Simulation Optimization of Urban Arterial Signals via Simultaneous Perturbation Stochastic Approximation (SPSA)

In this paper, we develop a simulation optimization procedure for optimizing the urban arterial traffic signal timings including a bunch of sequential intersections. The system performance is estimated via a stochastic discrete-event meso-scopic traffic simulator, and a gradient-based search algorithm on stochastic approximation is applied to give the optimal signal timings. Simultaneous perturbation analysis is used to derive both left-hand and righthand gradient estimators of the system performance with respect to the cycle lengths, green splits, and green offsets for those intersections within the arterial. Numerical experiments show that the meso-scopic traffic simulator provides reasonable system performance in much less running time if properly calibrated, compared with a widely-used commercial traffic microscopic simulation program CORSIM. In particular, for all scenarios designed, the optimizer converges to optimal signal timing plans which significantly increase the system performance. INTRODUCTION The vehicular delay at signalized intersections, which increases the travel time as well as reduces speed and reliability, is an obstacle that has a detrimental effect on cost-effectiveness of transportation system (6). Therefore, it has been the traffic engineer’s endeavor to quantify delay and optimize the signal system to increase the operational efficiency of the urban traffic system. Traffic simulation is an important tool for modeling the operation of dynamic traffic systems and helps analyze the causes and potential solutions of traffic problems such as congestion and safety. Various simulation models and optimization techniques have evolved and aided traffic engineer in the optimization process (1-6). The level of detail in simulation models ranges from macroscopic via meso-scopic to microscopic. Most of the existing traffic signal optimization programs, such as SYNCHRO, TRANSYT-7F, and PASSER-II(1), rely on deterministic and macroscopic simulation programs. One drawback of such applications is that the simulation program does not reflect real-world conditions (e.g. the left-turn bay capacity constraint). Microscopic simulation programs, such as CORSIM and VISSIM (6), can emulate traffic at signalized intersections in details. However, car-following and lanechanging logics are complicated to simulate and integrating signal optimization with this class of simulation is quite time and cost consuming. Meso-scopic models, which fill the gap between the aggregate level approach of macroscopic models and the individual tracking approach of the microscopic ones, can also simulate signal timing by translating signal states to road segment capacities. Examples are DynaMIT, DYNASMART, MITSIM and METROPOLIS (9). When the precise level more than macroscopic simulation is desirable and the detail of microscopic simulation is infeasible due to a large network or resources available are limited, meso-scopic models might be better choices.