Credit-Based Congestion Pricing: Equilibrium Properties and Optimal Scheme Design

Credit-based congestion pricing (CBCP) has emerged as a mechanism to alleviate the social inequity concerns of road congestion pricing - a promising strategy for traffic congestion mitigation - by providing low-income users with travel credits to offset some of their toll payments. While CBCP offers immense potential for addressing inequity issues that hamper the practical viability of congestion pricing, the deployment of CBCP in practice is nascent, and the potential efficacy and optimal design of CBCP schemes have yet to be formalized. In this work, we study the design of CBCP schemes to achieve particular societal objectives and investigate their influence on traffic patterns when routing heterogeneous users with different values of time (VoTs) on a multi-lane highway with an express lane (EL). To this end, we introduce a new non-atomic congestion game model of a mixed-economy, wherein eligible users receive travel credits while the remaining ineligible users pay out-of-pocket to use the EL. In this setting, we investigate the effect of CBCP schemes on traffic patterns by characterizing the properties (i.e., existence, comparative statics) of the corresponding Nash equilibria and, in the setting when eligible users have time-invariant VoTs, develop a convex program to compute these equilibria. We further present a bi-level optimization framework to design optimal CBCP schemes to achieve a central planner's societal objectives. Finally, we conduct numerical experiments based on a case study of the San Mateo 101 Express Lanes Project, one of the first CBCP pilots. Our results demonstrate the potential of CBCP to enable low-income users to avail of the travel time savings provided by congestion pricing on ELs while having comparatively low impacts on the travel costs of other road users.