12. Intersection Deadlock Probability: Stochastic Petri Net Approach

Traffic deadlock at intersections is a common occurrence during rush hours, yet metrics for quantifying deadlock formation, such as formation probability and duration, have not been established. In this chapter, we employ a Petri Net (PN)-based approach to investigate the probability and duration of deadlock formation. We formulate the key components of an intersection, including vehicle trajectory, traffic signal, vehicle arrivals, and conflict behavior, as Petri Nets, namely CellularPN, TrafficLightPN, DemandPN, and ConflictPN, respectively. These components collectively form an IntersectionPN, where three classes of states are defined: deadlock state, trap state, and live state. We formulate the occurrence of deadlock as an integer programming problem and study the formation probability and duration by constructing a reachability graph that leads to the system’s Markov chain. A case study demonstrates the model’s ability to reproduce intersection deadlock, highlighting two priority behaviors: “First Enter First Serve” and “Pure Stochastic.” The results reveal that different behaviors yield distinct deadlock formation metrics and that a degradation in saturation flow rate (e.g., due to severe weather conditions) accelerates deadlock occurrence. These research findings serve as a basis for preventing and controlling intersection deadlock.