Interval Optimization for Signal Timings with Time-Dependent Uncertain Arrivals

Abstract

Contending with excessive delays at signalized intersections due to traffic flow fluctuation has been recognized as one of the most challenging issues for traffic researchers and engineers. Due to the uncertainty of vehicle arrivals, a signal timing plan optimized with a fixed demand pattern may lead to ineffective control. In response to this need, this study adopts the theory of interval analysis and defines a set of demand intervals to represent the demand fluctuations. Depending on the demand interval patterns, an optimization model is proposed to maximize the overall robustness of signal design while maintaining an acceptable level of efficiency. A recursive two-stage solution procedure is also developed to solve the optimization problem. To ensure the global optimization, a modified branch-and-bound algorithm is developed for the exploration of solutions. The extensive experimental analyses in comparison with the deterministic optimization model reveal that the proposed model is quite promising for applications, especially under highly fluctuated demand patterns.