Intersection traffic deadlock formation and its probability: A petri net-based modeling approach

Although traffic deadlock at an intersection is a common phenomenon during rush hours, the deadlock formation metrics such as formation probability and duration have not been derived yet. As Petri Net (PN)-based approach can formulate the deadlock formation in analytical form and has been applied in numerous traffic flow studies, the PN is employed to investigate the deadlock formation probability and duration. First, each of the four main components of an intersection is formulated, namely vehicle trajectory, traffic signal, vehicle arrivals, and conflict behaviour, as a Petri Net (or IntersectionPN), and name them CellularPN, TrafficLightPN, DemandPN, and ConflictPN, respectively. Together, the entire intersection becomes an IntersectionPN, on which the system's three classes of states are defined, namely the deadlock state, the trap state, and the live state. The deadlock occurrence is formulated as an integer programming problem, while the formation probability and duration are studied by constructing a reachability graph that leads to the Markov chain of the system. A case study shows that the developed model is able to reproduce an intersection deadlock, and that the focus is on two priority behaviours: “First Enter First Serve” and “Pure Stochastic”. The results show that different behaviours lead to different deadlock formation metrics and that, when the saturation flow rate degrades (due to events such as severe weather conditions), a deadlock will occur more quickly. The research results provide the analysis tool for probabilistic deadlock formation. It can also be applied to the intersection deadlock prevention and control.