Combined Traffic Signal Control and Traffic Assignment: Algorithms, Implementation and Numerical Results
Chungwon Lee and Randy B. Machemehl, University of Texas at Austin, March 2005, 289 pp. (472840-00074-1)
The nonconvex combined traffic signal control and traffic assignment problem is examined using four different algorithms and four example networks. The heuristic iterative approach has been widely used (1) without any justification regarding solution quality and (2) without any treatment of the problem of nonconvexity. This is the first study designed recognizing the nonconvexity of the combined problem and examining quality of different algorithm solutions with convergence pattern analysis. Drivers are assumed to follow Wardrop’s first principle and link performance is described by the Webster curve. Origin-destination matrices are assumed fixed, green time per cycle ratios and cycle length are decision variables, and total system travel time minimization is the control objective. The iterative approach sequentially performing assignment and signal optimization finds mutually consistent points where flow is at user equilibrium and signal setting is optimal. Three different local search algorithms with six variations regarding gradient calculation are implemented. To counter the nonconvexity, two stochastic global searches, simulated annealing and a genetic algorithm are applied. Complex signal schemes with overlapping movements and multiple phases are included in the developed codes. The codes are preliminarily tested to address characteristics of the algorithms. Comprehensive experiments are designed using five different demand levels and four different size networks. An aggregate measure to determine the similarity of solutions by different algorithms indicated that the mutually consistent solutions are quite different from the other algorithm solutions and the difference grows as demand increases. Regarding solution quality, each algorithm has a relatively superior combination of demand level and network Size. The iterative approach and local searches converge quickly but the two global searches converge slowly. Numerical results confirm that the iterative approach is not always desirable and should be carefully applied at high demand in networks. At high demand, however, no algorithm is always outperforming. To improve code performance, a hybrid algorithm of global and local/iterative search utilizing their exclusive merits simultaneously and efficiently should be developed.
Keywords: Traffic Signal Control, Convergence Pattern Analysis, Signal Optimization, Iterative Approach
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