are recorded in Table Table Delay of Experiment 2c Using Lag Left Turns (Seconds) Experiment Left turn Major street Entire network Experiment 1c 21, , ,860 Experiment 2c 22, , ,260 Discussion From Table 6-13, it is seen that delays for left turns, the major street and the entire network increase after using lag-left turn phase. In these oversaturated conditions, through traffic enters the intersection during the 30 second long through-traffic phase, and then spillback occurs. The spillback blocks left turns. When the lag-left turn phase occurs, left turns are blocked during 87

106 the green time. The unused green time causes additional delay; whereas, when the lead-left turn phase is used in Experiment 1c, the left turns are cleared before the spillback happens. Thus, for the traffic volumes, signal cycle, and shift to leading left turn phases in the baseline, delay of left turns decreases and, consequently, that of entire network decreases. Experiment 2d Signal Timing Varies by Increasing Cycle Length In Experiment 2d, signal timing in the baseline experiment is changed by increasing the cycle length to 120 seconds. The input, results, and discussion of Experiment 2d are described in the following paragraphs. Input Values Possibility of conditional cell: 100% Possibility of occurrence of a useful gap: 10% Traffic demand: This is the same as used in the baseline experiment. Traffic signal timing: This is shown in Table

107 Table Phase Diagram of Experiment 2d Intersection Phases No. Movements Green split (Seconds) 1 40 A B C Results Delays of the major street and entire network are recorded in Table Table Delay of the Major Street and Entire Network of Experiment 2d (Seconds) Experiment Major street Entire network Baseline 67, ,930 Experiment 2d 105, ,030 Discussion From Table 6-15, it is seen that delay of the major street and entire network increases. It is known that cycle lengths that are either too long or too short increase delays. The effect of cycle length on delay is somewhat complex and is related to phase plans. However, this experiment shows that cycle length does greatly affect delay even when the phase plan remains the same. 89

108 Experiment 3: The Possibility of the Occurrence of a Useful Gap Input Values Possibility of conditional cell: 100% Possibility of occurrence of a useful gap: 10%, 50%, 90% Traffic demand: This is the same as used in Experiment 1c. Traffic signal timing: This is the same as used in Experiment 1c. Results Delays are recorded in Table Table Delay of Experiment 3 Probability of Occurrence of a Useful Gap (Seconds) Possibility of occurrence of a useful gap Left Turn Major Street Entire Network 10% 21, , ,860 50% 21, , ,810 90% 20, , ,850 Discussion The possibility of the occurrence of a useful gap has a direct effect on delay. The higher the possibility, the more opportunities vehicles have to cross the spillback through a useful gap. It helps to decrease the delay. By contrast, the lower the possibility, the more times vehicles are blocked by the spillback and cannot find a useful a gap accessible to the minor street. In this experiment, it is seen that when the possibility of the occurrence of a useful gap increases from 10% to 90%, the delays of left turns, major and entire network decrease by 5.4%, 2.6% and 2.0% correspondingly. This is the anticipated general trend. Although these decreases seem low, they 90

109 apply to the entire system even though they were generated at one intersection. For example the savings might be 27%, 13% and 10% if they were generated by a system of five similar intersections. To the knowledge of the author, this appears to be the first time that a simulation model has been able to identify the specific delay contributions associated with conditional blockage of an intersection related to gaps in the opposing flow. This is useful in assessing the effectiveness of increasing enforcement of the driving rule DO NOT BLOCK THE INTERSECTION as a way to reduce delay. 91

110 Experiment 4: The Possibility of a Conditional Cell versus Delay (CTM vs. CCTM) As described in Chapter 3, a conditional cell exists when a driver breaks the driving rule and crosses an intersection, even though the destination cell is full. Most drivers will not break the rule, but many do. In CCTM, users may input a parameter to set the probability of a driver breaking the driving rule. Thus, the occurrence of a conditional cell can be matched to the behaviors of local drivers. To investigate the effect of the possibility of a conditional cell on delay, Experiment 4 was designed. For comparison purposes, the possibility parameters were assumed to 0% (used in CTM) and 100% (used in CCTM), and delays of both models were recorded. The input, the results, and the discussion of experiment 4 are described in the following paragraphs. Input Values Possibility of conditional cell: 0%, 100% Possibility of occurrence of a useful gap: 10% Traffic demand: Three scenarios of traffic demands on each lane of the network are used: (a) light 360 vehicles/hour/lane with initial density of 0.4 jam density, (b) moderate vehicles/hour/lane with initial density of 0.75 jam density, and (c) heavy 1,800 vehicles/hour/lane with initial density of jam density. Traffic signal timing: This is the same as used in Experiment 1c. 92

111 Results respectively. Results of delays at light, moderate and heavy traffic demands are recorded in Table 6-17 Table Comparisons of Delays between CTM and CCTM (Seconds) Traffic Demands Light Moderate Heavy Movements CTM CCTM u s u s Difference Left turn 3, , % Major 52,020 1,490 52,190 1,530 0% Total 93,320 2,170 93,390 2,190 0% Left turn 9, , % Major 294,970 2, ,900 2,170 2% Total 375,090 2, ,020 2,930 1% Left turn 9, , % Major 367,890 3, ,060 3,250 13% Total 451,040 4, ,860 3,930 11% Discussion The delay in Table 6-17 is an average value of multiple simulation runs. Due to the stochastic feature of the saturation flow rate between cells, CTM and CCTM were run multiple times in order to conduct statistical tests of difference. For illustration purposes, the results of random running of CCTM at heavy traffic conditions from time step 1 to time step 90 is shown in Table A1 in Appendix A. Regarding the minimum number of model run repetitions, the guidelines of the Traffic Analysis Toolbox (FHWA, 2004) was followed. This is a step required to determine if delays of CTM and CCTM are significantly different. 93

112 The difference between CCTM and CTM at heavy traffic demand is most interesting in this research, so comparison of their delays of left turns at heavy traffic demand is shown below for illustration purposes. Estimation of Pooled Standard Deviation s 2 p = s 2 x + s 2 2 y = 2 = 131,650 (6-1) Selection of Desired Confidence Level: A 95% confidence level is typically selected for hypothesis testing. Selection of Minimal Difference in the Means x y = 21,760 9,180 = 12,580(seconds) (6-2) Computation of Minimum Repetitions: If the required number of runs is greater than the preliminary number of runs, the analyst perform the additional repetitions for each alternative and recomputed the mean difference and standard deviation using the augmented set of model run repetitions (FHWA, 2004). Referring to Table 10 in the Traffic Analysis Toolbox (2004), four repetitions of each alternative are required to reject the hypothesis that the observed differences in the simulation results for the two alternatives could be the result of random chance. Ten repetitions are used in this study, a number greater than required. Hypothesis Testing for Two Alternatives: To determine whether simulation output provides sufficient evidence that one alternative is better than the other, it was necessary to perform a statistical hypothesis test of the difference of the mean results for each alternative. 94

113 Null Hypothesis: H : µ µ 0 0 x y = Against: H : µ µ 0 1 x y Solution: t ( n+ m 2) s n m p (1 α = ) t 0.025( ) = 340 (6-3) x y = 12,580 > 340 (6-4) The Null Hypothesis is rejected. The difference between the delays of left turns from CTM and CCTM is statistically significant. From Table 6-7, it is seen that in light conditions, there is no difference between CTM and CCTM. In light conditions there are no spillbacks, because a network can accommodate traffic demands. There is no need for the conditional cell. In moderate conditions, there are some differences between CTM and CCTM. Compared to CCTM, CTM underestimates a delay of left turns by 40%. This is because CTM does not account for the delay when left turns are blocked by the spillback at an intersection. CTM assumes divers will not break the rule if there is no room for them in the far side of the intersection. In many urban areas, this assumption is not consistent with the reality. CCTM overcomes this disadvantage by adding conditional cells at an intersection. Evidence shows that drivers sometimes break the rule even when there is no room for them at the far side of the intersection. Therefore, spillback vehicles enter a conditional cell and block access into or out of minor streets. In other words, vehicles on the major street are prevented from making left turn onto the minor street during green signal time, and this situation causes additional delay. As evidenced by Table 18, the delay of left turns is underestimated by 58 % in this example when using CTM rather than CCTM when traffic demand is heavy. Additionally, CCTM can simulate phenomena in a segment in oversaturated conditions, which includes times when through flow blocks the left turn bay, left turns block the through 95

114 lane, and shock waves. Meantime, the unique contribution of CCTM is that it can simulate the blockages at an intersection by adding a conditional cell at an intersection. The conditional cell holds vehicles that break the driving rule DO NOT BLOCK THE INTERSECTION. Then CCTM uses the conditional cell to delineate the blockages of other movements caused by the spillback vehicles. 96

115 The following discussion provides five illustrations of how CCTM models phenomena that occur frequently in oversaturated conditions. Through Flow Blocks a Left-turn Bay As shown in Figure 6-8, at the intersection A, there is a left turn bay in addition to the through lane. The evolution of all cells from time step 1 to time step 90 is shown in Table A1 in the Appendix A. The overflow of through vehicles can be seen to block the left turn lane, which is a normal phenomenon in oversaturation conditions. At time step 28, the inflows to a left turn cell and a through cell close to signal A are determined by their available spaces. All flows are restricted if either of them is unable to accommodate its allocation of flow. In this illustration, the through cell has 13 vehicles and is fully occupied, and all flows are restricted even though the left turn cell still has 11 vehicle spaces available. This matches what happens in reality. Vehicles block the entrance of the through lane although there are one or more available spaces in the left turn bay. Figure 6-8. Through flow blocks left turn bay. Left Turns Block a Through Lane The overflow of left turn vehicles can block the through lane, which is another normal phenomenon in oversaturation conditions. An example is shown in Figure 6-9. At time step 7, at intersection B a left turn cell is full so the inflow is restricted. At the same time step, inflow to a 97

116 through cell close to signal B is restricted too although the through cell still has 4 vehicles spaces available. Vehicles block the entrance of the through lane although there is still storage space in the through lane. left-turn vehicles through vehicles Figure 6-9. Left turn flow blocks the through lane. Shock Waves Basically, shock waves can be generated whenever the traffic conditions change by signals, accidents, and a merging flows or other ways. Figure 6-10 is a portion of output from the model developed during this research (the entire output is shown in Table A1 in the Appendix A). At time step 14, the traffic is light and the signal indication for lane 3 is green. There is a forward wave through cell (2, 3, 1) in time step 14, cell (2, 3, 2) in time step 15, cell (2, 3, 3) in time step 16, cell (2, 3, 4) in time step 17 and cell (2, 3, 5) in time step 18. This is shown of Figure 6-10 as a line across the figure. Another example of a shock wave is a backward wave caused at intersection B when the signal for left turning vehicles turns to red as shown in Figure 6-11 (also taken from Table A1 in the Appendix A). The flow in front of the signal is stopped suddenly, causing a backward wave to happen. On the figure from time step 7 to time step 10, there is a forward wave through cell (2, 3, 7), cell (2, 3, 6), cell (2, 3, 5) and cell (2, 3, 4) which causes a spillback. This demonstrates another of CTMs abilities to model traffic flow phenomena. 98

117 Link 2 Time Position Position Position Position Position Position Position Lane No. step n f n f n f n f n f n f n Figure A screenshot depicting forward waves in CCTM. 99

118 Link 2 Time Lane Position Position Position Position Position Position Position 2 step No n f n f n f n f n f n f n f Figure A screenshot depicting backward waves in CCTM. Spillback at an Intersection During heavy duty traffic flows, spillback can occur at intersections when vehicles break the driving rule as shown in Figure In Table A1 in the Appendix A shows the number of spillback vehicles in a conditional cell in each time step. For example, in lane 3, at time step 9, there are 8 vehicles that spillback at intersection B. Whether these 8 vehicles block other movements depends on whether there is a useful gap between or behind the spillback vehicles, as discussed in the previous methodology section of the conditional cell. 100

119 Figure Spillback at an intersection. Left Turn is Blocked at an Intersection Spillback at signalized intersections may block left turns as shown in Figure For example, in time step 7, the conditional cell is full. So left turn vehicles in cell (2, 3, 7L) on the major street that desire to go to the minor street are blocked even it is green time is available. This causes the problem of defacto red, i.e., the signal might as well be red because they cannot move (Abu and Benekohal, 1997). Such a phenomenon is common in two-way oversaturated arterials and is simulated by CCTM successfully. 2,3,7L Figure Westbound left turn blocked by the spillback in the conditional cell. 101

120 CHAPTER 7 COMPARISON OF CCTM WITH THE HIGHWAY CAPACITY SOFTWARE To validate CCTM, it is compared with Highway Capacity Software 2000 (HCS) in terms of travel speed. Three scenarios of traffic demand are inputted into the HCS-arterials routine, and resulting travel speeds are compared with CCTM. For illustration purposes, the input data in the HCS at heavy traffic demand are used. These values are similar to those of light and moderate traffic demand conditions. In Table 7-1, the signal data file in the third column is imported from an existing file in HCS-signals. Segment No. Table 7-1. Data Input into HCS-arterials Cross street name Signal data file (imported from HCS-signals) Length (mile) Urban street class 1 Minor street 1 Signal plan at intersection A Minor street 2 Signal plan at intersection B Minor street 3 Signal plan at intersection C N/A N/A Free flow speed (mph) 102

121 Input Data to HCS-arterials File Geometry and Volume The geometry and volume data are shown in Figure 7-1. Volume data are calculated from traffic demand and the percentages of left and right turns at the three intersections Link Link 2 Link 3 Link 4 Link 5 Link 6 Link 7 Figure 7-1. The geometry and volume at Intersections A, B and C. Other input parameters related to geometry and traffic volume, which are default values for HCS, are listed in Table 7-2. Operation Parameters 7-3. Table 7-2. Geometry and Volume Parameters Parameters Value Peak hour factor (%) 0.9 Right turns on red (vph) 0 Percent queue spacing (ft) 25 Available Queue storage length (ft) 0 The input operation parameters, which are the default values for HCS, are listed in Table 103

122 Table 7-3. Operation Parameters Parameters Value Initial unmet demand (veh) 0 Arrival type or percent arriving during green 3 Unit extension (sec) 3 Upstream Filtering/Metering adjustment factor 1 Start up lost time (sec) 2 Extension of effective green (sec) 2 Pedestrian speed (ft/sec) 4 Pedestrian travel distance (ft) 0 Pedestrian cross walk width (ft) 10 Phasing Design in Chapter 6. This is the same value used for the experiment about the possibility of a conditional cell Saturation Flow Adjustment The input parameters, which are the default values for HCS, are listed in Table 7-4. Table 7-4. Saturation Flow Adjustment Parameters Value Ideal saturation flow rate (pcphgpl) 1,800 Lane width (ft) 12 Percentage heavy vehicles 0% Percentage grade (%) 0% Parking maneuvers per hour 0 Bus stops per hour 0 Conflicting bikes and pedestrians per hour 0 Adjustment factors (f w,f hv,f g,f p,f bb,f lu,f lt,f rt,f lpb,f rpb ) 1 104

123 Results of Analysis Using the a input parameters from the previous section, the HCS calculated 3.7 mph at heavy traffic demand, 10.0 mph at moderate traffic demand, and 23.1 mph at light traffic demand, as shown in Table 7-5. In CCTM, travel speed was computed from travel times on the arterials and the delay for the entire network under consideration. CCTM estimated speeds of 20.3 mph at light traffic demand, 11.6 mph at moderate traffic demand, and 6.9 mph at heavy traffic demand. These speeds are also shown in Table 7-5. Table 7-5. Comparison between CCTM and the HCS in Terms of Travel Speed Traffic Demands CCTM Travel Speed (mile/hour) HCS Travel Speed (mile/hour) Criteria in HCS (mile/hour) Light LOS B (19-25) Moderate LOS D (9-13) Heavy LOS F (<7) For light traffic demands in the HCS, the level of service (LOS) is B. The network did a good job of processing the traffic demand, and travel speed is close to free flow speed. In CCTM, vehicles in cells dissipated with cycle length, and there were no blockages (from Figure 22, evolutions of example cells in a light traffic flow condition). This is exactly what drivers expect at LOS B. Hence, the simulation of traffic flow in CCTM is consistent with the criteria of the HCS at light traffic demand. For moderate demands in the HCS, the LOS is D. The network is congested and increasing traffic demand is greatly decreasing travel speed. In CCTM, the number of vehicles in cells always reaches the capacity (13 vehicles), and there are occasional blockages (from Figure 23 - evolutions of example cells in moderate condition). Blockages cause additional 105

124 delay, which decreases travel speed. Again, the simulation of traffic flow in CCTM is consistent with the criteria of the HCS at moderate traffic demand. For heavy traffic demands in the HCS, the LOS is F. The network is processing the traffic demand poorly and travel speeds are very slow. In CCTM, cells are always full for a long time (from Figure evolutions of example cells in heavy condition). Spillback occurs frequently and causes delay to increase, which degrades the speed substantially. Hence, the simulation in CCTM is consistent with the criteria of the HCS at heavy traffic demand. The evaluation results from the HCS and the simulation results from CCTM are consistent for urban streets. The HCS used travel speed to evaluate the level of service, while CCTM tracked the evolutions of cells to judge the quality with which cells process traffic demands. The lower the speed, the more slowly the cells process traffic demands, and the lower the LOS plunges. In summary, a comparison of CCTM and the HCS shows that three traffic demands represent three classes of traffic conditions, as expected. At LOS B, the traffic flow is smooth, the travel speed is close to free flow speed and delay is low. At LOS D, the traffic demand is being processed poorly, the travel speed decreases, and the delay is high. At LOS F, traffic demand causes congestion, speeds greatly decrease, and delay is very long. The consistency between the HCS 2000 and CCTM show that CCTM is a reliable model for simulating two-way traffic flow in oversaturated conditions. 106

125 CHAPTER 8 CONCLUSIONS AND RECOMMENDATIONS Conclusions This research proposes a new traffic flow model based on the Cell Transmission Model (CTM). The new model is called the Conditional Cell Transmission Model (CCTM) and is capable of modeling traffic operations on an oversaturated two-way arterial. Development of CTM-based Theory Traditional CTM is a versatile simulation tool because it can accommodate all traffic conditions from light to oversaturated. However, it has limitations. First of all, applications of CTM have been largely limited to one-way arterials. Additionally, CTM has not been capable of simulating blockages at intersections. In an attempt to overcome these limitations, the following two improvements were made to CTM. Based on the formulations of merging and diverging in one-way flow, CCTM was developed to delineate the dynamic of traffic flow created by the merging and diverging activities in two-way arterials. CCTM includes the addition of a conditional cell at an intersection to simulate blockages and estimate delay. First, CCTM uses two events to simulate this blockage. One is adding a conditional cell at an intersection to simulate the spillback at an intersection and the other is determining whether there is an acceptable gap inside the conditional cell to allow a left turn. Second, the formulation of CCTM allows it to estimate the additional delay occurring due to the conditional cell. CCTM uses the possibility of an additional 107

126 cell to account for any vehicles that may stay inside an intersection for some amount of time thereby incurring delay, and uses the possibility of a useful gap to account for any vehicles that may wait for a useful gap for some amount of time thereby incurring delay. Results of Experiments To test the performance of CCTM, a series of experiments were designed and performed for a multilane, two-way, three-signal sample arterial network. Experiments focused on four user-defined parameters including traffic demand, traffic signal timing, the possibility of the formation of a conditional cell and the possibility of occurrence of a useful gap within the conditional cell. The results of experiments are as follows. Experiment 1 investigated the ability of CCTM to model relationship between traffic flow dynamics, specifically variations in traffic demand with time and direction, and travel delay within the modeled network. In Experiment 1a, a traffic demand of 720 vehicles/hour/lane was loaded in the 1st and 5th minute, and traffic demand of 360 vehicles/hour/lane was set from the 6th to the 10th minute. From the 1st to the 5th minute, the delay increased and reached the peak when traffic demand was kept at 720 vehicles/hour/lane. Delay remained constant at that level between the 5th and 6th minute but the delay decreased until the 10th minute when traffic demand decreased to 360 vehicles/hour/lane. This occurred because the demand dropped (fewer vehicles entered the network, and more vehicles exited the network. From the 11th to the 15th minute, the opposite occurred as delay increased again and reached the peak at 108

127 the 15th when traffic demand was restored to 720 vehicles/hour/lane. Hence, the results showed that the model performed in a logical and expected manner. In Experiment 1b, traffic demand was maintained at 720 vehicles/hour/lane for the westbound direction and increased to 1,080 vehicles/hour/lane for the eastbound direction. The results showed that the delay in the eastbound direction was much higher than that in the westbound direction. This is because the eastbound traffic demand (1,080 vehicles/hour/lane) was 50% higher than the westbound traffic demand during the 15- minute interval. Hence, this was the expected outcome, indicating that the model was adequately describing traffic flow dynamics. In Experiment 1c the purpose was to investigate the effect of the percentage of left turns (10%, 20% and 30%) on delay. The results showed as the percentage of left turns increased, the delay of left turns increased. Meanwhile, delays on the major street and the entire network decreased. In other words, the delay decreased for a large volume of traffic (through vehicles) but increased for a smaller volume (left turns). Consequently, the net result was less delay for the system. This result was reasonable, because more left-turning vehicles were sharing the green time if the percentage of left turns increased. Hence, this experiment showed that CCTM appropriately models the relationship between demand of left turns and delay. In Experiment 2a, the signal timing in the baseline experiment was changed by shifting green time between two directions on the major street. The results show that the delay of westbound decreased to 18,450 seconds, and the delay of eastbound increased to 69,460 seconds. That is because the longer green time allowed more westbound vehicles to cross the intersection. However, eastbound vehicles on the major street had to wait a 109

128 longer time before the signal was green for them. This caused additional delay. Hence, this result was expected and indicates the model was responsive to changes in the tested green splits of the signal-timing plan. In Experiment 2b, signal timing in the baseline experiment was changed by shifting green time from the minor street to the major street. Compared with the baseline experiment, the delay of the major street decreased, and the delay of the minor street increased. The reasons for these results is that the longer green time allowed more vehicles on the major street to cross the intersection; whereas, vehicles on the minor street had to wait longer before the signal was green for them. Thus, the delay decreased for the largest share of vehicles (major street) and increased for the minor share of vehicles (minor street), resulting in a net reduction in delay. This was the expected pattern and, again, affirms the correct operational pattern for CCTM. In Experiment 2c, signal timing in Experiment 1c was changed by using a lag-left turn phase instead of a lead-left turn phase. It was observed that delays for left turns on the major street and the entire network increased after using lag-left turn phase. In these oversaturated conditions, through traffic entered the intersection during the 30-second long through-traffic phase, and then spillback occurred. When the lag-left turn phase occurred, left turns were blocked by the spillback during the green time. The unused green time caused additional delay; whereas, when the lead-left turn phase was used in Experiment 1c, the left turns were cleared before the spillback happened. Hence, the experiment showed that CCTM appropriately responds to changes in phase sequence of the signal timing plan. 110

129 In Experiment 2d, signal timing in the baseline experiment was changed by increasing the cycle length to 120 seconds. It was seen that delay of the major street and entire network increased. Cycle lengths that are either too long or too short increase delays. The effect of cycle length on delay is somewhat complex and is related to phase plans. However, this experiment showed that CCTM appropriately models the relationship between signal timing parameters and delay. Experiment 3 investigated the effect of the possibility of the occurrence of a useful gap on delay. In this experiment, it is seen that when the possibility of the occurrence of a useful gap increases from 10% to 90%, the delays of left turns, major and entire network decrease by 5.4%, 2.6% and 2.0% correspondingly. The higher the possibility of the occurrence of a useful gap, the more opportunities vehicles have to cross the spillback. It helped decrease the delay. By contrast, the lower the possibility of the occurrence of a useful gap, the more times vehicles are blocked by the spillback. The results showed that the possibility of the occurrence of a useful gap has a direct effect on delay and the effect was an anticipated general trend from CCTM. Experiment 4 compared CTM and CCTM. It was observed that in light conditions, there was no difference between CTM and CCTM. This is because a network can accommodate traffic demands in light conditions and there is no congestion and subsequent blockages. In moderate conditions, there were some differences between CTM and CCTM. In comparison to CCTM, CTM underestimated the delay of left turns by 40%. This was because CTM did not account for the delay when left turns are blocked by the spillback at an intersection due to the formation of a conditional cell. In heavy conditions, the difference between CTM and CCTM appears more obvious. In 111

130 comparison to CCTM, CTM underestimated 58% of the delay of left turns and 11% of delay of the entire network. This was because more drivers broke the rule even when there was no room for them at the far side of the intersection. Spillback vehicles entered a conditional cell and blocked access into or out of minor streets. This situation caused additional delay. Experiment 4 also illustrated how the conditional cell works and how CCTM delineates phenomena in oversaturated conditions including left turns blocking a through lane, through flow blocking a left-turn bay, shock waves occurring, spillbacks occurring at an intersection, and left turns being blocked at an intersection. Again, Experiment 4 demonstrated that CCTM provided an accurate representation of traffic flow. Contributions of CCTM In summary, the major contributions of CCTM to the field of transportation engineering are as follows: CCTM may be used to simulate traffic conditions in two-way arterials. Since two-way arterials are more common than one-way arterials in the real world, CCTM has the potential for more wide-spread use that CTM. CCTM uses a condition cell to simulate the spillback and blockages at an intersection. In CCTM, users may input the probability of a conditional cell and the probability of the occurrence of a useful gap to match the behaviors of local drivers. This feature is a unique contribution of CCTM. This is the first time a simulation model (i.e., CCTM) has been able to identify the specific delay contributions associated with conditional blockage of an intersection 112

131 related to gaps in the opposing flow. Such information would be useful to law enforcement officials. CCTM can assess the effectiveness of increased enforcement of the DO NOT BLOCK THE INTERSECTION driving rule as a way to reduce traffic delay. 113

132 Recommendations The following sections present recommendations for future research to improve and apply CCTM. The recommendations are presented in the form of objective statements for potential future research projects. The first set of recommended projects are intended to address the limitations of CCTM as developed in the current research and documented herein. The second set of recommended projects is potential applications of the new, unique capabilities of CCTM methodology. Recommendations for Future Research to Further Develop CCTM Sensitivity Analysis of the Length and Shape of Cells The purpose of the project is to develop a guideline to determine the appropriate length and shape of cells. The key idea of CCTM is to divide an entire traffic network into cells. So the length and the shape of each cell are sensitive parameters that affect the accuracy of CCTM. Cells that are too short increase the volume of simulation calculations; cells that are too long might miss important information along the arterials. On the other hand, the shape of each cell is rectangular in all research so far. This shape is proper for the cells in a segment. However, cells might need to change their shapes to fit the geometry at an intersection. For example, the shape of a cell which holds queued left turns could be a curve. The purpose of the project is to develop a guideline to determine the appropriate length and shape of cells. Take Account of Random Variations of Built-in Parameters in CCTM The purpose of the project is to calibrate the parameters in CCTM. The original CTM is widely used because of its simplicity and relatively accurate representation of traffic flows. It assumes that all parameters 114

133 are constant. However, random variations in traffic flows play a significant role in accuracy. There are many variations in traffic flow that can affect the traffic flow including the random behavior of drivers, the alignment of the road, the time of day, the location of the road and the weather. Hence the assumption of constant parameters may limit accuracy and flexibility of the model. To increase CCTM s accuracy and the realism of traffic flow representation, take account of random variations in built-in parameters including jam density, free flow speed and saturation flow rate is feasible. This might be handled by adding random distribution functions of these parameters. Add Operation Parameters to CCTM HCS is well-developed commercial software and has a comprehensive list of input parameters. For example, peak hour factor, arrive type, start up lost time, pedestrian speed are input parameters. The current CCTM does not consider these factors. In the future, they can be added into CCTM to increase its accuracy. Peak hour factor and arrive type can be formulated into a function of traffic demands to reflect variations in traffic demand whereas the current model assumes it to be constant. Start up lost time should be considered in the saturation flow rate. The effect of pedestrian movements on traffic flow can be taken account into by constructing a function of assigning right-of-way between vehicles and pedestrian. With these new features, CCTM can represent the traffic flow with more detail. Verification of CCTM using Field Data Collect field data to verify CCTM. MOEs should be chosen for comparison between CCTM and field data. For example, CCTM provides a convenient way to estimate delay and throughput. Collecting this data would allow a comparison and could be used to calibrate CCTM. 115

134 Develop a Friendly Interface of CCTM CCTM can be developed to commercial software to compete with other simulation software like the CORSIM and TRANSYT-7F since CCTM has an advantage over them in simulating blockages at an intersection. To do that, a friendly interface must be developed to allow users to input traffic demands, traffic signal timing, etc., in a simple and accurate method. Recommended of Future Applications of CCTM CCTM is suitable to simulate oversaturated arterials, and therefore has potential applications in the following areas. Before and After Studies of Operations of Traffic Management Some traffic management strategies attempt to relieve congestion at oversaturated arterials. DO NOT BLOCK THE INTERSECTION driving rule is one of them. To assess the effectiveness of increased enforcement of this driving rule as a way to reduce traffic delay, CCTM can be used to simulate the traffic flow and estimate the delay before and after this driving rule is enforced respectively. Feasible Study for Urban Planning CCTM, with its ability to simulate oversaturated conditions, can predict whether a given network can accommodate the desired traffic demand. If blockages and spillback frequently occur, the planned traffic network needs to be adjusted. If the network processes vehicles well, the planned traffic network is feasible. Hence, CCTM provides a way to predict and measure blockages in a traffic network. 116

135 Theoretical Study of Estimate of Delay Webster s formulation of delay is used only for an isolated intersection. So far a complete guideline to estimate delay for a network is lacking. In CCTM, the delay of a network is obtained by aggregating all cells during the simulation time. It is a convenient and reasonable method to estimate network delay. CCTM can be improved as an effort to study traffic flow fundamentals. Modifying guidelines for left-turn lane at intersections Left turn lane design is of interest to traffic and geometric design engineers. This research studies two blockages associated with leftturn bays under oversaturated condition. One is that the overflow of left turns blocks the throughlane entrance. The other is that the overflow of through vehicles blocks the left-turn entrance. Both problems are uncharted in the Highway Capacity Manual (FHWA, 2000). With the capability to simulate potential blockages, CCTM can evaluate the geometric design and signal design of left turn lane. The modified guidelines should ensure that the appropriate geometry and signal strategy for left-turn vehicles is provided at intersections to avoid blockages associate with left turn lane. Summary In light of aforementioned specific contributions, it is asserted that CCTM is the foundational for a new tool or set of tools that will allow for improved simulation and investigation of oversaturated arterial traffic operations. It is a relatively easy to use and understand tool. With the improvements and validation proposed earlier in this chapter, it could be developed into a more versatile, robust tool for modeling the complexity of oversaturated 117

136 traffic conditions. With additional enhancements it could be developed into useful simulation tool to support new research to further the understanding of oversaturated traffic operations, their origins and potential means of mitigating their impacts. 118

137 REFERENCES Abu-Lebdeh, G., and R. Benekohal. Development of a Traffic Control and Queue Management Procedure for Oversaturated Arterial. Presented at the Annual Meeting of the Transportation Research Board, Washington, D.C., Ahn, G. H. Methodology of Traffic Signal Timing in Oversaturated Arterial Networks. Dissertation of University of Texas at Austin AIMSUN User s Manual, Version 5.1. TSS-Transportation Simulation System, Alecsandru, C.; and S. Ishak. Accounting for Random Driving Behavior and Nonlinearity of Backward Wave Speeds in the Cell Transmission Model. Presented at the Annual Meeting of the Transportation Research Board Meeting, Washington, D.C., Bloomberg, L.; and J. Dale. A comparison of the VISSIM and CORSIM Traffic Simulation Models on a Congested Network. In Transportation Research Record: Journal of the Transportation Research Board, No. 1727, Transportation Research Board of the National Academies, Washington, D.C., 1999, pp Chow, A. H. F., and H. K. Lo. Sensitivity Analysis of Signal Control with Physical Queuing Delay Derivatives and an Application. Transportation Research Part B, Vol. 41, 2007, pp CORSIM User's Guide, Version 6.0. ITT Industries, Inc., Systems Division, Daganzo, C. F. The cell transmission model: A Simple Dynamic Representation of Highway Traffic. Transportation Research Part B, Vol. 28, 1994, pp Dans, G. C., and D. C. Gazis. Optimal Control of Oversaturated Store and Forward Transportation Network. Transportation Science, Vol. 10, 1976, pp Enrique. G. V. Adaptivation of VISSIM, a Dynamic Simulation Model to the Traffic Behavior at Intersections in Mayaguez, Puerto Rico. Thesis of University of Puerto Rico, Gazis, D. C. Optimum Control of a System of Oversaturated Intersections. Operation Research, Vol. 12, No.6, 1064, pp

138 Girianna, M., and R. F. Benekohal. Dynamic Signal Coordination for Networks with Oversaturated Intersections. In Transportation Research Record: Journal of the Transportation Research Board, No. 1811, Transportation Research Board of the National Academies, Washington, D. C., Highway Capacity Manual. Transportation Research Board of the National Academies, Washington, D.C., Jones, S. L., A. Sullivan, N. Cheekoti, and M. Anderson. University Transportation Center for Alabama (UTCA) Report Number Traffic SimulationSoftware Comparison Study. UTCA, The University of Alabama, Tuscaloosa, AL, Kikuchi, S., N. Kronprasert, and M. Kii. The Length of Turn Lanes on Intersection Approaches: The Case of Three-Branch Fork Lanes. Presented at the Annual Meeting of the Transportation Research Board, Washington, D.C., Kim, Y. Development of Optimization Models for Signalized Intersections during Oversaturated Conditions. Dissertation of Texas A& M University, Li, Z., and G. L. Chang. Modeling Arterials Signal Optimization with Enhanced Cell Transportation Formulations. Presented at the Annual Meeting of the Transportation Research Board, Washington, D.C., Light, M. J., and B. Whitham. On Kinematic Waves. I. Flow Movement in Long Rivers. II. A Theory of Traffic Flow on Long Crowed Roads. Proceedings of Royal Society A, No. 229, 1955, pp Lin, W. H., and D. Ahanotu. Validating the Basic Cell Transmission Model on a Single Freeway Link, Technical Note, UCB-ITS-PATH-TN-95-3, University of California, Berkeley, CA Lo, H. K. A Cell Based Traffic Control Formulation: Strategies and Benefits of Dynamic Timing Plans. Transportation Science, Vol. 35, No.2, 2001, pp Lo, H. K. A Novel Traffic Signal Control Formulation. Transportation Research Part A, Vol.33, 1999, pp Lo, H. K., E. Chang, and Y. C. Chan. Dynamic Network Traffic Control. Transportation Research Part A, Vol. 35, Lo, H. K., and A. H. F. Chow. Control Strategies for Oversaturated Traffic. Journal of Transportation Engineering, Vol. 130, No. 4, Lonnie, E. H., and S. L. Ming. Traffic Flow Simulation for an Urban Freeway Corridor. Proceedings of the Annual Meeting of the Transportation Research Board, Washington, D.C.,

139 Manual on Uniform Traffic Control Devices (MUTCD). U.S. Department of Transportation, Federal Highway Administration, Washington, D.C., May, D. A. Traffic Flow Fundamentals. Englewood Cliffs, NJ, Prentice Hall, Michalopoulos, P., and G. Stephanopoulos. Oversaturated Signal Systems with Queue Length Constraints. Transportation Research Part B, Vol. 11, 1977, pp Paksarsawan, S., F. O. Montgomery, and S. D. Clark. How Traf-Netsim Works, ITS Working Paper 380. Universiy of Leeds, Institute for Transportation Studies, Park B., C. J. Messer, and T. Urbanik. Traffic Signal Optimization under Congested Conditons Genetic Algorithms Approach. In Transportation Research Record: Journal of the Transportation Research Board, No. 1683, Transportation Research Board of the National Academies, Washington, D. C., 1999, pp PASSER V User s Guide. Texas Transportation Institute, Pignataro, L. J., W. R. McShane, K W. Crowley, B. Lee, and T. W. Casey. Traffic Control in Oversaturated Street Networks, NCHRP Report 194. Transportation Research Record, National Research Council, Washington, D.C., Richards, P. I. Shockwaves on the Highway. Operation Research, No. 4, 1956, pp Roess, R. P., E. S. Prassas, and W. R. Mcshane. Traffic Engineering, 3rd edition. Englewood Cliffs, NJ, Prentice Hall, Schrank, D.; and T. Lomax Urban Mobility Report. Texas Transportation Institute of the Texas A & M University System, Simtraffic User s Manual, Version 6.0. Trafficware, Smilowitz, K. R., and C. F. Daganzo. Prediction of Time Dependant Traffic Backups and other Reproducible Traits in Experimental Highway Data. Working paper UCB-ITS-PWP-99-5, California PATH Program, Institute of Transportation Studies, University of California, Berkeley, CA, Traffic Analysis Toolbox Volume III: Guidelines for Applying Traffic Microsimulation Modeling Software. Publication No. FHWA-HRT , TRANSYT-7F User s Guide, Version Federal Highway Administration, VISSIM User s Manual, Version 4.1. PTV Planung Transport Verkehr AG,

140 Yin Y. F., H. X. Liu, J. A. Laval, X. Lu, M. Li, J. Pilachowski, and W. B. Zhang. Development of an Integrated Microscopic Traffic Simulation and Signal Timing Optimization Tool. California PATH Research Report,

141 APPENDIX A Table A1 Evolution of cells for heavy duty traffic Tim e La n e Tra ffic Link 1 Link 2 Link 3 Lin k 4 S t e p N o. D e m a n d P o s itio n P o s itio n P o s it io n P o s itio n S ig n a l C o nditio n a l P o s itio n P o s itio n P o s itio n P o s it io n P o s itio n P o s itio n P o s it io n S ig na l C o n ditio na l P o s itio n P o s itio n P o s itio n P o s itio n S ig na l C o nd it io n a l P o s itio n P o s itio n P o s it io n Tra ff ic A C e ll B C e ll C C e ll D e m a nd n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n

142 Table A1 (Cont d) Evolution of cells for heavy duty traffic Tim e La n e Tra ffic Link 1 Link 2 Link 3 Lin k 4 S t e p N o. D e m a n d S ig n a l S ig na l S ig na l P o s itio n P o s itio n P o s it io n P o s itio n C o nditio n a l P o s itio n P o s itio n P o s itio n P o s it io n P o s itio n P o s itio n P o s it io n C o n ditio na l P o s itio n P o s itio n P o s itio n P o s itio n C o nd it io n a l P o s itio n P o s itio n P o s it io n Tra ff ic A B C C e ll C e ll C e ll D e m a nd n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n

143 Table A1 (Cont d) Evolution of cells for heavy duty traffic Tim e La n e Tra ffic Link 1 Link 2 Link 3 Lin k 4 S t e p N o. D e m a n d P o s itio n P o s itio n P o s it io n P o s itio n S ig n a l C o nditio n a l P o s itio n P o s itio n P o s itio n P o s it io n P o s itio n P o s itio n P o s it io n S ig na l C o n ditio na l P o s itio n P o s itio n P o s itio n P o s itio n S ig na l C o nd it io n a l P o s itio n P o s itio n P o s it io n Tra ff ic A C e ll B C e ll C C e ll D e m a nd n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n

144 Table A1 (Cont d) Evolution of cells for heavy duty traffic Tim e La n e Tra ffic Link 1 Link 2 Link 3 Lin k 4 S t e p N o. D e m a n d P o s itio n P o s itio n P o s it io n P o s itio n S ig n a l C o nditio n a l P o s itio n P o s itio n P o s itio n P o s it io n P o s itio n P o s itio n P o s it io n S ig na l C o n ditio na l P o s itio n P o s itio n P o s itio n P o s itio n S ig na l C o nd it io n a l P o s itio n P o s itio n P o s it io n Tra ff ic A C e ll B C e ll C C e ll D e m a nd n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n

145 Table A1 (Cont d) Evolution of cells for heavy duty traffic Tim e La n e Tra ffic Link 1 Link 2 Link 3 Lin k 4 S t e p N o. D e m a n d S ig n a l S ig na l S ig na l P o s itio n P o s itio n P o s it io n P o s itio n C o nditio n a l P o s itio n P o s itio n P o s itio n P o s it io n P o s itio n P o s itio n P o s it io n C o n ditio na l P o s itio n P o s itio n P o s itio n P o s itio n C o nd it io n a l P o s itio n P o s itio n P o s it io n Tra ff ic A B C C e ll C e ll C e ll D e m a nd n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n

146 Table A1 (Cont d) Evolution of cells for heavy duty traffic Tim e La n e Tra ffic Link 1 Link 2 Link 3 Lin k 4 S t e p N o. D e m a n d S ig n a l S ig na l S ig na l P o s itio n P o s itio n P o s it io n P o s itio n C o nditio n a l P o s itio n P o s itio n P o s itio n P o s it io n P o s itio n P o s itio n P o s it io n C o n ditio na l P o s itio n P o s itio n P o s itio n P o s itio n C o nd it io n a l P o s itio n P o s itio n P o s it io n Tra ff ic A B C C e ll C e ll C e ll D e m a nd n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n

147 Table A1 (Cont d) Evolution of cells for heavy duty traffic Tim e La n e Tra ffic Lin k 1 Link 2 Link 3 Link 4 S t e p N o. D e m a n d P o s it io n P o s itio n P o s itio n P o s itio n S ig n a l C o nditio na l P o s itio n P o s itio n P o s itio n P o s itio n P o s itio n P o s itio n P o s itio n S ig n a l C o nd it io n a l P o s it io n P o s itio n P o s itio n P o s itio n S ig na l C o n ditio na l P o s itio n P o s itio n P o s it io n Tra ff ic A C e ll B C e ll C C e ll D e m a nd n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n

148 Table A1 (Cont d) Evolution of cells for heavy duty traffic Tim e La n e Tra ffic Link 1 Link 2 Link 3 Lin k 4 S t e p N o. D e m a n d P o s itio n P o s itio n P o s it io n P o s itio n S ig n a l C o nditio n a l P o s itio n P o s itio n P o s itio n P o s it io n P o s itio n P o s itio n P o s it io n S ig na l C o n ditio na l P o s itio n P o s itio n P o s itio n P o s itio n S ig na l C o nd it io n a l P o s itio n P o s itio n P o s it io n Tra ff ic A C e ll B C e ll C C e ll D e m a nd n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n

149 Table A1 (Cont d) Evolution of cells for heavy duty traffic Tim e La n e Tra ffic Link 1 Link 2 Link 3 Lin k 4 S t e p N o. D e m a n d S ig n a l S ig na l S ig na l P o s itio n P o s itio n P o s it io n P o s itio n C o nditio n a l P o s itio n P o s itio n P o s itio n P o s it io n P o s itio n P o s itio n P o s it io n C o n ditio na l P o s itio n P o s itio n P o s itio n P o s itio n C o nd it io n a l P o s itio n P o s itio n P o s it io n Tra ff ic A B C C e ll C e ll C e ll D e m a nd n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n f n

150 APPENDIX B Figure B1 A Screenshot depicting HCS results for arterial analysis in light duty traffic 132

151 Figure B2 A Screenshot depicting HCS results for arterial analysis in moderate duty traffic 133

152 Figure B3 A Screenshot depicting HCS results for arterial analysis in heavy duty traffic 134