A Theoretical Approach to Optimizing Offsets of Coordinated Traffic Signal Controls

Traffic signals on urban arterials and in grid networks operate in coordinated systems to provide for smooth progression of major traffic movements. In the past decades, continued efforts have been made to the research and development of coordinated traffic signal control strategies. The models and systems that have been developed include both the off-line models such as TRANSYT and PASSER, and on-line systems such as SCOOT, SCATS, UTCS, and the latest RT-TRACS, which is a framework still under development. Despite the availability of so many models and systems, all of them have been designed by using heuristic algorithms to optimize the signal offset. On the other hand, most of existing theoretical methodologies for optimizing the signal offset are deterministic in nature, which ignore the stochastic variations of vehicles. The lack of a sophisticated theoretical basis in the state-of-the-art for optimizing the signal offset has significantly limited the researcher's ability to evaluating existing models and systems in an objective manner. This paper presents a stochastic process-based approach for determining the optimal offset of two adjacent traffic signals for one directional traffic flow, which minimizes the average total delay and/or average total number of stops. By using the probability theory and queuing theory, the proposed approach incorporates both platoon dispersions and the stochastic variations of the queue at the intersection. A computational algorithm for determining the optimal offset is presented. With a possible expansion of the proposed algorithm to more complicated scenarios, it has a high potential to be incorporated into existing models or systems for both evaluation and implementation purposes.