Regret-Based Max-Pressure Traffic Signal Control under Uncertain Traffic States

Abstract

Max-pressure (MP) traffic signal control selects phases using pressure scores computed from estimated traffic states, but these states are uncertain and their consequences depend on whether they alter phase ranking and how much pressure is lost. This paper develops a decision-oriented Regret-Based Max-Pressure framework that represents uncertainty through phase-selection regret, defined as the pressure loss of a candidate phase relative to the pressure-maximizing phase under each plausible latent state. We propose Stochastic Regret MP, which minimizes expected regret under a calibrated residual distribution, and Distributionally Robust (DR) Regret MP, which minimizes worst-case expected regret over a Wasserstein ambiguity set. Robustifying regret rather than absolute pressure makes the formulation invariant to state-dependent pressure components shared by all candidate phases, thereby focusing robustness on relative phase quality. We further derive an explicit queue-linear pressure-loss bound and establish strong queue stability when the net-service reserve exceeds the resulting loss coefficient. Numerical experiments show that both methods reduce normalized true-state pressure regret by about 70% relative to Point-estimate MP, while DR Regret MP yields lower network queues than direct robustification of absolute pressure. In microscopic SUMO experiments on a 28-intersection real-world network, Stochastic Regret MP and DR Regret MP reduce mean delay by 18.9% and 14.9%, respectively, and retain benefits under detector undercount and failure. The results show that representing uncertainty through its decision consequences can improve reliable traffic control under imperfect state information.