Simple abstract models to study stability of urban networks with decentralized signal control

Traffic Signal Controllers (TSCs) used to manage intersections can influence the residual queues at intersections. These residual queues can lead to an irreversible state of network gridlock. This paper discovers the advantages of locally adaptive TSCs utilizing traffic information on both upstream and downstream approaches of an intersection (e.g., back-pressure or BP control) over employing only upstream approaches information (e.g., proportional control) in avoiding gridlock. Although BP algorithms are mathematically proven to be throughput optimal as they bound network queues for all feasible demands, the proofs exist only for networks with infinite link capacities, fixed-route choices, or for TSCs with no minimum green-time requirement. We propose a simple asymmetric two-bin model to study the influence of the BP control on network behavior (e.g., gridlock probability, average time to gridlock and maximum throughput) and compare it with the other control policy. Theoretical insights from the asymmetric two-bin model are verified using microsimulation results of the asymmetric two-ring model. Both analytical and simulation results imply that BP-based TSCs have an increased capability of delaying or avoiding gridlock in heavy traffic with a larger time step at the cost of potentially lower throughput in undersaturated networks. The paper provides a framework to evaluate control policies in inhomogeneous networks and shows the superiority of BP-based TSCs against gridlock in grid networks with finite capacities of links.