Stability of Modified Max Pressure Controller with Application to Signalized Traffic Networks

This work describes a type of distributed feedback control algorithm that acts on a vertical queueing network where flow dynamics may greatly outpace the rate of feedback and actuation. The modeled network has a known, finite set of feasible actuations for the binary controllers located at each network node. It also has known expected demands, split ratios, and maximum service rates. Previous work proposed the application of a max pressure controller to maximize throughput on such a network without the need for centralized computation of a control policy. Here we extend the max pressure controller to satisfy practical constraints on the frequency of switching and guarantees on proportional actuation. We fundamentally alter the formulation of max pressure to a setting where the controller may only update at a rate significantly slower than the dynamics of queue formation. Furthermore, the set of allowable controllers is extended to any convex combination of available signal phases to account for signal changes within a single signal “cycle”. We show that this proposed extended max pressure controllers stabilize a vertical queueing network (queue lengths remain bounded in expectation) given slightly increased restrictions on admissible network demand flows. This work is motivated by the application of controlling traffic signals on arterial road networks. Max pressure provides an intriguing alternative to existing feedback control systems due to its distributed implementation and theoretical guarantees, but cannot be directly applied as originally formulated due to hardware and safety constraints. We ultimately apply our extension of max pressure to a simulation of an existing arterial roadway and provide comparison to the control policy that is currently deployed on this site.