Efficient Derivation of Optimal Signal Schedules for Multimodal Intersections

This is an extended abstract of the journal paper [2]. Specifically, we illustrate an approach to efficiently derive optimal signal schedules for multimodal intersections among vehicle flows and right-of-way tram lines, minimizing the maximum expected percentage of queued vehicles of each flow. We model trams by Stochastic Time Petri Nets (STPNs), capturing periodic tram departures and bounded delays and travel times with general (i.e., non-Exponential) distribution, and we model vehicles by finite-capacity vacation queues, with general vacation times determined by the intersection availability. For each vehicle flow, we study the expected queue size, deriving both its transient behavior and its steady-state distribution at multiples of the hyperperiod (resulting from nominal tram arrival times and vehicle traffic signals). By doing so, we study the behavior of each vehicle flow over arbitrary-duration intervals by performing transient analysis for the hyperperiod duration, starting from the steady-state distribution of the expected queue size. Experimental results on case studies of real complexity with time-varying parameters show the approach effectiveness at identifying optimal traffic signal schedules, notably exploring in few minutes hundreds of schedules requiring tens of hours in Simulation of Urban MObility (SUMO).