Stability and implementation of a cycle-based max pressure controller for signalized traffic networks

Intelligent use of network capacity via responsive signal control will become increasingly essential as congestion increases on urban roadways. Existing adaptive control systems require lengthy location-specific tuning procedures or expensive central communications infrastructure. Previous theoretical work proposed the application of a max pressure controller to maximize network throughput in a distributed manner with minimal calibration. Yet this algorithm as originally formulated has unpractical hardware and safety constraints. We fundamentally alter the formulation of the max pressure controller to a setting where the actuation can only update once per multiple steps of the modeled dynamics. This is motivated by the case of a traffic signal that can only update green splits based on observed link-counts once per time of 60-120 seconds. Furthermore, we extend the domain of allowable actuations from a single signal phase to any convex combination of available signal phases to model intra-cycle signal changes dictated by pre-selected cycle green splits. We show that this extended max pressure controller will stabilize a vertical queueing network given restrictions on admissible demand flows that are slightly stronger than those suggested in the original formulation of max pressure. We ultimately apply our cycle-based extension of max pressure to a simulation of an existing arterial network and provide comparison to the control policy that is currently deployed at the modeled location.