Modeling and simulation of vehicle projection arrival discharge process in adaptive traffic signal controls

Transcription

1 JOURNAL OF ADVANCED TRANSPORTATION J. Adv. Transp. 2010; 44: Published online 2 July 2010 in Wiley InterScience ( Modeling and simulation of vehicle projection arrival discharge process in adaptive traffic signal controls Fang Clara Fang 1 * and Lily Elefteriadou 2y 1 Department of Civil Engineering, College of Engineering, Technology, and Architecture, University of Hartford, West Hartford, CT 06117, U.S.A. 2 Department of Civil and Coastal Engineering, University of Florida, Gainesville, FL 32611, U.S.A. SUMMARY Real-time signal control operates as a function of the vehicular arrival and discharge process to satisfy a prespecified operational performance. This process is often predicted based on loop detectors placed upstream of the signal. In our newly developed signal control for diamond interchanges, a microscopic model is proposed to estimate traffic flows at the stop-line. The model considers the traffic dynamics of vehicular detection, arrivals, and departures, by taking into account varying speeds, length of queues, and signal control. As the signal control is optimized over a rolling horizon that is divided into intervals, the vehicular detection for and projection into the corresponding horizon intervals are also modeled. The signal control algorithm is based on dynamic programming and the optimization of signal policy is performed using a certain performance measure involving delays, queue lengths, and queue storage ratios. The arrival discharge model is embedded in the optimization algorithm and both are programmed into AIMSUN, a microscopic stochastic simulation program. AIMSUN is then used to simulate the traffic flow and implement the optimal signal control by accessing internal data including detected traffic demand and vehicle speeds. Sensitivity analysis is conducted to study the effect of selecting different optimization criteria on the signal control performance. It is concluded that the queue length and queue storage ratio are the most appropriate performance measures in real-time signal control of interchanges. Copyright # 2010 John Wiley & Sons, Ltd. KEY WORDS: adaptive signal control; real-time control; vehicle projection; arrival discharge dynamics; API simulation; diamond interchanges 1. INTRODUCTION Adaptive signal control optimizes the operation of traffic signals based on current traffic flow, demand, and system capacity. The traffic flow is predicted, in either short term or long term, by surveillance. Miller [1] initiated adaptive signal control and proposed an algorithm for adjusting signal timings in small time intervals. A decision to be made is whether to extend the current green duration or terminate it immediately. The decision is repeatedly made at a very short fixed interval (of 1 2 seconds) by the examination of a delay-based control function. This function estimates the net benefits in vehicle seconds of delay between the gain to the extra vehicles that will be allowed to cross the intersection during an extension interval and the loss to the queuing vehicles on the cross-street that results from the extension. The Miller s approach may be regarded as a binary choice decision-making process [2], because it considers a decision of either extending or terminating only the current green duration. Following the Miller s original principle, a number of adaptive systems have been developed, such as TOL the Traffic Optimization Logic [3], SCOOT the Split, Cycle, and Offset Optimization Technique [4], MOVA the Modernized Optimized Vehicle Actuation Strategy [5,6], SAST Stepwise *Correspondence to: Fang Clara Fang, Associate Professor, Department of Civil Engineering, College of Engineering, Technology, and Architecture, University of Hartford, West Hartford, CT 06117, U.S.A. fang@hartford.edu y Director, Transportation Research Center; Professor, Department of Civil and Coastal Engineering. Copyright # 2010 John Wiley & Sons, Ltd.

2 MODELING AND SIMULATION OF VEHICLE PROJECTION 177 Adjustment of Signal Timing [7], and ALLONS-D a decentralized real-time traffic control scheme [8]. Abu-Lebdeh et al. [9] have also presented models to capture traffic output of intersections in congested interrupted flow conditions with explicit consideration of interactions, over space, and time, between traffic streams at successive signals. Real-time adaptive signal control of signalized intersections over a large future horizon may be formulated in dynamic programming (DP), which could be continuous-time and discrete-time. The control decision may be made in either finite or infinite period of future time. Grafton and Newell [10] developed a continuous-time DP model for signal control of an undersaturated intersection of only two competing traffic streams. The DP is defined over an infinite horizon. The traffic is treated as if it were a continuous fluid, arrival rates are assumed to be constant for all time, and the departure rates are constant during the green time for each lane. The assumption of constant arrivals guarantees that, for any initial state, the system will eventually achieve a limit cycle for which the average equilibrium delay per car is a minimum. The objective of an optimal policy is to minimize the total delay of all cars entering the system. The DP system is characterized at any time by state variables (i.e., the queue lengths and the direction of light) and at any time the controller has two choices to switch the light or not. In addition to the common major problem with DP approach (i.e., the advance information of future traffic flow), the assumption of constant arrivals is apparently not applicable as the traffic flow in future time is random and hardly predicted particular for a large look ahead. Robertson and Bretherton [11] presented a so-called DYPIC (dynamic programmed intersection control) algorithm. It finds the optimal signal control policy for any look ahead horizon and takes as objective the minimization of the total delay aggregated over all intervals of a finite horizon. As an extension of DYPIC, there have been a few systems developed: OPAC (optimization policies for adaptive control) by Gartner et al. [12,13], RHODES (real-time hierarchical optimized distributed effective system) by Sen, Head, and Mirchandani [14,15], and the adaptive signal control by authors (2006). They optimize signal policy over a finite horizon while the DP algorithms were formulated in different ways to suit different applications. In OPAC, from upstream detectors, actual arrival data are obtained for r intervals at the head of the projection horizon. For the next (k r) intervals, the tail part, flow data are obtained from a simple model that considers the average of all previous arrivals on the approach. Although OPAC uses a rolling horizon concept which states the optimal policy is calculated for the entire horizon but implemented only for the head section, however, since a great portion of arrival information in the projection horizon is modeled as the average flow rate, whether the optimal solution is responsive to the real demand needs to be further investigated. RHODES [16] develops a prediction model that estimates the flow approaching to a downstream intersection based on the detected information on upstream intersection approaches that will contribute the traffic arrival of downstream. The simulation has demonstrated the results are promising. But the model depends on turning percentage probability, link travel time, and queuing delay caused by upstream signal states. There were recently some competing and advanced optimization methods that were found effective for signal control problems such as mixed-integer programming, hill climbing, simulated annealing (SA), and genetic algorithms (GA). Some representative research include the lane-based optimization of isolated signal-controlled junctions solved by mixed-integer programming [17], the application of metaheuristics (hill climbing, SA, GA, and others) for urban road network design [18], hill-climbing optimization method for area traffic control by Ceylan [19], group-based optimization of signal timings using the TRANSYT s hill climbing model [20], GA approach for signal timing optimization [21], and parallel algorithm for coordinated traffic signal control [22], stochastic traffic signal optimization using GA [23]. Mirchandani and Lucas [24] proposed a strategy, so-called categorized arrivals-based phase reoptimization at intersections (CAPRI), which integrates transit signal priority and rail/emergency pre-emption within a DP-based real-time traffic adaptive signal control system. Girianna and Benekohal [25] described an algorithm to generate optimal (real-time) signal timings that distribute queues over a number of signalized intersections and over a number of cycles on any signalized intersection. A discrete-time signal-coordination model is formulated as a dynamic optimization problem and solved using GA. Venkatesan et al. [26] modeled heterogeneous traffic using an objectoriented programming approach. By means of this model, unique traffic characteristics can be considered and the traffic information obtained can be applied effectively in adaptive signal controls.

3 178 F. C. FANG AND L. ELEFTERIADOU The aforementioned applications of advanced optimization methods have shown their effectiveness in enhancing traffic signal control performance in urban road network with a primary focus on off-line traffic signals. Their extensive computation requirements might have prevented their claims in the area of real-time adaptive control. The further study is needed to bridge the balance between algorithm optimization accuracy and efficiency and the practical usage in field implementation. In our newly developed signal control for diamond interchanges [27 29], a microscopic model is incorporated to estimate the traffic flows at the stop-line, which describes the dynamic interaction of vehicular detection, arrival, and departure by taking into account varying speed variations, length of queues, and signal. As the signal control is optimized over a rolling horizon that is divided into intervals, the vehicular detection for and projection into the corresponding horizon intervals are also modeled. The signal control algorithm is based on DP, which is formulated in a way different from OPAC and RHODES to suit diamond interchanges, and the optimization of signal policy is performed using a performance measure involving delays, queue length, and storage ratio. An application programming interface (API) via AIMSUN, a microscopic stochastic simulation program, is built to simulate the signal control and implement the optimized signal policy. Sensitivity analysis is conducted to study the effect of different performance measures on the signal control performance. The results are discussed and the conclusion is drawn. 2. VEHICLE PROJECTION DYNAMICS FOR ARRIVAL AND DISCHARGE The DP solution approach to an optimal signal plan is performed over a horizon. It is achieved by evaluating the reward of using various candidate signal plans. The reward is a performance measure function of variables affected by signal such as delay and queue length. The reward is calculated over each interval of the horizon under every possible signal. As the variables (e.g., delay, queue) are dictated by arrival discharge process at the stop-lines, which is predicted by loop detectors in the adaptive signal control, the vehicular flow from the time being detected to the time being queued or discharged over the detector-to-stopline segment must be modeled. In this section an individual approach is examined at a microscopic level to track the movement of a detected vehicle before it is discharged Vehicle travel time Figure 1 depicts the variation of the speed of a detected vehicle with respect to time. Detectors are set upstream of the stop-line. The distance between the detector and the stop-line is denoted as D. Itis assumed that a vehicle passes the detection line and travels with a constant speed (detected speed V) for T 1, then it starts to decelerate with a deceleration rate a to join the back of queue at the stop-line. The deceleration period is denoted as T 2. Avehicle s travel time, T, from the detector to stop-line or the back of queue is calculated as below. Case a: If there is no queue and the signal is green, the vehicle travels with speed V, T ¼ D V (1) Figure 1. Travel time model.

4 MODELING AND SIMULATION OF VEHICLE PROJECTION 179 Case b: If there is no queue and the signal is red, the vehicle is decelerating, T ¼ T 1 þ T 2 ¼ D ðv2 =2aÞ þ V V a (2) Case c: If there are initial queued vehicles, and signal is either red or green, T ¼ T 1 þ T 2 ¼ D ðqsþ ðv2 =2aÞ þ V (3) V a in which q is the number of queued vehicles at the stop-line and S the average space headway of queued vehicle. Assuming that no queued vehicle is discharged, according to Equation (3), the travel time difference between two consecutive vehicles joining the back of queue is found as, Traveltimedifference ¼ S V (4) If an average vehicle spacing of S ¼ 23 ft and average vehicle speed of V ¼ mph ( ft/ second), then the travel time difference calculated from the above equation is about 0.5 seconds ( seconds). That is, one more (or less) queued vehicle at stop-line will decrease (or increase) the travel time duration by 0.5 seconds Vehicle projection and arrival discharge for one interval (Dt) In OPAC algorithms, the number of vehicles arriving at and stopped at the stop-line during a DP interval Dt is assumed same as the one detected by detectors during a detection interval DT ¼ Dt. However, the assumption does not hold when there is a queue of at least one vehicle, and an extreme scenario is presented in Figure 2, where DT Dt. The arrival projected from the detected vehicles and its discharge is a dynamic tempo-spatial process due to the detectors not placed the stop-line, which must be modeled at microscopic level. The detection range (DT) is the time duration in which vehicles arrive at detectors and will be projected onto Figure 2. Detected vehicles projecting onto the back of queue or stop-line an extreme case.

5 180 F. C. FANG AND L. ELEFTERIADOU Figure 3. Vehicle projection dynamics. the back of queue or the stop-line during the corresponding interval (Dt) for DP algorithm. For an interval (Dt) at the stop-line, the chance in queue length is estimated at either green or red signal. As the queue length changes, the space between the back of queue and the detector line changes and so does the travel time. As a result the number of the detected vehicles which are able to arrive at the stopline or back of queue changes. Thus, the detection period that matches the DP interval varies dynamically. As shown in Figure 3, the detection range for vehicle projection in an interval is adjusted due to vehicle projection dynamics. Vehicle projection dynamics states that the net increase in queue length shortens the vehicle travel time, therefore, with one more (or less) vehicle queued at the stopline, the detection period is 0.5 seconds longer (or shorter). This conclusion is reached based on the travel time estimation in the above section. The following presents the mathematical relationship between the time interval at the stop-line (Dt) and the corresponding detection range (DT) in terms of the change of queue length at the stop-line. If the queue length remains unchanged during an interval (Dt), If the queue length changes during an interval (Dt), DT ¼ Dt (5) DT ¼ Dt þ dt (6) where dt is the adjustment of detection range due to vehicle projection dynamics at the stop-line and it can be calculated by dt ¼ðQ projected Q discharged Þ0:5 (7) where Q projected is the number of vehicles detected during [T 0, T 0 þ Dt] that will be projected to the stop-line or the back of queue during the interval; and Q discharged is he number of vehicles discharged during the interval. This calculation is based on average discharge headway at stop-line. If queue length becomes longer (when Q projected > Q discharged ), then the detection range is larger than Dt. Otherwise, the detection range is shorter than Dt. The starting time of each detection range, T 0,as shown in Figure 4, can be determined by T 0 ¼ T ði DtÞ (8)

6 MODELING AND SIMULATION OF VEHICLE PROJECTION 181 Figure 4. Vehicle projection interactive dynamics. in which T 0 is the starting time of detection range, expressed as the time in advance of the optimization horizon; and i is interval index, i ¼ 1, 2, 3, 4. This vehicle projection arrival discharge process can be applied for moderate to lightly congested traffic, but advised cautiously used for highly congested and queue spillback conditions Optimization horizon and its corresponding detection range Figure 5 describes the relationship between the DP optimization horizon and the corresponding detection range using the following assumptions: vehicle average speed is 30 mph (i.e., 44 ft/second), average vehicle deceleration rate is 19.5 ft/second 2, and queued vehicle spacing is 23 ft. Detectors are Figure 5. Detected vehicle projection scheme I.

7 182 F. C. FANG AND L. ELEFTERIADOU Figure 6. Detected vehicle projection scheme II. setback some distance (e.g., 565 ft) from the stop-line. How to determine the location of detectors was discussed in authors previous paper [29]. During the detection period, the detectors detect the presence of a vehicle and its speed, which are used to estimate its arrival time at the stop-line. Depending on the queue length at stop-line, the detection period is not constant rather varies from 16 to 2 seconds in advance of the beginning of the corresponding optimization horizon. The boundaries of the detection range correspond to the scenarios when there is no queued vehicle in the beginning of the horizon and there are maximum queued vehicles in the end of the horizon. These boundary values (e.g., 16 and 2 seconds) vary with the field detected vehicle data such as speed, etc. Each vehicle s detection time is also located according to the vehicle projection dynamics presented in the above section. After determining the detection range, the number of vehicles detected during that period are projected to the horizon intervals (0 2.5), (2.5 5), (5 7.5), and (7.5 10). To increase the measurement precision and also for possibility of the algorithm implementation, two consecutive DP optimization horizons are designed to have one interval of 2.5 seconds overlapped. Consequently, there is also an overlap between detection periods. As shown in Figure 6, two consecutive DP horizons can share the same detection information for up to 6.5 seconds ( 8.5 to 2 seconds). 3. REAL-TIME SIGNAL CONTROL 3.1. The principle A methodology has been developed by Fang and Elefteriadou [29] to provide optimal signal control of diamond interchanges in response to real-time traffic fluctuations. The optimization problem is formulated as a decision network that includes all possible signal switching decisions over an optimization period of 10 seconds that rolls forward. Each decision is made over each interval with 2.5 seconds. DP method is applied to find the optimal signal plan that is a decision trajectory of one phase in each interval. Signal phase is defined as green time (right-of-way) given to certain movement. A global optimal solution is pursued with respect to certain objective function that specifies operational performance of a diamond interchange. The objective function is defined as performance measure index (PMI) in this paper, which is the sum of performance measures, e.g., delay, queue length, or other variables of eight movements in a diamond interchange.

8 MODELING AND SIMULATION OF VEHICLE PROJECTION 183 Various definitions of PMIs, based on vehicle projection arrival discharge model, will be explained in next section. Major inputs to the DP optimization are traffic arrivals on individual approaches predicted from upstream detectors, while outputs are signal phases at discrete times over entire optimization period. Vehicle trajectories from detections till future arrivals and departures are modeled at the microscopic level to estimate traffic flows at the stop-line for each horizon, which has been described in the above section Performance measure Various performance measures namely PMI, due to different signal decision, either green or red can be calculated. A PMI is defined for each interval, but calculated over the optimized horizon that consists of four intervals. It serves as an optimization criteria in the DP algorithm. Therefore, different PMI will result in different signal control plan that subsequently affects the interchange operational performance. Four types of PMI related to queue length, delay, and storage ratio are described as follows: PMI 1: Sum of average queues per lane for all movements! PMI ¼ X4 X 8 w½išq final ½iŠ (9) j¼1 i¼1 j PMI 2: Sum of average delay per lane for all movements PMI ¼ X4 PMI 3: Sum of total delays for all movements PMI ¼ X4 X 8 w½išdelay½iš! j¼1 i¼1 j X 8! NL½iŠDelay½iŠ j¼1 i¼1 j (10) (11) PMI 4: Sum of storage ratio for all movements PMI ¼ X4 j¼1 where,w: The weight associated with movement i; there are eight movements involved for a diamond interchange.q final : Average queue length per lane on movement i in the end of a DP interval j. Itis calculated as: Q final ¼ Q initial þ Q projected Q discharged in which Q final is the number of queued vehicles in the end of an interval; and Q initial is the number of queued vehicles in the beginning of an interval.delay: Average delay per lane on movement i for total vehicles for a DP interval j. Itis calculated asdelay ¼ 2.5 Q initial þ (Q projected Q discharged ). Note that this calculation assumes that during an interval of 2.5 seconds, the delay is the sum of delays experienced by the queued vehicles and the back-of-queue catching vehicles. Thus, the initial vehicles are delayed for 2.5 seconds and arrived vehicles are delayed for half of 2.5 seconds.nl: The number of lanes of movement i.sr: Storage ratio on movement i in the end of a DP interval j. It is calculated as SR½iŠ ¼ Q final½iš L½iŠ=S½iŠ in which L is link length of turning movement i Algorithm implementation A framework and procedure for implementing the vehicle projection and the DP adaptive signal control algorithm is proposed, as presented in Figure 7. Inputs include continuously undated vehicle information at detectors and given initial signal phase and queue length of each movement. The vehicle X 8 i¼1 SR½iŠ! j (12)

9 184 F. C. FANG AND L. ELEFTERIADOU Figure 7. Framework of algorithm implementation. projection model is performed on each movement independently to estimate the vehicle arrivals over entire optimization horizon at the stop-line. Based on the traffic arrival data, the optimization algorithm computes optimal signal switching decisions which are updated at controllers in due time. With the time rolling one horizon after another, the process repeats. When the time reaches to a user-defined time, calibration or reset of the program becomes a necessary to avoid the error accumulation. 4. APPLICATION PROGRAMMING INTERFACE (API) FOR SIMULATION To select a simulation model for evaluation purposes, it is necessary to examine the characteristics, functions, and flexibilities of each candidate model, with special respect to the potential being used to simulate the proposed vehicle projection and adaptive signal control. Several common microsimulation models including Paramics [30], AIMSUN [31], VISSIM [32], and CORSIM [33] have been considered after the capabilities of each model are examined. Finally, AIMSUN has been selected as the simulation model in this study because (a) it provides an extension module which can be used to

10 MODELING AND SIMULATION OF VEHICLE PROJECTION 185 develop an API interface for external signal control applications either in C/Cþþ or Python scripting language, and (b) it can assign a controller to a set of movements in two or more nodes/intersections, which is essential to simulate signal controls at a diamond interchange. The selected AIMSUN simulation model has been calibrated using field data of the diamond interchange connecting I-17 with Indian School road in Arizona [29] to ensure that it can accurately replicate field conditions. Detailed calibration process, methods, and guidelines for interchange operational analysis are described [27,28]. Fang and Elefteriadou [27,28] have developed some guidelines on how to evaluate interchange traffic operational performance in microscopic simulation environment. Based on this preliminary study, the optimization algorithm development and simulation evaluation of an adaptive signal control at diamond interchange has been presented [29] GETRAM extension module The simulation of the DP algorithm is carried out by the GETRAM extension module embedded in AIMSUN. The module is used to develop the API linking simulation environment with the algorithm that requires to access to some internal data such as vehicle information during simulation run time. Figure 8 shows the process of the information exchange between AIMSUN, vehicle projection, and the algorithm via GETRAM extension module. First, the simulated interchange network equipped with detectors is modeled in AIMSUN. Next, during simulation, the real-time traffic measurements provided by those detectors feed the vehicle projection model, and the DP algorithm that, after processing, makes the decision of signal controls, e.g., implement phase for arterials for next 7.5 seconds. Finally, these decisions are transferred back to the simulated network, which emulates their operations through the signal controllers Simulation scheme for vehicle projection model Detectors are placed 656 ft upstream of the stop-line for each approach at the diamond interchange. These detectors have the capabilities of Count (the number of vehicles) and Speed (the mean speed for vehicles crossing the detector during the step. A simulation step of 0.5 seconds is used to collect vehicle detection information because smaller value means more accurate detected data, and a DP interval 2.5 seconds is 5 (an integer) times 0.5 seconds. The simulation time horizon is arranged so that the simulation starts at time 0 and the interchange is controlled in a fixed time signal control. When the time goes up to 300 seconds (5 minutes), the signal switches to the proposed adaptive signal control. Figure 5 shows the simulation scheme during this transition period between fixed time and adaptive signal control. The first optimization horizon is located at time seconds. Its corresponding detection period is 16 2 seconds in advance, i.e., detection time is seconds. The number of vehicles crossing the detectors and vehicle traveling speed are gathered for every simulation step 0.5 seconds for total eight movements during this detection time. The arrival projection arrival discharge and DP computing starts to be processed immediately after the detection period ends, but has to be completed before the time 300 when the implementation starts. Initial queue length and signal Figure 8. Simulation of the DP algorithm in AIMSUN via GETRAM extension module.

11 186 F. C. FANG AND L. ELEFTERIADOU Figure 9. Development of the API for real-time simulation of the DP algorithm. status for the beginning of optimization horizon is obtained from the simulation time at 298 seconds. To increase the measurement precision, two consecutive DP optimization horizons are designed to have one interval of 2.5 seconds overlap Development of API for the DP algorithm In order to achieve the data exchange and have the network dynamically implementing the DP signal plan, the external algorithm is compiled into a DLL (dynamic link library) file using Microsoft Visual Cþþ 6.0 by combining the functions available from GETRAM module. These functions are made available for users to obtain detection information from AIMSUN model, such as the number of vehicles that have crossed a detector during a simulation step or an aggregated time interval, vehicle speed, detector occupancy, etc. The vehicle projection and adaptive signal control algorithm is programmed according to five routines defined by the GETRAM extension module to build the API which allows communication between AIMSUN and the DP algorithm in real time. As illustrated in Figure 9, each of these five routines is called during simulation to serve different functions. GETRAM extension is loaded or unloaded via GetExtLoad or GetExtUnLoad. GetExtInit starts the simulation and initializes some parameters including the simulation/detection step ( isimustep ), DP rolling horizon ( idprolling ), and DP interval counts ( idp ), while GetExtFinish is called to complete the simulation. GetExtManage is the key one that primarily contains the code for DP optimization and vehicle arrivals discharge projection model. It is called in every simulation step at the beginning of the cycle to request and update detector measures, vehicle information, and interaction

12 MODELING AND SIMULATION OF VEHICLE PROJECTION 187 Figure 10. Implementation of the API in simulation. with junctions. There are four blocks embedded in the routine. Block 1 serves for vehicle detection and initial status. If it is the first DP cycle, vehicles arriving from time 284 to 298 seconds at detectors are saved, otherwise, the detection overlap is considered. Block 2 includes subroutines to compute PMIs used for DP calculation and determine vehicle detection period and its starting time point by considering vehicle projections arrival discharge model. Three scenarios are identified in the subroutine: (a) no queue and signal green; (b) no queue and signal red; and (c) initial queues present; finally, Blocks 3 and 4 declare the optimal signal plan and implement it. In this experiment, the simulation is arranged to provide flexibility in switching between different control strategies. When simulation time is less than 300 seconds (5 minutes), the interchange is operated as fixed time control; when time reaches to 300 seconds, fixed time control is disabled, then the DP adaptive control is applied and continue to operate till time at 7200 seconds (2 hours) to switch back to fixed time control. Figure 10 is a snapshot during the simulation run time. The computing of the DP algorithm is updated continuously (in each simulation step) and can be visualized through a Local X console pop-up window. 5. SENSITIVITY ANALYSIS Based on simulation results, a sensitivity analysis is conducted on how the interchange system delay is affected by different definitions of PMI in the DP algorithm. Table I presents how each of the PMI definitions affects the system delay for various demand scenarios. Six types of demand scenarios ranging from low demand to high demand are considered in this study. The results have shown that generally the simulated interchange experiences less delay in PMI 1: Sum of average queues per lane for all movements and PMI 4: Sum of storage ratio for all movements than PMI 2 and 3 which are defined based upon delays. The reason that the queue-based PMIs have resulted in better performance is that the change of queues, directly modeled in the vehicle projection arrival discharge model, determines the state transition function (i.e., a function about how the signal state is switched) in the optimization algorithm. The results of PMI 1 and PMI 4 are very similar in this study due to the geometric configuration of this particular interchange selected for simulation. Each approach of the

13 188 F. C. FANG AND L. ELEFTERIADOU Table I. System delay (seconds/vehicle) with respect to each PMI and various demand levels. # Movement type O-D Demand (vehicle/hour) Demand PMI 1: Sum of level average queues per lane for all movements PMI 2: Sum of average delay per lane for all movements PMI 3: Sum of total delays for all movements PMI 4: Sum of storage ratio for all movements 1 Arterial EB/WB L 400 H TH 3000 R 250 Ramp NB/SB L 650 TH 300 R Arterial EB/WB L 400 H TH 3300 R 250 Ramp NB/SB L 650 TH 300 R Arterial EB/WB L 200 M TH 2000 R 250 Ramp NB/SB L 500 TH 300 R Arterial EB/WB L 200 M TH 2500 R 250 Ramp NB/SB L 400 TH 250 R Arterial EB/WB L 250 L TH 1000 R 250 Ramp NB/SB L 350 TH 150 R 350 (Continues)

14 MODELING AND SIMULATION OF VEHICLE PROJECTION 189 Table I. (Continued) # Movement type O-D Demand (vehicle/hour) Demand PMI 1: Sum of level average queues per lane for all movements PMI 2: Sum of average delay per lane for all movements PMI 3: Sum of total delays for all movements PMI 4: Sum of storage ratio for all movements 6 Arterial EB/WB L 400 H TH 3500 R 250 Ramp NB/SB L 750 TH 300 R 750 H, M, and L represents high, medium, and low demand, respectively.

15 190 F. C. FANG AND L. ELEFTERIADOU simulated interchange has the same link length (i.e., same maximum storages for queued vehicles). Therefore, the definition of the sum of storage ratio can be regarded the same as the sum of average queue length for this particular interchange. However, in the case of a diamond interchange that has left turn pocket lane or each approach has different length, PMI 1 should result in different result from PMI 4. There is a discrepancy in the system delay for scenario 6 (high demand) between PMI 1 and PMI 4. This could be further developed delays under over-saturated conditions happened on some approaches. Additionally, the research conducted more sensitivity analysis on how the interchange delay is affected by different definition of weights on each approach and demand levels. The simulation results have exhibited that the DP algorithm is superior to PASSER III and TRANSYT-7F in handling demand fluctuations for medium to high flow scenarios when the field demand is increased from the one used in off-line optimization. TRANSYT-7F is a macroscopic, deterministic model for optimizing arterial and network signal timing by applying a hill-climbing search technique. PASSER III is the only existing model designed for evaluating and optimizing pre-timed signal timings at diamond interchange. It can only search for a signal plan or a value of the signal parameter with the minimum delay from the restricted alternative. Detailed results are provided in Refs. [27 29]. 6. CONCLUSIONS Traffic dynamics of the vehicles detected at the detectors, arrived, and then stopped or discharged at the stop-lines was modeled and an interactive projection scheme was developed at the microscopic level for real-time signal control in this research. The arrival information was predicted from arrivals detected at the upstream detector line. Detection range varies with the change of the number of queues at stop-line because it shortens the travel distance between detection line to the back of queues. According to the travel time estimation, one more (or less) vehicle queued increase (or decrease) the detection period by 0.5 seconds. During the detection period, the detectors detect the presence of a vehicle and its speed, which are in turn used to estimate its arrival time at the stop-line sometime during the projection horizon. Based on vehicle projection and arrival discharge relations, performance measures were defined as the criteria for signal optimization objective functions. Four PMIs were defined PMI 1: Sum of average queue length per lane for all movements; PMI 2: Sum of average delay per lane for all movements; PMI 3: Sum of total delays for all movements; and PMI 4: Sum of storage ratio for all movements. The developed vehicle projection model was integrated into the real-time signal control for simulation evaluation. An API via AIMSUN, a microscopic stochastic simulation program, was built to simulate the signal control by accessing internal data including detected traffic demand and vehicle speed that are inputs to the microscopic model, and implement the optimal signal policy. Sensitivity analysis is conducted to study the effect of different performance measures on the signal control performance. The results are discussed and the conclusion is drawn that the queue length and storage ratio are most appropriate as the performance measure for real-time signal control of interchanges. The results have shown that PMI 1 and PMI 4 are better optimization criteria than PMI 2 and PMI 3 in terms of minimizing system delay of the simulated interchange under medium to high and high demand scenarios. In the low demand scenarios, all four types of PMI definitions have resulted in very close operational performance. The specific geometric layout of the simulated interchange results in no difference between PMI 1 and PMI 4 as optimization criteria. In the future research, a diamond interchange with left pocket lane or different approach length can be applied to find out which PMI is superior. It is worth noting that this paper contributes mainly in the vehicle projection dynamics during arrival discharge process, which is badly needed in adaptive traffic signal control algorithms. This contribution differs from what we claimed in our previous papers [27 29] where a DP-based adaptive traffic signal control was proposed. 7. LIST OF SYMBOLS AND ABBREVIATIONS T D V a vehicle s travel time from the detector to stop-line or the back of queue. the distance between the detector and the stop-line. the detected vehicle speed.

16 MODELING AND SIMULATION OF VEHICLE PROJECTION 191 T 1 the time after a vehicle passes the detection line and travels with a constant speed. T 2 the deceleration period. a deceleration rate. q the number of queued vehicles at the stop-line. S the average space headway of queued vehicle. Dt the time interval at the stop-line. DT the corresponding detection range. d t the adjustment of detection range due to vehicle projection dynamics at the stop-line. T 0 the starting time of a detection range. i interval index, i ¼ 1, 2, 3, 4. Q projected the number of vehicles detected during an time interval that will be projected to the stop-line or the back of queue; Q discharged the number of vehicles discharged during a time interval. W[i] the weight associated with movement i. Q final average queue length per lane on turning movement i in the end of a DP interval j. Q final the number of queued vehicles in the end of a time interval Q initial the number of queued vehicles in the beginning of a time interval. Delay[i] average delay per lane on turning movement i for total vehicles for a time interval. SR[i] storage ratio on turning movement i in the end of a time interval. NL[i] the number of lanes of turning movement i. S[i] the average space headway of queued vehicle for turning movement i. L[i] link length of turning movement i. AIMSUN computer simulation software name API Application Programming Interface CAPRI Categorized Arrivals-Based Phase Re-optimization at Intersections CORSIM computer simulation software name DLL Dynamic Link Library DP Dynamic Programming DYPIC Dynamic Programmed Intersection Control GA Genetic Algorithm GETRAM computer module embedded in the software AIMSUN MOVA Modernized Optimized Vehicle Actuation Strategy OPAC Optimization Policies for Adaptive Control Paramics computer simulation software name PASSER III computer simulation software name PMI performance measure index RHODES Real-Time Hierarchical Optimized Distributed Effective System SA Simulated Annealing SAST Stepwise Adjustment of Signal Timing SCOOT Split, Cycle, and Offset Optimization Technique TOL Traffic Optimization Logic TRANSYT-7F computer software name VISSIM computer simulation software name REFERENCES 1. Miller AJ. Settings for fixed-cycle traffic signals. Operational Research Quarterly 1963; 14(4): Lin FB, Vijayakumar S. Adaptive signal control at isolated intersections. ASCE Journal of Transportation Engineering 1988; 114(5): Bang KL. Optimal control of isolated traffic signals. Traffic Engineering and Control 1976; 17(7): Hunt PB, Robertson DI, Bretherton RD, Royle MC. The SCOOT on-line traffic signal optimization technique. Traffic Engineering and Control 1982; 23(4):

17 192 F. C. FANG AND L. ELEFTERIADOU 5. Vincent RA, Young CP. Self-optimizing traffic signal control using microprocessors the TRRL MOVA strategy for isolated intersections. Traffic Engineering and Control 1986; 27: Kronborg P, Davidson F. MOVA and LHOVRA: traffic signal control for isolated intersections. Traffic Engineering and Control 34(4): 1993; Lin FB, Cooke D, Vijayakumar S. Use of predicted vehicle arrival information for adaptive signal control. In Transportation Research Record: Journal of The Transportation Research Board, No TRB, National Research Council, Washington, DC, 1987; Porche I, Lafortune S. Adaptive look-ahead optimization of traffic signals. Journal of Intelligent Transportation Systems 1999; 4(3): Abu-Lebdeh G, Chen H, Benekohal RF. Modeling traffic output for design of dynamic multi-cycle control in congested conditions. Journal of Intelligent Transportation Systems 2007; 11(1): Grafton RB, Newell GF. Optimal policies for the control of an undersaturated intersection. In Vehicular Traffic Science. Proceedings of the Third International Symposium on the Theory of Traffic Flow. Elsevier Science Publishing Company, Robertson DI, Bretherton RD. Optimum control of an intersection for any known sequence of vehicle arrival. Traffic Control and Transportation Systems, Proceedings of the 2nd IFAC/IFIP/IFORS Symposium, Monte Carlo, edited by AFCET, 1974; Gartner NH. OPAC: A demand-responsive strategy for traffic signal control. In Transportation Research Record: Journal of the Transportation Research Board, No TRB, National Research Council, Washington, DC, 1983; Gartner NH, Pooran FJ. Implementation and field testing of the OPAC adaptive control strategy in RT-TRACS. In 81st TRB Annual Meeting. CD-ROM, Transportation Research Board, of the National Academies, Washington, DC, Mirchandani P, Head L. A real-time traffic signal control system: architecture, algorithms and analysis. Transportation Research, Part C 2001; 9: Sen U, Head KL. Controlled optimization of phases at an intersection. Transportation Science 1997; 31(1): Head KL. Event-based short-term traffic flow prediction model. In Transportation Research Record: Journal of The Transportation Research Board, No TRB, National Research Council, Washington, DC, 1995; Wong CK, Wong SC, Tong CO. A lane-based optimization method for the multi-period analysis of isolated signalcontrolled junctions. Transportmetrica 2006; 2(1): Cantarella GE, Pavone G, Vitetta A. Heuristics for urban road network design: lane layout and signal settings. European Journal of Operational Research 2006; 175(3): Ceylan H. Developing combined genetic algorithm hill-climbing optimization method for area traffic control. Journal of Transportation Engineering 2006; 132(8): Wong SC. Group-based optimization of signal timings using the TRANSYT traffic model. Transportation Research, Part B 1996; 30(3): Ceylan H, Bell MGH. Traffic signal timing optimization based on genetic algorithm approach, including drivers routing. Transportation Research, Part B 2004; 38(4): Cheng SF, Epelman MA, Smith RL. CoSIGN: a parallel algorithm for coordinated traffic signal control. IEEE Transactions on Intelligent Transportation Systems 2006; 7(4): Park B, Kamarajugadda A. Development and evaluation of a stochastic traffic signal optimization method. International Journal of Sustainable Transportation 2007; 1(3): Mirchandani PB, Lucas DE. Integrated transit priority and rail/emergency preemption in real-time traffic adaptive signal control. Intelligent Transportation Systems 2004; 8: Girianna M, Benekohal RF. Using genetic algorithms to design signal coordination for oversaturated networks. Intelligent Transportation Systems 2004; 8(2): Venkatesan K, Gowri A, Sivanandan R. Development of microscopic simulation model for heterogeneous traffic using object oriented approach. Transportmetrica 2008; 4(3): Fang FC, Elefteriadou L. Some guidelines for selecting micro-simulation models for interchange traffic operational analysis. ASCE Journal of Transportation Engineering 2005; 131(7): Fang FC, Elefteriadou L. Optimal and adaptive signal control of diamond interchanges. In 84th TRB Annual Meeting. CD-ROM, Transportation Research Board of the National Academies, Washington, DC, Fang FC, Elefteriadou L. Development of an optimization methodology for adaptive traffic signal control at diamond interchanges. ASCE Journal of Transportation Engineering 2006; 132(8): Paramics User Guide. QUADSTONE Ltd., Edinburgh, UK, AIMSUN User Manual, Version 4.1. TSS-Transportation Simulation System, Spain, VISSIM 3.5, User Manual. VISSIM PTV Planung Transport Verkehr AG, Germany, Traffic Software Integrated System 97 User s Guide. Federal Highway Administration, 1997.