  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)
in a multi-lane highway with an express lane. 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
express lane. 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 North American CBCP pilots.
Our results demonstrate the potential of CBCP to enable low-income travelers to
avail of the travel time savings provided by congestion pricing on express
lanes while having comparatively low impacts on the travel costs of other road
users.
