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MODELING TRAFFICACTUATED CONTROL WITH TRANSYT7F By DAVID HALE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2000 TABLE OF CONTENTS Page A B ST R A C T ..................................................................... ................ iv CHAPTERS 1 INTRODUCTION .................................................. ......... ................. 1 Problem Statement ...................................................................... 2 O objectives ...... .................................... ................... ...... .. .. 3 Organization of Chapters.............................................................. ... 8 2 LITERATURE REVIEW ......... ...................................................... 10 Phase Time Estimation ....................................................... ......... 11 Vehicle Delay Estimation ..................................... ........................... ... 49 Control Parameter Design and Optimization.......................................... 55 Chapter Two Summary.................................................................... 61 3 MODEL DEVELOPMENT................................................................ 63 Queue Service Time ................................................................ ....... 64 Green Extension Time................. ...................... ........................... 70 Model Implementation ...................................................................... 88 Chapter Three Summary.................................................................. ..103 4 MODEL TESTING.............................. ..................................... ...... 105 List of Candidate Models.................................................................... 106 Testing Strategy ............................... ........................ .............. ....... 107 Calibration of CORSIM and TRANSYT7F...................................... .. 109 Chapter Four List of Experiments......................................................... 110 Single Intersection Testing................................................................. 110 Arterial Street Testing....................................................................... 124 Optimization Applications Testing............................................. 147 Chapter Four Summary.......................... ..... ..... ........ ............. 154 5 CONCLUSIONS AND RECOMMENDATIONS...................................... 156 Conclusions ................. .................. ...... ........... ......... ......... 156 Summary of New Modeling Capabilities ......................... ..... ............... .... 163 Recommendations .......................................... ................ 164 APPENDIX Brief Tutorial on Actuated Control..................................................... 167 Brief Tutorial on TRANSYT7F........ .... ................ .......... ................ 171 Calibration of CORSIM and TRANSYT7F............................................ ..177 Automated Process: Experimental Version of TRANSYT7F......................... 190 REFERENCES .................................................. .............. .......... 193 BIOGRAPHICAL SKETCH............ ...................... ... ........... ............. 196 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy MODELING TRAFFICACTUATED CONTROL WITH TRANSYT7F By David Hale August 2000 Chair: Kenneth G. Courage Major Department: Civil Engineering Research suggests that traffic congestion in U.S. cities has grown rapidly in recent years, and that numerous solutions are needed to address the problem. This dissertation describes new research for producing basic improvements to the practice of traffic signal timing optimization, in order to improve one of the many available weapons for fighting congestion and delay. TRANSYT7F is one of the most comprehensive signal timing tools in existence, and has evolved into a benchmark within the transportation profession. Although TRANSYT7F was developed in an era of pretimed signal control, it was modified in the 1980s to automatically estimate the average green times for actuated controllers. Although effective at eliminating wasted green time, the existing actuated control submodel within TRANSYT7F is oversimplified. The model does not recognize most of the signal settings associated with today's controllers. In addition, this and other actuated control models from the literature do not recognize numerous operational characteristics affecting phase times. The end result is that performance estimates and timing plans generated by the program are potentially less accurate and optimal. The overall goal of this study was to develop an improved actuated control methodology for usage within TRANSYT7F, and perhaps within other programs and procedures. A literature review was performed to ascertain available technology on actuated control including phase time calculation, vehicle delay estimation, and control parameter design or optimization. Subsequently, certain models from the literature were chosen as candidates for improvement of TRANSYT7F performance. In addition, new prototype models were developed during the course of the study. Along with existing literature models, these prototypes were subjected to a battery of tests in order to scrutinize their strengths and weaknesses. The wellknown CORSIM simulation program was used as a reference point for model comparison. Significant amounts of experimental data revealed dramatic improvement in the accuracy of actuated phase time calculation when the candidate models were applied by TRANSYT7F. A smaller amount of data was also collected to demonstrate improvements in the optimal timing plans, based on the new methodology. Conclusions and recommendations, regarding new modeling capabilities and future research, are provided in the final chapter. CHAPTER 1 INTRODUCTION Research from the Texas Transportation Institute (TTI) suggests that traffic congestion in U.S. cities has grown rapidly in recent years, and that "a full array of solutions and measures are essential in addressing the mobility problem" [Lomax and Schrank, 1998]. Simple solutions such as carpooling, or building additional roadway lanes, are reportedly inadequate for dealing with increasing traffic problems. Lomax and Schrank report that in 1997, the financial cost of congestion exceeded $72 billion per year, up from $66 billion in 1996, and that increases in delay have been more prevalent in small to mediumsized cities than in the nation's largest cities. Numerous congestionreducing strategies have been proposed for improving transportation efficiency in an existing roadway network. Some strategies involve modification of driver behavior (e.g., the use of public transit), whereas other strategies involve better traffic management. This dissertation focuses on one aspect of better traffic management, namely the optimization of traffic signal timing plans in centrally coordinated traffic control systems. While no single device or strategy can be expected to "solve" the problem of traffic congestion by itself, signal timing optimization has been demonstrated to be an extremely costeffective strategy. When properly applied, it has proven effective in reducing delay, stops, fuel consumption and other measures related to operating costs and driverperceived disutility [Deakin et al., 1984]. Any technique that offers a potential improvement in traffic control system performance should provide a useful contribution in combating this growing national problem. Problem Statement The importance of efficient traffic signal operation has been recognized for many years. Various signal system simulation and optimization models are now available for analysts and engineers. Simulation models offer a realistic interpretation of traffic flow and performance, but their function is limited to evaluating the performance of a specified operational alternative. In other words, they do not provide features that explicitly optimize the performance. Optimization models, as the name implies, do attempt to find the "best" set of operating parameters for a specified performance objective. However, they often lack certain detailed treatment of traffic flow characteristics found within simulation models. The simplifying assumptions required to support a productive optimization process have, in many cases, compromised the quality of the final product. The result is that the timing plans being implemented in many traffic control systems today still have significant room for improvement. One of the most promising areas for improvement is the modeling of "traffic actuated" control, in which instantaneous information from traffic detectors is incorporated into the control tactics for finetuning intersection performance. Existing optimization models apply the simplifying assumption of "pretimed" control, in which the operation at each intersection is characterized by a series of fixedduration intervals. The optimization process determines the optimal duration and position of each interval. Some adjustments are made in an attempt to represent the effects of trafficactuated control, but the results to this point have not proven to be entirely satisfactory. Objectives The overall goal of this study is to develop an improved treatment of traffic actuated control for application within deterministic optimization models. Regarding the type of actuated control to be analyzed, the scope of this study involves "basic" actuated control, where presence detectors are installed at the stop line. To accomplish the overall goal, it is necessary at the outset to choose a specific optimization model for improvement, as well as a simulation model for evaluation of the improvements. These two choices will establish the scope of the project. The Traffic Network Study Tool (TRANSYT) program [Robertson, 1968] is the most logical choice for the optimization model. TRANSYT was developed by the Transport Research Laboratory in the United Kingdom. It is used extensively throughout the world for traffic control system timing design and evaluation. The specific version of the TRANSYT model to be used in this study will be TRANSYT7F, release 8. TRANSYT7F was developed as a derivative work by the University of Florida Transportation Research Center [Wallace et al., 1981]. It is distributed worldwide by the University of Florida and currently has approximately 1,400 registered agencies worldwide. The extensive recognition of TRANSYT7F, combined with the institutional support of the University of Florida, make it a natural choice for purposes of this project. More detailed descriptions of the TRANSYT7F modeling and calibration process are presented in the appendix. Ideally testing and validation of the project results would be accomplished through the collection and analysis of field data; however, an adequate empirical validation would require resources several orders of magnitude beyond those available to this project. This limitation dictates the need for simulation as a surrogate for field data collection. The choice of a simulation model is not difficult in this case. The CORridor SIMulation (CORSIM) [ITT Systems and Sciences Corporation, 1998] model has been developed and enhanced continually over the past 25 years by the Federal Highway Administration (FHWA). It was designed specifically for the purpose intended by this project (i.e., a surrogate for field data) and is used extensively for this purpose. CORSIM is especially strong in the treatment of trafficactuated control. It models this type of control explicitly, using a software module developed from the same source code as the realtime control logic contained within the actual field hardware. Chapter 2 (literature review) contains a reference that illustrates field validation of CORSIM's actuated phase times. Therefore CORSIM will be used for testing and validation of the optimization enhancements to be developed as a part of this project. Consider, for example, the comparison between signal phase times estimated by a deterministic optimization model (TRANSYT7F) and a detailed microscopic simulation model (CORSIM), as shown in figure 11. 5 40 R = 0.8063 30 * 10 0I I 0 10 20 30 40 TRANSYT7F Phase Time (sec) Figure 11: Actuated Phase Time Comparison CORSIM vs. TRANSYT7F The level of correlation evident in this comparison suggests that the optimization model is not replicating simulation model conditions satisfactorily. A corollary to this observation is that the "optimal" design (i.e., the final product of the optimization process) will be based on incorrect information and will not therefore realize its potential for optimizing system performance. It is therefore possible, and definitely desirable, to improve the treatment of trafficactuated control in the design and optimization of traffic control system timing plans. This would provide the opportunity to improve efficiency of performance at thousands of signalized intersections throughout the USA. As an alternative, consider an updated comparison between phase times estimated by TRANSYT7F and CORSIM, given the new methodologies to be presented within the body of this study, as shown in figure 12. Figure 12: Updated Phase Time Comparison CORSIM vs. TRANSYT7F TRANSYT7F and other optimization models are based on a series of simulation or evaluation runs. Typically the simulation or evaluation run that results in the best performance is reported as optimal. In other words, the effectiveness of optimization is predicated on the accuracy of simulation or evaluation. Because of this, improvements in actuated phase time calculation (as illustrated in figures 11 and 12) can result in an improved optimization process. Table 11 shows an example of traffic network 40  R2 = 0.9574 ,u, 30  S20 O ** S10 .) 0 0 10 20 30 40 TRANSYT7F Phase Time (sec) performance improvements that are possible under the updated methodologies for actuated control. Table 11: Sample Optimization Based on Improved Actuated Control Treatment CORSIM output based on timing from: Old New T7F T7F Control Delay 25.6 24.2 Total Delay 29.7 28.4 Stop Delay 22.0 20.5 Vehicle Trips 8116 8242 In summary, the objectives of this project are to improve the treatment of traffic actuated control within deterministic models, to demonstrate the improvements using TRANSYT7F release 8, and to validate the improvements using CORSIM. In support of these objectives, the following tasks will be carried out: 1. Identify specific shortcomings of the existing TRANSYT7F actuated timing model: Related to this, generalized shortcomings of existing optimization models were discussed earlier in this chapter. Technical details regarding shortcomings of the existing TRANSYT7F actuated timing model are provided in chapter 2. 2. Establish requirements for an improved model: To obtain an improved actuated timing model, it is necessary to keep in mind the minimum requirements for such a model. This prevents the possibility of wasted time in evaluating a new model that contains unacceptable weaknesses. 3. Survey candidate models for improvement of TRANSYT7F performance: In the literature, there are a number of models that contain good ideas and methodologies, related to the subject matter at hand. It is necessary to survey these existing models, in order to learn whether existing methodologies may be helpful in developing a new model for improvement of TRANSYT7F performance. 4. Evaluate candidate models per requirements: The minimum requirements, to be established by task #2, will be used to determine the existing models that are appropriate for further consideration. 5. Select one or more models for additional testing and development: Existing models that meet the minimum requirements for an improved model will be selected for additional analysis and consideration. 6. Develop models: Candidate actuated timing models must be developed for application in conjunction with TRANSYT7F. 7. Formulate a test plan: Devise a comprehensive test plan to compile evidence of model effectiveness. 8. Test models per test plan: Testing will be performed on a variety of field conditions, in order to compile evidence on the effectiveness of the candidate models. 9. Recommend specific improvements: Conclusions and recommendations, regarding TRANSYT7F actuated control modeling, will be formed based on the results from model testing. Organization of Chapters Table 12 illustrates the organization of chapters within this dissertation. It also shows which chapters will be used to address specific tasks and objectives listed earlier. The potential benefits of traffic signal timing optimization were briefly discussed in this chapter. Also, shortcomings of the existing TRANSYT7F actuated timing submodel were introduced, and the minimum requirements for an improved model were established. Thus, this chapter was used to address task 1. In support of tasks 25, chapter 2 provides background information on numerous models for trafficactuated control. The third chapter is used to provide a frame of reference for each objective in this study. It describes technical aspects of the existing model including methodology, sample calculations, strengths and weaknesses, and preliminary test results (task 6). Chapter 4 outlines the testing plan, and contains the detailed testing results for the candidate models (tasks 7 & 8). The fifth and final chapter discusses implementation strategies, plus proposed additional testing and development of selected models (task 9). Table 12: Study Objectives and Associated Chapters Objective Chapter 1. Identify shortcomings of the existing model 1 Introduction 2. Establish requirements for an improved model 2 Literature Review 3. Survey existing models 2 Literature Review 4. Evaluate candidate models per requirements 2 Literature Review 5. Select models for additional testing 2 Literature Review 6. Develop models 3 Model Development 7. Formulate test plan 4 Model Testing 8. Test models per test plan 4 Model Testing 9. Recommend specific improvements 5 Conclusions and Recommendations CHAPTER 2 LITERATURE REVIEW This chapter summarizes the available literature on trafficactuated control modeling, because such literature may be useful in determining the best strategies for improvement of TRANSYT7F performance. Tasks 2 through 5 from chapter 1 (table 1 2) are addressed by this chapter, in which models from the literature will be summarized, evaluated, and possibly selected for further development. Because this discussion is primarily targeted at persons with experience in traffic operations, tutorial summaries on the basics of TRANSYT7F and trafficactuated control were moved from this chapter and are presented in the appendix. Throughout the literature, it appears that models for trafficactuated control can be classified into three major categories. This chapter contains three major sections for distinguishing between these model types. One of the basic requirements for an improved TRANSYT7F model is that it must estimate average actuated phase times. Actuated phase time inaccuracy is the most significant perceived deficiency of the existing model. Because of this, models (in the literature) that are capable of estimating average actuated phase times may be especially useful. In addition, an improved model must be suitable for practical implementation within the TRANSYT7F program. Phase Time Estimation Existing Model within TRANSYT7F Before investigating the candidate models for improvement of TRANSYT7F performance, it is helpful to better understand the existing model. A candidate model must be considered superior to the existing model in order to warrant implementation, which is one reason that the existing model should be understood. Another reason is that one of the candidate models to be considered works similarly to the existing model. Finally, general understanding of the existing model facilitates general understanding of the candidate models and of actuated control. The existing model for trafficactuated control within TRANSYT7F, developed at the University of CaliforniaBerkeley [Skabardonis, 1988], is primarily based on target degree of saturation. The model is designed to give actuated phases as little green time as possible, and gives all remaining green time to the major street through movement. How is it possible to give the actuated phases "as little green time as possible"? It is necessary to give them a certain amount of green time that will result in near saturation on that phase. This is consistent with typical operation, because the basic strategy of an actuated controller is to terminate the phase soon after the queue has been serviced. This results in a degree of saturation somewhat lower than 100%, although the exact degree of saturation is difficult to predict. The default value currently applied by the TRANSYT7F program is 85%. Figure 21 illustrates the minor movements at 85% saturation. Figure 21: Existing Model Strategy Actuated Phases at 85% Saturation Degree of saturation concept At this time it is necessary to define "degree of saturation." Mathematically, degree of saturation equals volume divided by capacity; or, X = v/c. Conceptually, if there is only enough green time (on average) to service the initial queue (on average), then that movement operates at 100% degree of saturation. In this case of 100% saturation, the expected volume (during each cycle) will receive just enough green time (during each cycle) to be served, and the capacity of the movement is equal to the expected volume. If there were not enough green time to service the initial queue, degree of saturation would exceed 100%. If there were enough green time such that the initial 85% 85% 885% 85% queue could be served, plus some additional vehicle arrivals thereafter, degree of saturation would be less than 100%. Suppose that the leftturning vehicles shown in figure 22 have just been given the green arrow to indicate the beginning of a protected leftturn phase. On the westbound approach, the initial queue contains six vehicles, whereas on the eastbound approach, the initial queue contains two vehicles. What if the eastbound approach were to receive enough green time such that the initial two vehicles, plus the two straggling vehicles behind them, were all served? Degree of saturation for that movement would be less than 100%. What if the westbound approach were to receive enough green time such that only four out of the six vehicles in the initial queue were served? The "residual queue" would be two vehicles, and the movement would be "oversaturated" with degree of saturation greater than 100%. In order to know the exact value of degree of saturation in any of these cases, it would be necessary to perform additional calculations regarding the value of capacity. This is illustrated later. Figure 22: Degree of Saturation Concept Example Using LeftTurn Movement Volume (v) Capacity (c) Degree of Saturation (X= vic) Returning to the discussion about the existing TRANSYT7F model, it was stated that the model is designed to give the actuated phases as little green time as possible, and gives all remaining green time to the major street through movement. Further, in order to give the actuated phases as little green time as possible, the model gives them enough green time such that their movements achieve 85% saturation. Why 85%? In the real world, arrival rates and queues vary from cycle to cycle. Although the analyst typically knows the expected average arrival rate and average queue length, these values should be exceeded about half of the time. It would be highly undesirable to exceed 100% saturation during any given cycle, because when that occurs, vehicle delay tends to rise exponentially. In the existing model, target degree of saturation should be low enough such that 100% is rarely exceeded. On the other hand, when target degree of saturation decreases for the minor movements, their allotted amount of green time increases. This conflicts with the desired objective of giving as much green time as possible to the major street through movement. Any unnecessary, wasted green time on the minor movements would be better spent on achieving arterial progression on the major street through movement. In the existing model, target degree saturation should be high enough such that green time is not wasted on the minor movements. To summarize, in choosing target degree of saturation for an actuated phase, it is desirable to have it as high as possible, provided that 100% saturation is rarely exceeded. Skabardonis [1988] recommends target degree of saturation in the range of 8590%. The value of 85% has been chosen as the default value in TRANSYT7F, although the user is allowed to specify any value between 50 and 100%, applicable to specific phases, or applicable to the entire network. Sample calculation To understand its relative effectiveness, it is helpful to walk through a sample calculation with the existing model. Figure 23 illustrates a set of hypothetical conditions at a signalized intersection. Figure 23: Existing Model Sample Calculation Intersection Conditions 50 100 100 JL 100 50 500 500 50  100 100 100 50 20 sec 30 sec 20 sec 20 sec 1. Calculate Capacity Consider the northsouth leftturn phase in the figure 23 timing plan. The largest individual movement volume on this phase is 100 vehicles per hour. In order to achieve 85% saturation, the phase must receive enough green time such that it could actually serve 118 vehicles per hour. Thus, movement capacity is equal to 118 vehicles per hour. Volume (v) =100 vehicles / hour v X = 0.85 v 100 c =118 vehicles / hour 0.85 0.85 Figure 24: Existing Model Sample Calculation Step #1 2. Calculate Required Percentage of Green Time per Hour In step 1 it was shown that movement capacity must equal 118 vehicles per hour in order to achieve 85% saturation. Next, it is necessary to determine the amount of green time per hour needed to serve 118 vehicles on that movement. Suppose that the movement is capable of serving 1710 vehicles per hour if it could have an hour's worth of green time. If an hour's worth of green time results in 1710 vehicles served, how much green time results in 118 vehicles served? By simple math, if the movement received green time during 6.9% of the hour, then 118 vehicles would be served. Figure 25: Existing Model Sample Calculation Step #2 3. Calculate Phase Time In step 2 it was shown that the movement must receive green time during 6.9% of the hour. This means that it must also receive 6.9% of the green time available during each signal cycle. The calculations illustrated show that, after adding on two seconds of 6.9% of the hour is required Cycle Length (C) = 90 seconds Total Lost Time (1) = 8 seconds 6.9%= green time 908 green time = 82* 0.069= 5.6 seconds phase time = 5.6 + 2 8 seconds Figure 26: Existing Model Sample Calculation Step #3 Capacity (c) = 118 vehicles / hour S\ Saturation Flow (s) = 1710 vehicles / hour green Required Time Capacity Hour Saturation Flow c 118  = = 6.9% of the hour is required s 1710 yellow and all red clearance time, the leftturn phase time is 8 seconds according to the existing model. 4. Donate Unused Green Time to the NonActuated Phase In step 3 it was shown that the existing model estimates the average length of the first phase as 8 seconds. The same computations from steps 13 are performed to estimate the average length of each actuated phase. Subsequently, all remaining green time in the cycle is allocated to the nonactuated phase, as illustrated in figure 27. 8 66 8 8 I II \t 8 66 8 8 Figure 27: Existing Model Sample Calculation Step #4 The TRANSYT7F output in table 21 presents the existing model sample calculation results. Along the rows labeled "Intvl Length" and "Splits," the signal timing table shows that 63 seconds have been allocated to the coordinated, nonactuated phase. Along the row labeled "Phase Start," the signal timing table shows that phase number 4 is the nonactuated phase (NAP). Along the row labeled "Links Moving," the signal timing table lists the link numbers moving on each phase. For example, through and rightturn links (105, 107, 111, 112) are moving during the nonactuated phase. Along the column labeled "Deg Sat," the measures of effectiveness table shows that simulated degree of 19 saturation was approximately 85% for the critical actuated movements (102, 104, 101, 103, 106, 108). Table 21: TRANSYT7F Program Output for Sample Calculation Intersection 1 Actuated Splits Estimated Interval Number : Intvl Length(sec): Intvl Length (%): Pin Settings (%): Phase Start (No.): Interval Type Splits (sec): Splits (%) Links Moving Offset = 0.0 sec 1 2 3 4 5 6 7 8 6.0 2.0 64.0 7 2 71 100/0 6.0 2.0 7 2 2.0 2 7 9 80 82 89 91 98 1 ACT 2 NA P 3 ACT 4 AC T V Y V Y V Y V Y 8 9 106 108 66 73 105 107 111 112 8 9 102 104 8 9 103 101 109 110 0 %. Movement/ Node Nos. Deg/ Total Sat Travel % vmi Travel Time Total Avg. vhr sec/v 101 : 83 50.02 4.20 151.3 102 103 104 105 106 107 108 109 110 111 112 50.02 50.02 50.02 250.10 50.02 250.10 50.02 25.01 25.01 25.01 25.01 4.52 4.20 4.52 10.91 4.52 10.91 4.52 1.62 1.62 1.06 1.06 162.9 151.3 162.9 78.5 162.9 78.5 162.9 116.7 116.7 76.4 76.4 Delay Total Total Avg/LOS Stops vhr sec/v No. (%) 2.19 78.8E 140(140) 2 106 2.51 2.19 2.51 0.85 2.51 0.85 2.51 0.61 0.61 0.06 0.06 90.4F 78.8E 90.4F 6.1A 90.4F 6. 1A 90.4F 44.3D 44.3D 4.0A 4.0A 151(152) 140(140) 151(152) 190( 38) 151(152) 190( 38) 151(152) 50(101) 50(101) 14( 29) 14( 29) NODE 1: 88 900.37 53.69 17.46 34.9C 1392( 77) 57.4 Max Back of Queue Est.Cap. Fuel Cons. gal 4.2 4.5 4.2 4.5 12.6 4.5 12.6 4.5 1.8 1.8 1.2 1.2 106 106 106 106 106 106 106 106 106 106 106 5. Subsequent Simulation or Optimization Once the existing model has arrived at its estimates for phase times, the resulting timing plan is then used as a starting point in simulation or optimization. If optimization has not been requested whatsoever, then the phase time estimates will not be modified during simulation. If thorough optimization has been requested, then the phase time estimates are simply used as a starting point in a hill climb search for a better signal timing plan. If optimization of offsetsonly has been requested, then TRANSYT7F will not modify the phase time estimates as it searches for better offsets. If the initial timing plan is close to the global optimum solution, then the hill climb procedure has a higher probability of locating that global optimum. Also, when there is more green time available for the coordinated through movement, then there is a higher probability of achieving progression. Thus, when the actuated model estimates phase times and allocates extra green time to the coordinated movement, TRANSYT7F gets a better starting point for optimization of a congested artery. Accurate phase time estimation can be critical. Inaccurate phase time estimation will result in the wrong amount of green time being allocated to the coordinated movement. Thus, the output measures of effectiveness and/or optimal offset timing produced by TRANSYT7F may be overly optimistic or pessimistic. It depends on whether the amount of green time allocated to the coordinated movement, and the resulting available green band throughout the arterial, is too large or too little. Specific shortcomings Although effective at eliminating wasted green time, as an actuated controller would, the existing model for trafficactuated control within TRANSYT7F is oversimplified. Predicted phase times are simply a function of the number of actuated phases and the target degree of saturation. The target degree of saturation strategy is inherently inaccurate because it is not responsive to numerous factors that affect actuated phase lengths. As stated in chapter 1, actuated phase times and measures of effectiveness reported by TRANSYT7F are potentially less accurate, because the existing model is not sensitive to several key factors. In addition, since actuated phase times are often estimated prior to optimization, any phase time inaccuracies could lead to inferior optimization results. What are these key factors, and how do they affect actuated phase times? Gap setting: If a phase is actuated, then its associated lanes contain detectors that search for a gap in the traffic stream. The gap setting indicates the size of the gap being searched for, measured in units of seconds. Larger gap settings produce larger actuated phase times. This is because large gaps in traffic occur less frequently than small gaps, and phases will continue to last longer if the desired gap is not detected. The existing model for actuated control within TRANSYT7F gives the phase enough green time to achieve 85% saturation, as stated previously. Theoretically, for a given phase, there exists a gap setting that will produce a certain green time resulting in 85% saturation on average. Using this gap setting, the existing model would produce accurate phase time estimates. For example, suppose that someone in the field carefully observes the north and southbound leftturn phase from figure 23 for several cycles of operation. Suppose they conclude that the average phase time was indeed 8 seconds during that period of observation, just as predicted by the existing TRANSYT7F model in table 21. For these conditions, the existing model is accurate. But what if the associated gap setting were to be increased, and other factors and variables held constant? In the field, average phase time would be expected to increase along with the gap setting, thus reducing the average degree of saturation to somewhere below 85%. Because the analysts are unaware of the degrees of saturation associated with various gap settings, they are unable to estimate a target X other than 85%, which causes inaccurate phase time estimates. This is how a change in the gap setting can render the existing model less effective. Detector configuration: As stated above, if a phase is actuated, then its associated lanes contain detectors that search for a gap in the traffic stream. The configuration includes the type (presence vs. passage), length, and lane location of detectors. Longer presence detectors lead to larger actuated phase times. This is because longer detectors have a better chance of detecting vehicles prior to a controller's irrevocable decision to terminate the phase. For a given phase, a given presence detector length exists that, in conjunction with a given gap setting, will produce a certain green time resulting in 85% saturation on average. If this hypothetical detector length is exceeded and all other factors and variables are held constant, the resulting degree of saturation would fall somewhere below 85%. Thus, a change in detector length can also render the existing model less effective. Forceoff: As previously stated, if a phase is actuated, then its associated lanes contain detectors that search for a gap in the traffic stream. What if traffic happens to be heavy enough such that the desired gap is never detected? It is necessary to impose a maximum green time setting on the actuated phase. The phase must not be allowed to 23 continue for an unreasonable amount of time. When signals are coordinated, the force off setting is used to terminate actuated phases that do not gapout. For a given phase, a range of forceoffs exists that will allow green times resulting in 85% saturation on average. In other words, if the forceoff setting is sufficiently high, the phase is capable of termination via gapout, and 85% saturation may occur. But what if this forceoff setting was decreased, and other factors and variables held constant? In the field, if the forceoff occurred early enough in the cycle, the phase would be expected to terminate via maxout before locating the specified gap, and thus increase average degree of saturation to somewhere above 85%. Thus a change in forceoff can also render the existing model less effective. Physical factors: The previous subsections discuss the way in which individual actuated control parameters can affect average phase lengths. There are also some additional factors that may affect average phase lengths, according to the literature presented later in this chapter. These include vehicle length, number of lanes, and approach speed. The existing model for trafficactuated control within TRANSYT7F does not take these physical factors into consideration. Operational characteristic effects: In the existing model, what if it were possible to make target degree of saturation sensitive to all of the control parameters and physical factors mentioned in the previous subsections? Would this fix the model? It would be a step in the right direction; however, there would still be no clearcut way for dealing with operational characteristic effects on actuated phase times. The effects of early returns to green, overlap phasing, stochastic behavior, progression, permitted left turns, spillback, and optimization, are based on performance at neighboring signals, and are thus difficult to quantify without simulation. Chapters 3 and 4 illustrate the technical aspects of operational characteristic effects with more technical detail. Trying to predict degree of saturation: In the field, actuated phase times result in a certain degree of saturation. If the user were able to predict degree of saturation based on available input data, it would be possible to effectively use the existing model by specifying the appropriate target degree of saturation for each phase. However, degree of saturation is too difficult to predict. Nonuniform arrival rates, link length, lane channelization, control parameters, and detector layout, for numerous phases and intersections, interact as significant variables at many levels, and thus conspire to produce complex and unpredictable results throughout the network. This is why programs such as CORSIM (to be described later) and TRANSYT7F are needed. This is also why an alternative method for estimating actuated phase times, besides trying to forecast the degree of saturation, is desirable. Pitfalls of inaccurate phase time estimation: A simple example is helpful for illustrating the potential pitfalls of inaccurate phase time estimation. The phasing diagram in figure 28 illustrates a hypothetical signal timing plan. This signal timing plan has leading leftturn phases with no overlaps. Average phase times are listed below the box that represents each phase. Under pretimed control, phase times should be approximately equal for each phase in the event that traffic volume demands and saturation flow rates are approximately equal for each movement. In the fourphase situation illustrated by figure 28, phase times should be 25 seconds for each phase if the cycle length is 100 seconds. Although leftturns typically have lower volumes and saturation flow rates than through movements, suppose for this simple example that they have equal volumes and saturation flow rates, and that phase times should be equal in order to optimize the situation. 25 25 25 25 Figure 28: Sample Phasing Diagram with Average Phase Times Now suppose that control type at this signal is to be converted to coordinated actuated, with the eastwest (lefttoright) through movement to be served by a coordinated phase. This means that the coordinated phase will have priority, and that the minor movement actuated phases are to be terminated as soon as possible after their initial queues have been served, such that the coordinated phase will receive extra green time. What will the new signal timing plan look like? Presumably something like the updated timing plan illustrated in figure 29. In this timing plan, actuated phase times are now much lower than their original pretimed counterparts, and the coordinated phase benefits by receiving the extra green time. This type of control is typically preferable for achieving progression along the major street, provided that performance on the actuated phases does not deteriorate to unacceptable levels. Figure 29: Sample Timing Plan Computed by the Existing Model As mentioned earlier, accuracy of the existing actuated phase time model within TRANSYT7F leaves much room for improvement. Figure 210 illustrates a hypothetical outcome of this situation. Actuated phase times that materialize in the field are actually 14 seconds apiece instead of 10, and the coordinated phase time occurring in the field is actually 58 seconds instead of 70. In the context of capacity analysis, the result would be an inappropriately pessimistic analysis, in terms of vehicle delay and level of service, of the actuated phases. Perhaps more dangerous, such results would cause overly optimistic analysis of the coordinated phase serving the major street movements. In the context of signal timing optimization, inaccurate phase time estimates can result in compromised estimates of the available green band, or green window, available for optimization of offsets or phasing to achieve progression along the major street. 10 10 10 70 Figure 210: Example of ModelPredicted vs. Actual Actuated Phase Times NCHRP Model The model for estimating actuated phase times in appendix II of the 1997 Highway Capacity Manual is an example of a method that provides an alternative strategy to forecasting the degree of saturation. This model was developed as part of National Cooperative Highway Research Program (NCHRP) Project 348 [Courage et al., 1996]. An upcoming description of its methodology will be followed by a sample calculation using the same data from the existing model sample calculation (figure 23). Methodology In general, actuated phase lengths are estimated using the structure illustrated in figure 211. The NCHRP model specifies that the length of an actuated phase can be estimated by summing the queue service time (gs), the green extension time (ge), and the intergreen (yellow plus all red) time. Note that the green extension time should not be confused with the extension of effective green (EEG) parameter, which is applied by numerous deterministic traffic models. Although figure 211 does not illustrate startup lost time, this parameter affects the phase time as well. According to the HCM terminology, queue service time begins where startup lost time ends. However, in figure 211 and in other parts of this paper, queue service time includes startup lost time. 1J 10 10 10 70 14 14 14 58  Actuated Phase Duration Figure 211: Individual Phase Length Structure within the NCHRP Model Initial timing plan: The NCHRP model requires an initial timing plan in order to perform calculations. This initial timing plan makes it possible to determine the effective red time, and thus the expected initial queue, that is experienced by each actuated phase. Subsequently, the model is able to appropriately adjust the phase times in response to the differing characteristics of each phase, such as traffic volume demand and the actuated control parameters. It is important to note that differing initial timing plans should not prevent the model from computing the same final solution each time. Only the input parameters affecting the model should impact the final solution; however, an initial timing plan that is close to the final solution results in fewer model iterations and faster running times for the computer program. Queue service time: The queue service time for each phase is calculated using the queue accumulation polygon (QAP). The QAP concept is robust, reliable, and well documented in the Highway Capacity Manual [Transportation Research Board, 1997] Queue Service Time Green Extension Time Intergreen Time and in other parts of the literature. The shape of the polygon is affected by several relevant parameters affecting vehicle queuing and delay, including traffic volume arrivals, saturation flow rate, effective red time, and effective green time. Figure 212 illustrates a sample QAP. SQueue Ser Cu 0 o TRed Green Time (seconds) vice Time Ext. Time Figure 212: Sample Queue Accumulation Polygon Figure 212 illustrates a polygon in the shape of a triangle, which implies that the rate of vehicle arrivals on red and the rate of vehicle departures on green are both constant, uniform rates. Unless traffic volume is very heavy, the slope of the lefthand side is not expected to be as steep as the slope of the right hand side, because when a queue is present, the rate of vehicle departures is very high (i.e., the saturation flow rate). The shape of the polygon is useful in determining queue service time among other things. The shape of the polygon can become complex in response to field conditions causing MWOMEMMNOW nonuniform arrivals or departures, allowing queue service time to be computed accurately under complex conditions. The HCM discussion lists a formula for computing queue service time. This formula (21) is an algebraic interpretation of the queue accumulation polygon, targeted at computing queue service time. qrr gT =fq q.) (21) where, q,, qg = red arrival rate (veh/s) and green arrival rate, veh/s, respectively, r = effective red time, s, s = saturation flow rate, veh/s, and fq = queue calibration factor fq = 1.080.1imum actual green (22) maximum green Green extension time: The queue accumulation polygon is not as useful in determining the green extension time. Figure 212 illustrates that green extension time takes place beyond the polygon boundaries, and cannot be directly computed from the shape of the polygon. The HCM appendix states that green extension time for each phase can be calculated using equations developed by Akcelik [1993, 1994]. e (eo+toA) 1 g, = (23) where eo = unit extension time setting to = time during which the detector is occupied by a passing vehicle to d L) (24) where Lv = vehicle length, assumed to be 5.5 m Ld = detector length, DL, m, v = vehicle approach speed, SP km/h A = minimum arrival (intrabunch) headway, s, = proportion of free (unbunched) vehicles, and = a parameter calculated as: A 1= (25) 1 Aq where q is the total arrival flow, veh/s for all lane groups that actuate the phase under consideration. Akcelik [1999] has also developed formulas for computing actuated phase degrees of saturation. These formulas that compute degree of saturation will be presented later on in this chapter, but should not be confused with Akcelik's green extension time formulas above, which are an integral part of the NCHRP model. Actuated phase lengths: The phase length is computed as the sum of the queue service time, the green extension time, and the yellow plus all red time. Yellow and all red times are, of course, given parameter values that do not require calculation. Subsequently, the estimated average phase length is subject to the constraints of the associated minimum green, maximum green, and forceoff settings. If the estimated phase length is lower than the minimum green time, it is set equal to the minimum green time. If the estimated phase length is higher than the maximum green value created by the forceoff, it is set equal to that maximum green time. Overall timing plan: The new set of estimated phase lengths associated with any given intersection may not sum to the background cycle length. This is not an issue under isolated intersection conditions, where the cycle length is simply recalculated as the sum of the individual phase lengths. Under coordinated conditions, adjustments are necessary to conform the new solution to the background cycle length. If an estimated phase time indicates phase termination prior to reaching the forceoff setting, then the unused green time must be reassigned within the cycle. Assignment of unused green time is performed in accordance with the iterative computational structure described in the HCM guidelines. If an estimated phase length is lower than its original phase length from the initial timing plan, its new value is set equal to the midpoint between those two values. The other half of the slack time is then donated to the coordinated phase. For example, suppose the initial timing plan contains a 15 second actuated phase and a 45 second nonactuated phase. If the actuated phase is estimated as 9 seconds by the NCHRP model, then donating half of the slack time (instead of all of it) to the coordinated phase results in a 12second actuated phase time and a 48second nonactuated phase time for the second iteration. Donating half of the slack time to the coordinated phase, instead of donating all of the slack time, may increase the probability of convergence within the iterative model structure. Iteration and convergence: After obtaining the overall timing plan, the new design must be tested for convergence. This is necessary because when the overall timing plan changes, it causes flow patterns to change throughout the analysis. Changing flow patterns result in changing phase lengths, and vice versa. This iterative process can be terminated when the timing plan on any iteration is observed to be identical to the one from any previous iteration. For example, if the timing plan in iteration 5 were identical to the one from iteration 3 or 4: Table 22: NCHRP Model Intermediate Outputs Iteration 1 Critlink Start MnG Fq Gs Ge Y+R Split Max Min 106 0 4 .98 6.38 4.58 2 16 20 6 0 20 4 1 0 0 2 42 72 30 102 50 4 .98 6.38 4.58 2 16 20 6 103 70 4 .98 6.15 4.58 2 16 20 6 Sample calculation A sample calculation is presented here to demonstrate an application of the NCHRP model. The initial timing plan (20 30 20 20) in iteration 1 reflects the same sample calculation conditions from figure 23, which was used earlier to demonstrate the existing model within TRANSYT7F. Individual phase times: Intermediate outputs provide details on how individual phase lengths are estimated. Consider the intermediate output from iteration 1: Table 23: NCHRP Model Iterations of Overall Timing Plan The start time within the cycle for north/south leftturn phase 3 (link 102) is time 50. Indeed, the search for a zerolength queue begins at the phase starting time. For phase 3, a zerolength queue must have been found after 6.38 seconds, because the queue Iteration Phase Times 1 12 20 20 24 9 40 2 10 15 18 22 8 52 3 9 12 18 22 8 56 4 8 12 18 22 8 57 Convergence has been achieved service time (gs) is reported as 6.38 seconds. The green extension time (ge) for phase 3 is reported as 4.58 seconds. This value was computed using Akcelik's formula. Yellow and allred times for phase 3 are given for each phase as 2 and 0 seconds, respectively. Therefore, the actuated phase time for phase 3 in this iteration is computed as gs + ge + yellow + allred = 6.38 + 4.58 + 2 + 0 = 13 seconds (approximately). However, in the output file generated by the experimental version of TRANSYT7F, "Split" is reported as 16 seconds for phase 3 in iteration 1. This is because half of the unused green time was donated to the nonactuated phase, in accordance with the NCHRP model procedures. The estimated phase time of 16 seconds for phase 3 does not exceed the forceoff time of 20 seconds and does not fall below the minimum phase time, reported in the output file as 6 seconds. Therefore, the estimated phase time does not violate either the minimum or the maximum constraints, and does not need to be readjusted prior to the next iteration. Overall timing plan: After determining the each of the individual phase times in this manner, it is necessary to derive the overall timing plan to be used in the next iteration. The phase time for phase 3 was computed as 13 seconds. The NCHRP model calls for donation of half of the slack time. Because the leftturn phase lasted 20 seconds in the first iteration, it is reduced to 16 seconds in the second iteration, and 4 seconds are donated to the coordinated phase. Table 24 shows that in the first iteration, a total of 12 seconds is donated to the coordinated phase from the three actuated phases. Thus, green times for the individual phases are reassigned in this manner until a brandnew timing plan has been established for use in the second iteration. At this point, the process would terminate if the brandnew timing plan were identical to any timing plan from a previous iteration. In this case, the overall timing plan has changed and will be used in the second iteration. The new design is used to assist in determining the timing plan for the third iteration, and so on. In this case, convergence has been achieved after iteration number 7. The average phase times listed in the final line (14 48 14 14) are the ones that are expected to occur, given the input parameter values. Table 24: NCHRP Model Timing Plan Iterations Iteration Phase Durations 1 20 30 20 20 2 16 42 16 16 3 15 47 14 14 4 14 49 14 13 5 14 48 14 14 6 14 49 14 13 7 14 48 14 14 Existing model: Recall that the existing model for trafficactuated control within TRANSYT7F was also applied to analyze conditions from the sample calculation input file. The table 25 output reveals that phase times estimated by the existing model (8 66 8 8), are different than the ones produced by the NCHRP model (14 48 14 14). Specific shortcomings The NCHRP model is constrained by certain simplifying assumptions The equations for green extension time listed earlier assume that detectors operate in the presence mode, and assume that detectors are installed at the stop line. Passage detectors, or detectors of any type that are not installed at the stop line, are not taken into account by the formula for green extension time. In addition, computer execution time for the NCHRP model exceeds that of the existing model by many orders of magnitude, since numerous iterations are required. Table 25: Existing Model Timing Plan for NCHRP Sample Problem  Intersection 1 Actuated Splits Estimated  Interval Number : 1 2 3 4 5 6 7 8 Intvl Length(sec): 6.0 2.0 64.0 2.0 6.0 2.0 6.0 2.0 Intvl Length (%) 7 2 71 2 7 2 7 2 Pin Settings (%) 100/0 7 9 80 82 89 91 98 Phase Start (No.): 1 AC T 2 NA P 3 AC T 4 ACT Interval Type : V Y V Y V Y V Y Splits (sec): 8 66 8 8 NCHRP model summary The NCHRP model has the potential for improved accuracy over the existing model. It accounts for numerous elements that affect phase lengths, including actuated signal settings and detector layout. By varying these input conditions during testing, it is possible to show that the NCHRP model produces more accurate results than the existing model. Test results such as this are presented later on in this paper. Iterative Target Degree of Saturation Model Appendix II of the 1997 HCM states that there are two methods of determining the required green time given the length of the previous red. One of these methods is the NCHRP model, as described earlier The second method describes the general procedure for computing phase times as a function of the target degree of saturation. The existing model within TRANSYT7F, also described earlier, employs this strategy. However, Akcelik [1999] has developed a unique model that combines these two strategies. Earlier in this chapter it was stated that one of the specific shortcomings of the TRANSYT7F existing model is its inability to respond appropriately to changes in trafficactuated control parameters. Akcelik's model avoids this shortcoming to some extent by using special equations to compute the target degree of saturation. The equations specify that target degree of saturation is affected by the values of certain actuated control parameters, in addition to a couple of other relevant parameters. Akcelik's model also involves elements of the NCHRP model. The NCHRP model procedure is iterative because of the circular dependency between individual actuated phase times. A change in phase length 'A' has an impact on the effective red time experienced by subsequent phase 'B'. This affects the average queue length at the beginning of phase 'B', which affects phase length 'B', possibly affecting the effective red time experienced by phase 'A', etc. Thus, the circular dependency between actuated phase times is recognized by dynamic changes in the queue service times. In Akcelik's model, the circular dependency between actuated phase times is recognized by dynamic changes in the target degree of saturation Two formulas are provided for calculating the target degree of saturation. The first formula is intended for use with initial calculations, when the effective red time is not known: Xa = 1.5y05eho (26) subject to 0.40 <= xa <= 0.95 where, xa = target degree of saturation for actuated signals y = flow ratio (v/s) eh = effective headway (seconds) The second formula is intended for use with subsequent iterations, when the effective red time is known: x = 0.78y05eh0 018 (27) subject to 0.40 <= xa <= 0.95 where, r = effective red time (seconds) eh = 3.6(L, +L) (28) eh = e +tu +e Vac where, eh = effective headway (seconds) es = gap setting (seconds) tou = detector occupancy time (seconds per vehicle) Lv = average vehicle length (meters per vehicle) Lp = effective detection zone length (meters) vac = approach speed (km per hour) Effective headway setting is a function of detector length and vehicle length, in addition to the gap setting. Thus, the target degree of saturation generated by this method is responsive to physical factors as well as signal settings. Since flow ratio and effective red time are also taken into consideration through the first two formulas, target degrees of saturation are appropriately sensitive to volume demand on the subject movement, in addition to phase lengths of the other movements. On the surface this appears to be an ideal candidate for upgrading the existing model without requiring substantial changes to the existing degree of saturation strategy. Instead of using a default value or a user input value for the target degree of saturation, this formula could be used to intelligently predict degrees of saturation in response to numerous relevant parameters. However, earlier discussion on the existing model pointed out possible pitfalls of the target degree of saturation strategy. Specifically, there is no clearcut way for revising the target degree of saturation strategy to account for added complexities such as protected permitted leftturn phasing, or queue spillback. In order to view a sample calculation according to the Akcelik's model, it is only necessary to review the earlier sample calculation for the existing model within TRANSYT7F. Of course, the one exception to this is that target degrees of saturation for each phase would be calculated in advance via Akcelik's formulas, instead of using a default value or a user input value. Modified NCHRP Percentile Joint Poisson Probability Model Husch [1996] describes a procedure for estimating actuated phase times that is similar to the NCHRP model. It utilizes the queue service time green extension time strategy for calculating actuated phase times. However, Husch's model actually computes five hypothetical phase times, based on the 10th, 30t, 50th, 70th, and 90t Poisson percentile versions of the average traffic volume. Subsequently, a volume weighted average phase time is computed, based on the five hypothetical phase times. If any one of the five phase times violates the minimum or maximum phase time requirements, the average phase time can be adjusted accordingly. If the arrival rate on red for any one of the five hypothetical volumes is less than 0.69 vehicles, then the model assumes phase skipping (phase time = 0 seconds) for that volume scenario, based on a 0.5 Poisson probability of zero arrivals. Beyond this, the only clear difference between Husch's model and the NCHRP model lies in the calculation of green extension time. Queue service time Husch's queue service time formula is listed as equation (29) below. Tq =T, + x (Y, +R+T) (29) DA (29) where, Tq = queue service time (seconds) T, = startup lost time (seconds) A = arrival rate (vehicles per hour) D = saturation flow rate (vehicles per hour) R = actual red time (seconds) Yu = unused yellow time (seconds) This is essentially identical to the NCHRP model's formula for queue service time, presented earlier in this chapter as equation (21): f (qr2 = f sq)(21) Although there are some apparent differences in the formulas, these differences are mostly cosmetic, and would not produce any difference within the overall results. The two formulas are essentially identical because the term (Yu + R + T,) is the same as effective red (r), arrival rate A is the same as arrival rate q, and departure rate D is the same as saturation flow rate s. Husch's formula contains startup lost time (T,), which is not listed in the NCHRP queue service time formula. However, NCHRP procedures stipulate that startup lost time must be added to the queue service time and green extension time. The question of whether to define startup lost time as a separate entity, or as part of the queue service time, is purely semantic and would not affect results. Some differences are visible that could potentially introduce a bias into the results. The NCHRP formula contains two variables, qg and qr, to represent vehicle arrival rates on green and red, respectively. Husch's formula contains only one variable, A, to represent the arrival rate. In addition, Husch's formula does not implement the queue calibration factor, fq, which accounts for stochastic behavior. Therefore, in situations where the arrival rate on green differs from the arrival rate on red, or in comparing the results to those from stochastic simulation, the NCHRP formula would presumably produce better correlation. Green extension time Husch's green extension time model is completely different than the NCHRP green extension time model (Akcelik's formula). Husch's model stipulates that once the queue has been serviced, phase termination via gapout occurs when there is at least a 0.5 Poisson probability of zero arrivals. The Poisson calculations are performed for each second within the cycle, following the queue service time. For example, given a flow rate of 500 vehicles per hour, the Poisson probability of zero arrivals in the second that immediately follows queue service time is: (500 P(0)= e 3600 = 0.87 Given a gap setting of 3 seconds, the joint probability of three consecutive seconds of zero arrivals is: P(0,0,0)= 0.87 x 0.87 x 0.87 = 0.66 Since the probability of three consecutive zero arrivals is greater than 0.5, an immediate gap is assumed, and the green extension time is equal to 3 seconds. Under a different set of input conditions, if an immediate gap were not found, then the determination of whether a greater than 0.5 probability of gapout occurs on subsequent seconds changes slightly. Table 26 demonstrates the relationship between traffic volume and gap setting. This model computes an effective gap setting (GapEff) as a function of the actual gap setting and the detector layout. This allows phase times to be computed under various detector configurations. However, for standard presence detectors installed at the stop line, the effective gap setting would still be equal to the actual gap setting. In table 26, a cell value of zero indicates that the phase was not extended, and that the green extension time is equal to the gap setting. Analysis Although the volumeweighting approach may be useful in calculating an accurate average phase time, the individual phase times calculated for any given volume may be underestimated by Husch's model. First, by omitting the queue calibration factor, fq, the queue service time model is unable to increase phase times in response to stochastic effects. Second, by assuming phase termination whenever there is a better than 50% chance of gapout, the green extension time model is unable to increase phase times in response to vehicle extensions of the phase. In other words, if there were a 60 percent chance of gapout after 3 seconds, a 20 percent chance of gapout after 6 seconds, and a 20 percent chance of maxout after 9 seconds, this model would nevertheless compute a green extension time of 3 seconds. However, the appropriate green extension time in this scenario, considering each possible outcome, would actually be: g, = (0.6 x 3)+(0.2 x 6)+ (0.2 x 9)= 4.8 seconds Table 26: Husch's Green Extension Time Model Matrix Volume GapEff= 2 GapEff= 3 GapEff= 4 GapEff= 5 GapEff= 6 (vph) 500 0 0 0 1 1 700 0 0 1 2 3 1000 0 1 2 4 6 1500 1 3 6 10 17 2000 2 5 12 23 49 2500 3 9 22 48 101 The mathematics of this model make it appear as though it would tend to underestimate actuated phase lengths, and subsequently overestimate green time available on the coordinated, nonactuated phase. Nevertheless, more detailed analysis and testing will be conducted on Husch's green extension time model later on in this study, in order to confirm these appearances. Other aspects of Husch's overall phase time model need not be tested for the purposes of this study. The queue service time model is no different than that of the NCHRP, except that Husch's model does not incorporate the queue calibration factor and has fewer variables to describe the arrival rate in detail. The technique of performing calculations on five different Poisson percentile arrival rates seems only appropriate for external links, or at isolated intersections. The assumption of a Poisson distribution would invalidate the results on internal actuated links with a nearby upstream signal, where vehicle arrivals are clearly nonrandom. EVIPAS Program Similar to TRANSYT7F, the EVIPAS program was developed for the purpose of traffic signal timing optimization. The primary differences between the two programs are as follows. The primary feature of EVIPAS is that it was originally designed to optimize trafficactuated signal settings such as the maximum green and the gap setting. The primary limitation of EVIPAS is that it is only capable of analyzing isolated intersections. The following description of the program appears in a paper titled "Design and Optimization Strategies for TrafficActuated Signal Timing Parameters" [Hale, 1995]: EVIPAS (Enhanced Value Iteration Program for Actuated Signals) is a program that has the ability to explicitly simulate trafficactuated control. Its unique characteristic is the ability to optimize pretimed or trafficactuated signal settings by performing large quantities of iterative simulation runs. EVIPAS performs eventbased simulations (the events being green extensions or green terminations) of an isolated intersection [Halati, 1992]. Since the simulations are eventbased, they would tend to have much faster run times than individual CORSIM microscopic simulation runs for identical conditions. However, EVIPAS is only capable of modeling a single, isolated intersection. CORSIM and TRANSYT7F have the ability to model arterials or networks with multiple intersections. EVIPAS performs the iterative simulation runs while attempting to minimize internally calculated vehicle delay. Univariate and gradient search techniques are used to find the optimal signal settings for an intersection with numerous input field characteristics. The user can request to optimize any of the available traffic actuated signal settings for a given controller. The user can also request to hold constant any of the signal settings in any phase and to optimize the others. The reduced run time for a single simulation run allows the optimization routine to perform hundreds or thousands of iterative simulation runs in a reasonable amount of time. The EVIPAS program is unique to this study in the sense that it belongs within all three major categories of actuated control models in the literature (phase time estimation, delay estimation, and control parameter design/optimization). In the context of this literature review section on phase time estimation, EVIPAS appears to be an attractive candidate model for inclusion into, or evaluation of, TRANSYT7F. It not only reports average phase times as outputs, but it has the ability to explicitly simulate actuated control with reasonable computer execution time. However, the current structure of EVIPAS, which assumes isolated operations, does not allow a background cycle length to be applied during the analysis. This existing limitation makes the program less useful in the context of evaluating or enhancing TRANSYT7F network analysis of actuated control. Hopefully future versions of EVIPAS will have the added capability of optimizing trafficactuated signal settings when a background cycle length is in effect. CORSIM Program The CORSIM program explicitly simulates trafficactuated control. The same logic employed by actuated controller hardware in the field has been embedded within CORSIM. Therefore, CORSIM can be used as a tool in evaluating the candidate models for improvement of TRANSYT7F performance. Unlike TRANSYT7F, CORSIM (once known as TRAFNETSIM or NETSIM) was not developed for the purpose of signal timing optimization. It was meant to be an evaluation tool that could simulate a wide variety of traffic conditions. Like TRANSYT7F, the NETSIM component of CORSIM is a relatively old program that has earned a certain degree of recognition and acceptance within the transportation profession. The FRESIM component of CORSIM, used for simulating freeway links, is relatively newer. Since CORSIM was meant to be an evaluation tool, a fair amount of research has been done involving comparisons between its results and observed field data. One example of such comparisons involving fieldmeasured traffic actuated phase times is illustrated in figure 213 [Courage et al., 1996]. The realism of simulated trafficactuated phase times is important in the context of this study. 60 I 2= 0.96 (256 ob~srvolons) D / = 50 i ir Through Phases I Q 0  L 7 bi. Lefi Llurn Phases 10 C o 7,00 AM :O0 PMu 0 10 20 30 40 50 60 Phose Time from Feld Dolo (sec) Figure 213: TrafficActuated Phase Times CORSIM vs. Field Measured The following description of the program appears in the CORSIM User's Manual [ITT Systems & Sciences, 1998]: CORSIM applies intervalbased simulation to describe traffic operations. Each vehicle is a distinct object that is moved every second. Each variable control device (such as traffic signals) and each event are updated every second. In addition, each vehicle is identified by category (auto, carpool, truck, or bus) and by type. Up to 9 different types of vehicles (with different operating and performance characteristics) can be specified, thus defining the four categories of the vehicle fleet. Furthermore, a "driver behavioral characteristic" (passive or aggressive) is assigned to each vehicle. Its kinematic properties (speed and acceleration) as well as its status (queued or moving) are determined. Turn movements are assigned stochastically, asare freeflow speeds, queue discharge headways, and other behavioral attributes. As a result, each vehicle's behavior can be simulated in a manner reflecting realworld processes. Each time a vehicle is moved, its position (both lateral and longitudinal) on the link and its relationship to other vehicles nearby are recalculated, as are its speed, acceleration, and status. Actuated signal control and interaction between cars and buses are explicitly modeled. Vehicles are moved according to carfollowing logic, response to traffic control devices, and response to other demands. For example, buses must service passengers at bus stops (stations); therefore, their movements differ from those of private vehicles. Congestion can result in queues that extend throughout the length of a link and block the upstream intersection, thus impeding traffic flow. In addition, pedestrian traffic can delay turning vehicles at intersections. The above description of CORSIM highlights some of the fundamental differences between it and TRANSYT7F. Unlike TRANSYT7F, which is mesoscopic, CORSIM is a microscopic model in which "each vehicle is a distinct object" [ITT Systems & Sciences, 1998]. Moreover, CORSIM is a stochastic model: "Turn movements are assigned stochastically, as are freeflow speeds, queue discharge headways, and other behavioral attributes" [ITT Systems & Sciences, 1998]. The detailed nature of CORSIM also leads to significant input data requirements and relatively long execution times on the computer. Since it recognizes actuated control parameters as inputs and produces phase times as outputs, CORSIM does meet the minimum requirements as a model that may improve TRANSYT7F performance. The execution time of CORSIM prevents simultaneous processing with TRANSYT7F. As realistic as CORSIM is, it should at least be used as a key evaluation tool in this study. It can be used to evaluate the candidate models for improvement of TRANSYT7F performance. The model testing experiments in chapter 4 demonstrate that variation of relevant input parameters within CORSIM tends to cause the appropriate changes in the actuated phase times. Variation of the same input parameters within TRANSYT7F does not cause the appropriate changes in the actuated phase times, under the existing model. When the same input conditions are specified within TRANSYT7F, comparisons between the two programs become possible. Figure 11 from Chapter 1 illustrates mediocre correlation of actuated phase times calculated by CORSIM and the existing model within TRANSYT7F. Similar experiments later on in this study should indicate that better correlation is possible by implementing upgraded submodels for actuated control within TRANSYT7F. The appendix describes techniques for calibrating TRANSYT7F and CORSIM to achieve better general agreement between the two programs; however, calibration efforts are not capable of significantly improving actuated phase time estimates from the oversimplified TRANSYT7F existing model. Phase Time Estimation Summary To this point, the literature review has focused on models with the ability to estimate average phase times under trafficactuated control. In the context of this study, these models are important to consider while attempting to develop an improved treatment of actuated control within TRANSYT7F. The next two sections of literature review focus on the other classes of actuated control models, namely vehicle delay estimation and control parameter design and optimization. These two sections are useful for gaining perspective on the overall study; however, the upcoming models will not be immediately applicable for developing an improved model as described in the upcoming chapters. Vehicle Delay Estimation In the literature, models that calculate vehicle delay on an actuated phase have the tendency to predict better performance for that phase, compared to a nonactuated or pre timed phase of equal duration. This is understandable because an actuated phase has a lower probability of temporary oversaturation, due to its ability to respond to variations in traffic flow. These models in the literature that calculate vehicle delay on actuated phases will not, in the context of this study, be candidates for improvement of TRANSYT7F performance. However, in order to better understand the candidate models for estimating phase times, it may be useful to understand how these delay calculators work. In fact, TRANSYT7F currently implements one of these models for calculating vehicle delay on actuated phases. It currently implements the 1997 HCM delay equation [Transportation Research Board, 1997]. HCM Actuated Delay Model The Highway Capacity Manual (HCM) was written for the purpose of evaluating the performance of various highway facilities. Similar to CORSIM, it was originally designed to be an evaluation tool, having no algorithms directly associated with design or optimization. Unlike the computer programs mentioned in this chapter, the HCM has no capability for simulating the flow of traffic within a simulated intersection or network. Rather, it uses various tables and equations to estimate the capacity of a given facility; although in some cases simulation programs may have been used to assist in developing certain tables and equations. It also reports the associated "level of service" along with other measures of effectiveness for the given facility, based on user inputs and intermediate computations. Table 27 [Transportation Research Board, 1997] is an example of one of these tables. The HCM has been revised and published several times over the past few decades. At the time of this writing, the next update (HCM 2000) is scheduled to be published in October of the year 2000. The manual is a true benchmark within the transportation profession, and has earned a high degree of recognition Although the HCM is a manual or document, there are numerous software packages that incorporate portions of its procedures, including TRANSYT7F. Delay equations are implemented within multiple HCM procedures, including the one for signalized intersections. Table 27: HCM Level of Service Criteria for Signalized Intersections Level of Service Control Delay / Vehicle (sec) A 0 10 B 10 20 C 20 35 D 35 55 E 55 80 F 80 + The current (1997) delay model for signalized intersections begins with a large equation, having three "terms". These three terms contain numerous individual variables that are affected by many other tables, equations, and submodels within the procedure. The first term of the delay equation is used to calculate uniform delay. Generally speaking, uniform delay can be calculated by measuring the area inside the queue accumulation polygon (QAP) illustrated earlier in figure 212. Conceptually, this is the vehicle delay that would occur if traffic flow were not stochastic, that is; identical queues and green times on each cycle, identical performance by each driver and vehicle, etc. Therefore, the first term of the delay equation is not responsive to actuated control, which is a stochastic process. Uniform delay is typically unchanged when changing between actuated and nonactuated phase definitions, provided other inputs are held constant. The third term of the delay equation is used to calculate residual delay. This only becomes applicable when queues of unserved (by the previous green phase) vehicles are present at the beginning of the analysis. When conditions are temporarily oversaturated, actuated phases are typically driven to their maximum green time on each cycle, and thus behave like nonactuated phases. Therefore, the third term of the delay equation is not responsive to actuated control. Residual delay is typically unchanged when changing between actuated and nonactuated phase definitions, provided that all other input conditions are held constant. The second term of the delay equation is used to calculate incremental delay. The HCM states that incremental delay occurs "due to nonuniform arrivals and temporary cycle failures (random delay) as well as that caused by sustained periods of oversaturation oversaturationn delay)." Because trafficactuated control is effective at reducing the probability of temporary cycle failures, the second term of the delay equation is indeed responsive to this. Incremental delay typically decreases when changing between actuated and nonactuated phase definitions, provided that all other input conditions are held constant. This delay term is listed as equation (210). 8klX (210) d2 = 900T (X1)+ )2 kI cT where T = duration of analysis period, hours; k = incremental delay factors that is dependent on controller settings; I = upstream filtering/metering adjustment factor; c = lane group capacity, vph; X = lane group v/c ratio, or degree of saturation. TRANSYT7F currently implements the 1997 HCM delay equation. However, performance of the traffic flow simulation model has an impact on the estimated delay, because the values of several variables within the equation are computed based on the simulation results. The values of the other variables are obtained directly from user input. The end result is that TRANSYT7F usually computes the same vehicle delay as other programs implementing the HCM procedures. Differences in estimated delay will sometimes be introduced due to the differences within other submodels. For example, TRANSYT7F by default applies an Australian model to compute permitted leftturn capacities, whereas the HCM signalized intersection procedures contain their own unique permitted leftturn movement model. All in all, TRANSYT7F is considered uptodate in the way that it calculates vehicle delay, thanks to the HCM delay equation. It so happens that one of the variables that has a huge impact on the results of the delay equation is the average phase time. This underscores the importance of upgrading the actuated phase time calculation methodology that is currently implemented by TRANSYT7F. Improvements to the accuracy of phase time calculation will automatically improve the accuracy of vehicle delay calculation, without even changing the way vehicle delay is calculated. VolumeWeighted Average In order to calculate vehicle delay at actuated signals, Husch [1996] recommends implementing the delay equation five times in a row based on five hypothetical traffic volumes, and then using a volumeweighted average to calculate the overall average delay. The hypothetical traffic volumes are estimated by assuming random Poisson arrivals that are often observed on the minor street, and then calculating the expected 10th, 30th, 50th, 70th, and 90th percentile volumes. This allows for some actuated control related adjustments, depending on whether some of these volume levels would clearly cause the phase length to violate the minimum or maximum phase times. The equation for calculating the volumeweighted average is listed below: D DIO*VIO+D30*V30+D50*V50+D70*V70+D90*V90 (211) V10 +V30+V50+V70+V90 CORSIM and EVIPAS Programs CORSIM computes and reports three types of vehicle delay. Instead of using an equation to estimate delay, it is computed directly from simulation. Total delay is determined by CORSIM as the difference between actual travel time and the travel time if constantly moving at the free flow speed. Queue delay is accumulated for each second when a vehicle has an acceleration of less than 2 feet per second squared, and a speed of less than 3 feet per second. Queue delay is accumulated every other second when a vehicle has an acceleration of less than 2 feet per second squared, and a speed between 3 feet per second and 9 feet per second. Stop delay is accumulated for each second when a vehicle has a speed of less than or equal to 3 feet per second. Like CORSIM, EVIPAS computes delay directly from simulation. Exact measurement criteria similar to those listed above for CORSIM are unknown for EVIPAS. EVIPAS is therefore mentioned here so that all known models for calculating trafficactuated vehicle delay are listed in this chapter, and to document the fact that EVIPAS is not known to use a separate analytical model for calculating delay, as does TRANSYT7F. Vehicle Delay Estimation Summary This section of literature review has focused on models with the ability to estimate vehicle delay under trafficactuated control. Improved vehicle delay estimation is not the direct objective of this study. It is important to note that an improved methodology for calculation of actuated phase times should automatically result in better estimates of delay and other measures of effectiveness. The upcoming final section of literature review focuses on actuated control models for control parameter design and optimization. Again, this section is useful for gaining perspective on the overall study; however, the upcoming models will not be immediately applicable for developing an improved model as described in the upcoming chapters. Control Parameter Design and Optimization As mentioned earlier in this chapter, the requirements of an improved model include the ability to estimate average actuated phase lengths as outputs. Actuated phase lengths cannot be directly designed or optimized. They must instead be calculated as a function of numerous other parameters, some of which are indeed subject to design and optimization. The models presented in this subsection were instead developed to design actuated control parameter values as outputs. The possibility exists that TRANSYT7F could someday assist in directly designing actuated signal timing parameters. However, that is not the purpose of this study. These models presented in this subsection may provide a frame of reference. Although the overall objective of this study is to provide an improved methodology for calculation of actuated phase times, this methodology may result in a new facility for designing actuated control parameters within TRANSYT7F. Minimum Green Design Some trafficactuated signal settings, including the minimum green, cannot technically be optimized. The minimum green time should be set to a value that accommodates pedestrian traffic and driver expectations. Regardless of controller type, the value of the minimum green is generally at least 5 seconds for leftturn phases and 10 seconds for through phases, just to satisfy driver expectancy. The minimum green is increased and designed as a function of walking speed if pedestrians would require the extra time for crossing the intersection. These practices illustrate that design of the minimum green setting is governed by safety considerations. Gap Setting Design Engineering judgment is necessary in designing the gap setting (a.k.a. "unit extension"). If the driver of a queued vehicle is not paying attention when the queue begins moving, the detector may sense a gap and terminate the phase prematurely. A lowvalue gap setting can lead to premature phase terminations and excessive delays on an actuated phase unless the drivers are very attentive. On the other hand, a highvalue gap setting can lead to wasted green time on the actuated phase, leading to excessive delays on the other phases. Gap settings can thus be improper if they are too low, or too high. Several methods for design of the gap setting exist in the literature. Most methods are jurisdictionspecific recommendations of a certain value or a narrow range within x and y seconds. One method [Courage and Luh, 1989] recommends gap settings based on a statistical analysis that contains approximations. It assumes that a phase should be terminated when it may be concluded with 95 percent confidence that the current flow rate has dropped below 80 percent of the saturation flow rate. EVIPAS was designed to optimize the gap setting, but this feature may be inappropriate from a practical standpoint, since the program contains no methodologies for modeling inattentive drivers. Computer programs such as CORSIM, EVIPAS, and TRANSYT7F typically do not model inattentive drivers or premature phase termination. The engineer should thus select a gap setting with the prospect of premature phase termination in mind, and then define that value in the programs, realizing that the models will not simulate inattentive drivers. Maximum Green Design and Optimization Numerous design and optimization methods for maximum green exist in the literature. They include a mixture of charts, programs, graphs, tables, and guidelines. Each one is a function of a different set of field variables. The method for design of the maximum green setting described in the Methodology for Optimizing Signal Timing (MOST) manual [Courage and Wallace, 1991] can be applied through the SOAP program. The equations used by SOAP to calculate its maximum phase times involve computation of a trafficactuated cycle length based on a userspecified target volumetocapacity (v/c) ratio, and calculation of the phase times to be proportional to the critical flow ratios for each phase. This method is similar to the existing model for trafficactuated control within TRANSYT7F. The method developed by Lin [1985] normally performs calculation of the maximum green setting as a function of the peak hour factor and the optimal pretimed green setting. However, this method also incorporates compensation for the extra time that is required for exclusive rightturn lanes. The formulas recommended by Skabardonis [1988] and modified by Fambro et al. [1992] are sensitive to the volumeto capacity ratio, and recognize the impact of oversaturation on the design of the maximum green setting. Apart from their individual reference sources, the equations associated with these techniques for maximum green and gap setting design are compiled in a paper titled "Design and Optimization Strategies for TrafficActuated Signal Timing Parameters" [Hale, 1995]. Detector Configuration Design Appropriate detector configuration design is a function of numerous characteristics. Presence detectors are typically installed near the stop line in order to detect the first vehicle in queue (see figure 214). Detector length specification is another engineering judgment call. Detector lengths that are too short increase the risk of vehicles going undetected, and increase the risk of premature phase termination. Detectors that are too long become expensive to purchase, install, and maintain. Also, if premature phase termination does not occur, longer detectors may increase vehicle delay. Multiple detectors within the same lane can affect traffic performance. Evidence [Cribbins, 1975] [Lin, 1985] supports the intuitive notion that presence detectors that are too long lead to wasted green time and increased delay. In Florida, presence detectors are typically 30 feet long. Orcutt [1993] recommends 40foot presence detectors, but adds that 60 foot detectors are preferable when approach speeds exceed 35 mph. Passage or pulse detectors are recommended if all traffic to be detected will flow freely between the detector and the intersection. Because they are much smaller than presence detectors, they are generally less expensive to install and maintain. Detector length is not the primary design consideration as with presence detectors. Instead, detector setback is. As illustrated in figure 214, setback is the distance between the stop line and the detector. Figure 214: Sample Detector Layout or Configuration Several sources [Kell and Fullerton, 1991] [Lin, 1985] [Tarnoff and Parsonson, 1981] recommend that setback should be designed based on safe stopping distance, which is a function of approach speed. The main purpose is to avoid the dilemma zone in which a vehicle can neither pass through the intersection nor stop before the stop line [Lin, 1994]. Bonneson and McCoy [1993] propose the alternative strategy of carrying the last clearing vehicle only through the indecision zone (rather than into the intersection) upon gapout. Other sources [Bonneson and McCoy, 1993] [Fambro et al., 1992] describe the added benefit of using multiple advance loops in the detector design. Detector Length (Presence) < ~>""""""""" Detector Scbhack (Passainc or Pulse) ~s~ar~laaa~a~ao~aaooaooolraoaao~ Coordination Setting Design Certain trafficactuated signals settings, such as the yield point, forceoff, and permissive period settings, are applicable only in coordinated, actuated systems. However, some models recommend optimal values using the terminology of splits and offsets. The EVIPAS simulationbased optimization model, as well as other analytical design techniques, can recommend maximum green and gap setting values, but not coordination settings. As such, an additional analysis phase is sometimes recommended in the literature in order to obtain these settings. Skabardonis [1988], Courage [1989], Khatib and Coffelt [1999] have written guidelines and developed software packages associated with selection of coordination settings for actuated systems. The CORSIM Users Guide [ITT Systems and Sciences Inc., 1998] also contains guidelines for selection of coordination settings, though explained in the context of the CORSIM program. Control Parameter Design and Optimization Summary The control parameter design and optimization models in this subsection were presented primarily for informational purposes. In the context of this study, it is helpful to know that these models will not be immediate candidates for improvement of TRANSYT7F performance, even though they exist in the literature as models for actuated control. Some of the concepts involving the individual trafficactuated signal timing parameters were also discussed, which may be helpful as a review for the reader. Also, if it is ever decided that TRANSYT7F could be enhanced in order to design or recommend trafficactuated control parameter values, the models mentioned in this subsection may prove useful. Chapter Two Summary Many of the realistic components within these models for trafficactuated control are not taken into consideration within the current methodology of TRANSYT7F. However, not all of the available models in the literature for actuated control are able to meet the minimum requirements for improvement of TRANSYT7F performance. The following models do not meet the minimum requirements: Existing Model within TRANSYT7F CORSIM EVIPAS Husch's Queue Service Time and Percentile Models Vehicle Delay Estimation Models Control Parameter Design and Optimization Models The existing model within TRANSYT7F is not ideal because it is oversimplified, which compromises the accuracy of actuated phase times. CORSIM and EVIPAS provide good treatment of actuated control, but from a practical standpoint, they are not good candidates for implementation in conjunction with TRANSYT7F. Husch's queue service time model is essentially identical to the NCHRP queue service time model, and the percentile computation of actuated phase times is not ideal for internal links where random arrivals cannot be assumed. Finally, all vehicle delay estimation models, and all control parameter design and optimization models, do not meet the minimum requirement for this study associated with improved accuracy in calculating actuated phase times. The following models do meet the minimum requirements for improvement of TRANSYT7F performance: NCHRP Model Iterative Target Degree of Saturation Model Joint Poisson Probability Green Extension Time Model These models were examined and tested further, and these results are documented in the upcoming chapters. CHAPTER 3 MODEL DEVELOPMENT This chapter describes the development of new models during the course of this study. An experimental version of TRANSYT7F was developed in order to implement the new models, which address some of the existing deficiencies in estimating actuated phase times. Specific shortcomings of the target degree of saturation strategy, employed by multiple models from the literature, were discussed at length in chapter 2. Therefore, an ideal model for improvement of TRANSYT7F performance should not adopt this strategy. The queue service time green extension time strategy, employed by multiple models from the literature, seems to be the most viable strategy. Thanks to the queue accumulation polygon (QAP) concept, which is welldocumented within the Highway Capacity Manual and other sources, queue service time is readily and accurately calculated. Indeed, an actuated phase is not capable of gapping out in the midst of the queue service time, so this structure prevents modeling blunders. In addition, if the queue service time exceeds the maximum green time, maxout is the obvious result. Finally, taking queue service time out of the mix allows for more accurate estimation of green extension time. Therefore, the queue service time green extension time strategy will be pursued at this time. Queue Service Time In the literature, queue service time is computed by equations that are algebraic interpretations of the queue accumulation polygon. As mentioned in chapter 2, the QAP concept is flexible enough to adapt to complexities from the field that would alter vehicle arrival or departure rates. Here again is the queue service time equation (21) from the NCHRP model, initially introduced in chapter 2: qrr g (sq,) (21) where, qr, qg = red arrival rate (veh/s) and green arrival rate, veh/s, respectively, r = effective red time, s, s = saturation flow rate, veh/s, and fq = queue calibration factor f, = 1.080. tual green (22) Maximum green) Permitted LeftTurn Effects One advantage of the queue service time approach involves the modeling of permitted leftturns. Typically permittedonly leftturn phases, in which only a green ball is displayed by the signal in the field, are not actuated because the length of the phase is designed to handle through movement traffic. However, protectedpermitted leftturn phases, in which a green arrow followed by a solid green is displayed in the field, are frequently actuated. It is more complicated to estimate actuated phase times for the protected portion of a protectedpermitted phase. The results are dependent on how much traffic is served during the permitted portion of the phase. If the opposing movement has heavy traffic and few leftturns are served during the permitted portion of the phase, then the actuated phase time may be nearly equal to what it would be under protectedonly phasing. If the opposing movement has light traffic and many leftturns are served during the permitted portion, then the actuated phase time may be nearly equal to the minimum phase time, because the queues are so small during the protected portion. The queue accumulation polygon (QAP) illustrated in figure 31 shows that the queue length accumulated during the permitted portion directly affects the subsequent queue service time. Figure 31: Queue Accumulation Polygon (QAP) for ProtectedPermitted Phasing Gs? Protected Portion Permitted Portion The queue service time models are appropriately sensitive to how many vehicles were served during the permitted portion of the phase. Multiple QAPs from the HCM guidelines illustrate how the queue at the beginning of the protected portion of the phase can be adjusted to reflect the number of vehicles served during the permitted portion of the phase. Whereas deficiencies of the existing literature models were initially introduced in chapter 2, additional technical details regarding these deficiencies are supplied within chapters 3 and 4. For example, chapter 2 states that permitted leftturn effects (on actuated phase times) are one category of operational characteristic effects that are difficult to quantify without using simulation. The existing model within TRANSYT7F for calculating actuated phase times is inadequate because it does not attempt to estimate protected portion actuated phase times for protectedpermitted phases. Instead such phases are currently set to their minimum phase times automatically, as if all traffic was served during the permitted portion of the phase. No known methodology is available for automatically adjusting the (protected portion) actuated phase target degree saturation in response to how much traffic was served during the permitted portion of the phase. In order to rectify this model in its existing form, it would be necessary to readjust target degrees of saturation, based on the amount of traffic served during the permitted portion of the phase. Because phase times must be known prior to simulation, and because the amount of traffic served in the permitted portion is determined during simulation, an iterative target degree of saturation structure is required, similar to Akcelik's model from chapter 2. If permitted leftturn effects were the only complexity affecting the actuated phase model, then the target degree of saturation strategy could possibly be updated as described by Akcelik. Perhaps there would be no obvious disadvantages relative to the queue service time green extension time models; however, there are other complexities that further hinder this strategy, such as progression and spillback. Progression and Spillback Effects Unfortunately, the equations that interpret the QAP to compute queue service time are not flexible enough. They are oversimplified, and unable to interpret complex QAPs that are likely to occur due to networkwide interaction effects. The NCHRP queue service time equation implements two separate arrival rates, and one unique departure rate. The arrival rates are divided into two quantities: arrivals on red, and arrivals on green. The departure rate is the saturation flow rate. However, when analyzing a single system having multiple intersections, arrival rates and departure rates are unpredictable enough such that three variables are not adequate for calculating the correct results. For example, consider having only one variable to describe arrivals on green. This means that only one arrival rate on green can be modeled. However, nonuniform arrival rates on green will occur when a nearby upstream signal is present. Even if the average arrival rate on green is specified correctly, progression effects (nonuniform arrivals) can change the queue service time. Figure 32 illustrates an example of progression effects on queue service time. The slope of the queue accumulation polygon's right side is affected by a constantly changing arrival rate. Although 200 vehicles per hour are expected during the green phase, good progression from the upstream signal causes vehicles to arrive after the queue has been serviced. In this case, progression effects allow the average queue service time to decrease from 12.6 seconds to 10.6 seconds. However, the formula would still predict a queue service time of 12.6 seconds in this case. One variable is not enough to account for progression effects. Ideally, the arrival rate during each second should be known in order to calculate the correct queue service time. Figure 32: QAP Depiction of Good Progression Decreasing the Queue Service Time The formula is additionally constrained to having only one variable to describe departure rates. This means that only one departure rate can be modeled for each movement. However, nonuniform departure rates will sometimes occur when a nearby downstream signal is present. Even if the average departure rate is specified correctly, spillback effects (nonuniform departure rates) can change the queue service time. Queue Service Time C > Red Figure 33 illustrates an example of spillback effects on queue service time. The slope of the queue accumulation polygon's right side is affected by a constantly changing departure rate. Although 3515 vehicle departures per hour are expected when serving queues, spillback from the downstream signal decreases the departure rate and increases the queue service time. In this case, spillback effects allow the average queue service time to increase from 15.6 seconds to 24.4 seconds. However, the formula would still predict a queue service time of 15.6 seconds in this case. One variable is not enough to account for spillback effects. Ideally, the departure rate during each second should be known in order to calculate the correct queue service time. Figure 33: QAP Depiction of Spillback Increasing the Queue Service Time Queue Service Times from the Program Fortunately, TRANSYT7F continuously tabulates uniform or nonuniform arrival rates, departure rates, and queue lengths during each step of analysis and Queue Service Time Time (seconds) throughout the network. On external links with no nearby upstream signal, queue service times computed by TRANSYT7F and the NCHRP formula are identical, barring any differences introduced by permitted leftturn movement models. However, TRANSYT 7F has the added capability to adjust queue service times in response to traffic flow from upstream signals, and spillback from downstream signals. Queue service time should therefore be extracted directly from the results of TRANSYT7F stepwise simulation. This will allow queue service times and actuated phase times to be automatically responsive to progression and spillback effects, in addition to permitted leftturn effects. Green Extension Time A perceived deficiency of existing models in the literature for computing green extension time is the assumption of random vehicle arrivals. It is true that the assumption of random arrivals is reasonable on external links having no upstream signal nearby. However, many practitioners continue to conduct analyses with the assumption of uniform arrivals on external links. More importantly, an ideal green extension time model would not assume any specific pattern of vehicle arrivals, especially since platooned arrivals are expected on internal links having a nearby upstream signal. Rather, an ideal model would intelligently compute green extension times as a function of any possible pattern of vehicle arrivals. Here again is the green extension time equation (23) from the NCHRP model, initially introduced in chapter 2: e A(eo+trA) 1 g5e (23) (pq A' where eo = unit extension time setting to = time during which the detector is occupied by a passing vehicle to = (Ld + L) (24) v where Lv = vehicle length, assumed to be 5.5 m Ld = detector length, DL, m, v = vehicle approach speed, SP km/h A = minimum arrival (intrabunch) headway, s, = proportion of free (unbunched) vehicles, and = a parameter calculated as: 1= q (25) 1 Aq where q is the total arrival flow, veh/s for all lane groups that actuate the phase under consideration. This equation noticeably implements one unique arrival rate (q). This means that only one arrival rate on green can be modeled; however, when analyzing a single system having multiple intersections, arrival rates are unpredictable enough such that one variable is not adequate for calculating the correct results. Nonuniform and nonrandom arrival rates on green will occur when a nearby upstream signal is present. Even if the average arrival rate on green is specified correctly, progression effects (nonuniform, nonrandom arrival rates) can change the green extension time. Figure 34 illustrates an example of progression effects on green extension time. The histogram represents a constantly changing arrival rate. Although 200 vehicles per hour are expected during the green phase, good progression from the upstream signal causes vehicles to arrive after the queue has been serviced. In this case, progression effects cause the average green extension time to increase from approximately 3 seconds to more than 5 seconds. However, the formula would still predict the same green extension time in both cases by assuming the average arrival rate of 200 vehicles per hour (illustrated by the superimposed dashed line). One variable is not enough to account for progression effects. Ideally, the arrival rate during each second should be known in order to calculate the correct green extension time. Figure 34: Example of Good Progression Increasing the Green Extension Time Prototype Green Extension Time Model Using Applied Probability and Flow Profile As mentioned earlier in this chapter, the TRANSYT7F program continuously tabulates the arrival rate, departure rate, and queue length during each step of simulation and throughout the network. Knowledge of the networkwide arrival rate, or flow profile, should be useful in computing green extension time. However, the flow profile does not 0 Green Extension Time C Queue Service Time  200 ...... .. .. ... .. ..... . .. .. . .. .. . .. .... ...* .. ... .. .. .. .... ... ... .....Cj 2 0 0       _.. .... ... Time (seconds) automatically reveal the correct green extension time, in the way that queue profiles reveal the correct queue service time. The only way to explicitly compute green extension time is through microscopic simulation employed by programs like CORSIM. These programs simulate individual vehicles rolling over detectors and thus are able to know exactly when gapout occurs. The TRANSYT7F flow profile information allows the opportunity to calculate the maximum likelihood green extension time, which should be a better estimate than is possible using any model that assumes uniform or random arrivals. A new model was developed to compute the most probable location of gapout and thus the overall green extension time, based on the TRANSYT7F flow profile. Methodology and sample calculation #1 A sample calculation illustrates the methodology of this prototype model. Figure 35 illustrates an actual simulated flow profile for an actuated leftturn phase having a nearby upstream signal. Although the average flow rate is 200 vehicles per hour, arrival rates much higher than this are occurring during a certain part of the 100second cycle, due to progression effects. Note that flow intensity would be affected by multiple links in the case of a shared lane. Although figure 35 does not show this, the leftturn phase begins at step 92 towards the righthand side of the histogram in this example. The force off time for this phase occurs at step 29 towards the lefthand side of the histogram. In order to estimate the green extension time, it is only necessary to scrutinize the flow profile after the queue service time and until the forceoff time. Figure 36 illustrates this abbreviated flow profile that can be used for green extension time calculations. Looking at this flow profile, the flow rate occurring immediately after queue discharge is clearly higher than the 200 vph average. In fact, the average flow rate 1000. Time (seconds) Figure 35: Sample Calculation Internal Link Flow Profile 900 800 700 600 4. 300 .. 200 100 0 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Time Step (seconds) Figure 36: Sample Calculation Internal Link Flow Profile (Abbreviated) poll. I logo. ....... ..... . . . . up I ft I U1.0111 1 I II in this range is 380 vph. Therefore, a higherthanaverage green extension time is expected. The first step of the prototype model involves calculating the probability of zero vehicle arrivals during each second within the abbreviated flow profile. The Poisson distribution is used to calculate the probability of zero arrivals during each second. However, instead of using the average hourly traffic volume in the calculations, each individual flow rate at each individual simulation step is used to calculate numerous individual probabilities. For example, the probability of zero arrivals at step 3 immediately following queue discharge, is: P(0)= e727/3600 0.82 The second step of applying the prototype model involves calculating the probability of consecutive simulation steps having zero vehicle arrivals within the abbreviated flow profile. It is known that if zero arrivals take place on enough consecutive steps, the phase will terminate via gapout. Assuming a gap setting of 3 seconds, phase termination will occur if three consecutive steps have zero arrivals. For example, the probability of three consecutive steps with zero arrivals at step 5 immediately following queue discharge, is: P(0,0,0)= 0.82 x 0.81 x 0.82 ; 0.54 The third step of applying the prototype model involves calculating the probability of gapout within the abbreviated flow profile. At step 5, the probability of gapout is actually equal to the probability of consecutive zero arrivals at steps 3, 4, and 5. However, at step 8, the probability of gapout is not exactly equal to the probability of consecutive zero arrivals at steps 6, 7, and 8. It is known that there is only a 1 0.54 = 0.46 probability of not gapping out at step 5. Therefore, the probability of gapout at step 8 is: P(gap out)= 0.46 x (0.84x 0.86 x 0.87)q 0.29 The fourth step of applying the prototype model involves calculating the probability of maxout within the abbreviated flow profile. The probability of maxout is actually equal to one minus the summation of all gapout probabilities: P(max out) = 1 P(gap out) The fifth step of applying the prototype model involves calculating time step weighted averages. In this sample calculation, there was a 0.54 probability of phase termination at step 5. Therefore, the time step weighted average here is: T(step 5)= 0.54 x 5 ; 2.7 The sixth step of applying the prototype model involves calculating the average phase time by summing the time step weighted averages: PhaseTime = I T(step) Table 31 lists the entire set of values in the sample calculation. After summing the time step weighted averages, the final answer is time step 7.1 as the location of phase termination. Because the queue service time ended at step 2, the green extension time is 5.1 seconds. The Poisson distribution is not the only method available to calculate P(0). For 200 vph (an arrival every 18 seconds on average), the uniform P(0) would be 1/18, or 0.055. However, this method would only change the answer by one tenth of a second in table 31. Note that the probability of immediate gapout was 54%. Oddly, Husch's green extension time model specifies immediate gapout due to the value above 50%, even though the 46% chance of extension results in a 2.1 second increase (ge = 5.1 vs. 3). Also note that green extension times are potentially affected by the maximum green setting. Green extension time decreases to 4.4 seconds if the maximum occurs at step 8, because all of the remaining weighted average values would be rolled into step 8. Table 31: Prototype Model Sample Calculation of Green Extension Time Time Flow Rate P(0) P(0,0,0) P(gap) P Weighted Step (vph) cumulative Average 3 727 0.82 4 765 0.81 5 702 0.82 0.54 0.540 2.700 6 623 0.84 7 558 0.86 8 506 0.87 0.63 0.288 0.83 2.303 9 464 0.88 10 430 0.89 11 402 0.89 0.70 0.120 0.95 1.321 12 383 0.90 13 367 0.90 14 354 0.91 0.74 0.038 0.99 0.536 15 345 0.91 16 337 0.91 17 331 0.91 0.75 0.010 1.00 0.176 18 323 0.91 19 311 0.92 20 297 0.92 0.77 0.003 1.00 0.052 21 282 0.92 22 266 0.93 23 251 0.93 0.80 0.001 1.00 0.014 24 237 0.94 25 223 0.94 26 211 0.94 0.83 0.000 1.00 0.003 27 198 0.95 28 186 0.95 29 175 0.95 0.000 0.001 7.107 Another observation is that green extension time calculations begin at an integer step number such as step 3 because TRANSYT7F tabulates the flow profile by integer step sizes. Although queue service time is actually a real number and the green extension time actually begins at time step 2.6, the approximation of beginning the green extension time calculations at step 3 should have negligible impact on the result (5.1 seconds). In other words, there are so many calculations within the flow profile, that beginning the green extension time calculations at step 2 or step 3 would probably produce the same answer (5.1 seconds). Sample calculation #2 In order to better understand the prototype model, another sample calculation can be demonstrated in which changes to progression cause changes in the green extension time. In this sample calculation, all conditions except for one are identical to those from the previous sample calculation. The one difference is the offset design, which changes the observed traffic patterns on the arterial street. Figure 37 illustrates the updated flow profile for the actuated leftturn phase having a nearby upstream signal. Comparing the figure 37 flow profile with the original flow profile from figure 3 5, the shape and intensity of the platoon is similar. However, with the new offset design, the platoon arrives 5 seconds earlier at step 84. Again, to estimate the green extension time, it is only necessary to scrutinize the flow profile after the queue service time and until the forceoff time. Figure 38 illustrates the updated abbreviated flow profile that can be used for green extension time calculations. The queue service time ends at step 12, and the forceoff time occurs at step 37. Looking at this flow profile, the flow rate occurring immediately after queue discharge is Figure 37: Sample Calculation #2 Internal Link Flow Profile 180 160 140 120 . 100 80  60  LL 40 20 0 0 L ,, s Time Step (seconds) Figure 38: Sample Calculation Internal Link Flow Profile (Abbreviated) 1200 1000  800 cu 600 0o 400 LL 200 0 O () CO r oD L) J co Cj V O C CO) q n CD e cO o) 0 clearly lower than the 200 vph average. In fact, the average flow rate in this range is 84 vph. Therefore, a lowerthanaverage green extension time is expected. Table 32 lists the entire set of values in the second sample calculation. Table 32: Prototype Model Sample Calculation #2 of Green Extension Time P(0,0,0) P(gap) Time Step 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 P cumulative 0.88 Flow Rate (vph) 156 149 142 136 131 125 119 114 108 101 101 109 103 88 74 63 53 45 38 33 28 23 20 17 14 P(0) 0.96 0.96 0.96 0.96 0.96 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.98 0.98 0.98 0.99 0.99 0.99 0.99 0.99 0.99 0.99 1.00 1.00 After summing the time step weighted averages, the final answer is time step 15.4 as the location of phase termination. Because the queue service time ended at step 12, the green extension time is 3.4 seconds. The sample calculation demonstrates that when progression becomes worse, the prototype model responds logically by calculating a 0.88 0.90 0.91 0.92 0.93 0.96 0.97 0.98 0.108 0.011 0.001 0.000 0.000 0.000 0.000 0.99 1.00 1.00 1.00 1.00 1.00 1.00 Weighted Average 13.200 1.937 0.236 0.025 0.002 0.000 0.000 0.000 0.000 15.401 lower green extension time. This means that because the traffic flow pattern is light following queue discharge, there is a lower probability of the phase being extended. By comparison, the NCHRP model would not have recognized progression effects. It would have calculated the same green extension time in both scenarios. Prototype Green Extension Time Model Based on Uniform Vehicle Arrivals Another prototype model was developed during the course of this study as an alternative to the existing models from the literature designed with random arrivals in mind. This model carries with it the basic assumption of uniform vehicle arrivals. The model is simple because when vehicle arrivals may be assumed to be perfectly uniform, there are only two green extension times that are physically possible. After computing a weighted average based on these two possible green extension times, the result is an overall estimate for the average green extension time. When perfectly uniform arrivals are in effect, the two physically possible green extension times can be described as follows. The first possibility is that no vehicle arrives during the gap setting interval immediately following queue discharge. When this occurs, the green extension time is equal to the gap setting. The second possibility is that one vehicle arrives during the gap setting interval immediately following queue discharge. When this occurs, the green extension time is equal to 1.5 times the gap setting. If a vehicle extends the phase once, no additional extensions are possible because the interarrival time between vehicles will be larger than the gap setting. Assuming that one vehicle does extend the phase, it must arrive sometime within the gap setting interval, or on average halfway through the gap interval. After that, the phase will be extended by exactly 1 additional gap time. Sample calculation A sample calculation is useful for understanding the logic here. Suppose that the traffic volume demand is 600 vehicles per hour per lane. Assuming uniform arrivals, this translates into one vehicle arrival every six seconds. Given a gap setting of two seconds, there would be a 0.33 probability of a vehicle arrival within the gap interval, and a 0.67 probability of no vehicle arrival within the gap interval. Also, if a vehicle does arrive within the gap interval, then on average it will arrive halfway through the gap interval, or after 1 second in this case. In addition, a vehicle extension after 1 second automatically extends the phase by exactly 1 gap interval, or 2 seconds in this case. Therefore, there would be a 0.33 probability that the green extension time would be equal to 1.5 2 = 3 seconds, and a 0.67 probability that the green extension time would be equal to 2 seconds. Using the weighted average, overall green extension time is estimated as: ge = (0.33 x 3)+(0.67 x 2) 2.33 seconds These green extension time calculations are only valid given traffic volumes that are sufficiently low. High traffic volumes result in low interarrival times that may be lower than the gap interval. When vehicle interarrival times are indeed lower than the gap interval, and uniform arrivals are in effect, the end result is that gapout cannot occur, physically or mathematically. In this case, the phase is assumed to terminate via maxout or forceoff. For example, a per lane volume of 1800 vehicles per hour, producing one vehicle arrival every two seconds, would always cause maxout with gap settings of two seconds or higher. Likewise, a per lane volume of 1200 vehicles per hour, producing one arrival every three seconds, would always cause maxout with gap settings of three seconds or higher. Alternative queue service time model Interestingly, this second prototype green extension time model concept suggests a new and simplified calculation for queue service times. Indeed, if vehicle arrivals are perfectly uniform in nature, and if only 01 vehicle extensions of the green are physically possible, this implies that nearly all vehicles are queued while being served. Thus, the uniform arrivals queue service time could presumably be calculated by computing the number of vehicles served per cycle, multiplying this value by the queue discharge headway, and then adding in the startup lost time. Figure 39 illustrates the phase time calculation under this scenario. Figure 39 shows that four queued vehicles should be served on each cycle, although the fourth vehicle joins the queue in the midst of queue service time. The phase time of 15 seconds assumes no vehicle extensions. However, since the uniform arrivals green extension time should actually be the weighted average of 0 and 1 extension times, the estimated phase time would probably be something like 15.75 seconds. When the uniform queue service times are combined with the uniform green extension times, results may improve due to the consistency of assumptions. However, the process of determining an average number of vehicles served per cycle, which allows computation of uniform queue service times, is fragile. Determination of average queue per cycle can become difficult, given numerous complications from the field, which is why extraction of queue service times from TRANSYT7F simulation is preferable. Consequently, the uniform arrivals prototype model is expected to produce reliable results under simple conditions, but may break down under complex conditions. In order to adapt the model to complex conditions, it would be necessary to somehow adjust the expected average queue per cycle in response to numerous factors (permitted leftturns, spillback, etc.). gs = Startup Lost Time + (#veh Headway) = 2 + (4* 2) = 10 sec. ge = 3 sec. Phase Time = gs + ge + Y + R = 10+3+2+0 = 15 sec. Uniform Arrival Rate = 1 vehicle / 7.2 sec. Figure 39: Calculating Queue Service Times with the Uniform Arrivals Assumption The uniform arrivals prototype model may provide a good reference point during the testing process, and could be relatively effective at isolated intersections, where conditions tend to be less complicated. Practical advantages include better computing speed and easy programming, since it is not necessary to obtain queue or flow profile data from the optimization program. Preliminary Model Comparison Thorough testing of all candidate models is documented in chapter 4. For the sake of understanding the two prototype models for computing green extension times, some preliminary comparison is useful. Model comparison under platooned arrivals Recall that the sample calculations for the first prototype model involved an actuated, major street leftturn phase having platooned vehicle arrivals due to a nearby upstream signal. The traffic volume was 200 vph with a gap setting of 3 seconds. The first prototype model had predicted green extension times of 5.1 and 3.4 seconds, depending on the offsets and progression on the arterial street. Under these conditions, the second prototype model would calculate a green extension time based on one vehicle arrival every 18 seconds, and a one in six chance of an arrival during the gap interval: g, = (0.17 x 11.5 x3)+(0.83 x3)= 3.25 seconds Note that this green extension time would be applicable in both sample calculations because the second prototype model does not take progression effects into account. In addition, regardless of progression effects, the NCHRP model computes a single green extension time (4.6 seconds), as does Husch's Poisson probability model (3 seconds). Depending on the duration of the queue service time, differences in predicted phase times will not necessarily be equal to the differences in green extension times. This will be illustrated by a larger set of results in chapter 4. Model comparison under uniform arrivals Another interesting comparison between the prototype green extension time models occurs on external links with no nearby upstream signal. On these links, vehicle arrivals tend to be nearly uniform in nature, or perhaps random arrivals with uniform interarrival times on average. In theory, the first prototype model should be able to calculate good results under this scenario because uniform arrivals are simply another variation on the flow profile. Certainly the second prototype model, designed with uniform arrivals in mind, would be expected to calculate relatively accurate green extension times on external links, where vehicle arrivals are known to be close to uniform in nature. Suppose the green extension time must be calculated on an external link having 500 vehicles per hour, with a gap setting of 3 seconds. Figure 310 illustrates the uniform flow profile, and table 33 lists all calculations from the first prototype model. In this case the calculated green extension time is 4.5 seconds, because queue service time ends at step 12 and gapout occurs at step 16.5. Once again, substitution of uniform probabilities in place of Poisson probabilities of zero arrivals at step would only change the final answer by one tenth of a second. Although the first prototype model calculates a green extension time of 4.5 seconds, the NCHRP model and Husch's Poisson probability model calculate 6.1 and 3 seconds respectively for the same conditions. Since the 500 vph volume generates one arrival every 7.2 seconds, a 3second gap results in a 3/7.2= 0.42 chance of phase extension, the second prototype model computes: g, = (0.42 x 1.5 x 3)+(0.58 x 3)= 3.63 seconds Figure 310: Sample Calculation External Link Flow Profile (Abbreviated) Preliminary model comparison summary The differences in results from the two prototype models, given uniform arrivals, indicate that the first prototype model may be overestimating green extension times. However, results from the NCHRP model indicate the opposite. In the absence of additional test results, the only observation to be made on the first prototype model at this time is that it responds appropriately to maximum green and progression effects. More testing results are necessary to determine the accuracy of each candidate model. Extensive testing results are presented in chapter 4. 600 500  > 400 a 300 o 200 u. 100 N_ No (se o nds Time Step (seconds) Table 33: Calculations of the First Prototype Model Under Uniform Arrivals P(0,0,0) P(gap) Time Step 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 Flow Rate (vph) 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 P Weighted cumulative Average P(0) 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.66 0.66 0.66 0.66 0.66 0.66 0.66 0.66 0.66 Model Implementation Isolated Versus Coordinated Operation Control type (isolated vs. coordinated) is expected to have a fundamental effect on actuated phase time results. The top half of figure 311 illustrates the phasing diagrams under coordinated conditions. Diagram #1 illustrates typical operation under 0.66 0.224 0.076 0.026 0.009 0.003 0.001 0.000 0.000 9.900 4.035 1.604 0.625 0.239 0.091 0.034 0.013 16.540 0.88 0.96 0.99 1.00 1.00 1.00 1.00 0.00 the conditions from the first part of experiment #1. Suppose that a certain parameter, such as detector length, free flow speed, or vehicle length, has its value increased such that green extension time would tend to respond by increasing as well (diagram #2). Although this change by itself would tend to increase the average phase time, a feedback effect exists that reduces the upcoming queue service time. This is because the effective red time for phase #1 is equal to the length of phase #2. When the length of phase #2 is reduced, this reduces the effective red time for phase #1, thus reducing the subsequent queue and queue service time for phase #1 (diagram #3). The bottom half of figure 311 illustrates the phasing diagrams under isolated conditions. Diagram #1 illustrates typical operation under the conditions from the first part of experiment #1. Suppose that a certain parameter, such as detector length, free flow speed, or vehicle length, has its value increased such that green extension time would tend to respond by increasing as well (diagram #2). This change tends to increase not only the length of phase #1, but also the effective red time imposed on actuated phase #2. This in turn increases not only the queue, queue service time, and length of phase #2, but also the effective red time imposed on actuated phase #1 (diagram #3). At first glance this appears to be an infinite loop, but as described in chapter 2, this process converges reliably to a new actuated cycle length. These results for isolated conditions are expected and documented in chapter 2 and the HCM guidelines. However, the results for coordinated conditions are interesting. They imply that certain parameters (e.g. detector length, approach speed, vehicle length, maximum green) which when increased would normally tend to increase the green extension time, perhaps do not significantly increase the phase time due to the queue COORDINATED: < Cycle Length> < Phase #1 > < Phase #2 #1 1 Ge Y+R < Phase #1 > < Phase #2 I I Gs Ge Y+R < Phase #1 > < Phase #2 I s e Y+R Gs Ge Y+R ISOLATED: < Phase #1 Phase #2 > #1 Gs Ge Y+R Gs Ge Y+R < Cycle Length < Phase #1  Phase #2  #2 I I 1 i I Gs Ge Y+R Gs Ge Y+R "< Cycle Length < Phase #1 < Phase #2  #3 I I Gs Ge Y+R Gs Ge Y+R Figure 311: Feedback Effects under Coordinated and Isolated Conditions #2 #3 I service time feedback effect. This begs the question of whether some parameters affect the phase time at all. Do the queue service time and green extension time merely redistribute themselves such that the phase time is unmovable, or do phase time shifts occur anyway? This could be important because if certain parameters do not affect phase time, this simplifies the problem considerably and allows for shortcuts to be taken in modeling. Testing results related to this concept are discussed later on in chapter 4. To summarize, fundamental differences in the actuated phase times are expected when comparing results under different signal control types (coordinated vs. isolated). These differences are likely caused by the queue service time green extension time feedback effect. In the context of TRANSYT7F and coordinated signal systems, correct understanding and modeling of coordination behavior is a higher priority. However, important analyses are performed on isolated intersections also. Proper understanding and modeling of these conditions is also useful. Early Return to Green Effects One of the first things observed when looking at preliminary results on arterial street performance was that some of the oversaturated actuated phase lengths were being underestimated by the TRANSYT7F candidate models, relative to CORSIM. Figure 3 12 illustrates the pitfall that was occurring. CORSIM was showing that unused green time from the first actuated phase #1 was being taken by oversaturated phase #2. However, allocation of unused green time was originally been performed according to the NCHRP procedure, described in chapter 2, which specifies that all unused green time will be donated to the nonactuated phase under coordinated conditions. ACT ACT ACT NAP Phase #1 Phase #2 Phase #3 Phase #4 .. . ... .. . . .. . . . Incorrect 10 30 15 50 10 35 15 40 Correct ACT = Actuated Phase NAP = NonActuated Phase Figure 312: Allocation of Unused Green Time under Coordinated Conditions Before any significant testing was performed on arterial streets, the experimental version of TRANSYT7F was redesigned such that oversaturated actuated phases would be able to take unused green time from prior actuated phases if necessary. Note that this means actuated phase #1 from figure 312 is not able to take unused green time from the other actuated phases because they occur later on in the cycle. If no oversaturated actuated phase occurs following an undersaturated actuated phase, unused green time will be utilized by the nonactuated phase. Overlap Phasing Effects The next obvious problem observed when looking at preliminary results on arterial street performance was that some of the undersaturated actuated phase lengths were being overestimated by the TRANSYT7F candidate models. This was occurring due to a consistent, incorrect determination of the "critical link" within actuated phases. What is a critical link? In experiment #1 only one link was moving during each phase. However, under complex conditions, there will be multiple links moving in each phase. When this happens, the basic strategy of an actuated controller dictates that the rightofway should be terminated after all queues have been served on all links. Therefore, the overall phase should be terminated after the longest queue has been served, or rather after the queue that takes the longest time to dissipate has been served. The link that happens to possess relatively heavy traffic, resulting in a queue that takes the longest time to dissipate, is known as the critical link. Figure 313 illustrates a hypothetical phase sequence where multiple links are moving on each phase. If the hourly traffic volume demand on each link is known, then normally the link having the highest volume during each phase would be critical and affect phase termination. For example, the link having 300 vph will affect when phase #1 terminates, the link having 500 vph will affect when phase #2 terminates, etc. It may take more than knowledge of the traffic volume in order to determine the true critical link. Suppose the 500 vph link in phase #2 actually has two lanes to use, unlike the 400 vph link that only has one lane to use. This means the queues on the 500 vph link will dissipate twice as quickly, behaving almost like two 250 vph lanes, and the 400 vph link will then have the longest queues on average and tend to affect phase termination. ACT ACT ACT NAP 300 vph 500 vph 200 vph 400 vph Phase #1 Phase #2 Phase #3 Phase #4 Figure 313: Sample Problem for Determination of Critical Link In addition to number of lanes, there are numerous field conditions that can slow down or speed up queue service time, including vertical grade, lane width, heavy vehicle percentage, percentage of turns from a shared lane, and parking or bus maneuvers, just to name a few. The effect of these field conditions is quantified by the saturation flow rate (s) parameter. The flow ratio (v/s) can be used to quantify the combined affect of volume and saturation flow rate. This becomes a better quantity to use than volume in determining the critical link because the queue service rate is taken into account Thus, in the early stages of data collection for arterial streets, flow ratio was used to determine the critical links. Unfortunately, critical link determination using this parameter can be shown to be inadequate due to the overlap phasing effects frequently observed at actuated signals, as illustrated in figure 314. ACT ACT ACT NAP 300 vph 500 vph 200 vph 400 vph Phase #1 Phase #2 Phase #3 Phase #4 Figure 314: Sample Determination of Critical Link with Overlap Phasing Effects Figure 314 shows that the 200 vph actuated leftturn phase terminates earlier than the 300 vph leftturn phase. This means that the 500 vph through movement link, which is adjacent to the 300 vph leftturn link, gets a head start and begins to move earlier (phase #2) than the opposing 400 vph through movement link. Assuming these links have the same saturation flow rate, this means that even though the 500 vph link has the highest flow ratio (v/s), its queue doesn't necessarily take longer (than the 400 vph link) to dissipate because its vehicles begin moving earlier in the cycle. If flow ratio was the only technique available for determining critical link, the noncritical link would sometimes be chosen as critical by the candidate models, resulting in underestimated phase times. Because of the overlap phasing effects, the only way to really know which link is critical and will extend the phase is to apply the candidate models to each candidate link 