Dynamics in credit-based mobility systems: Convergence to periodic mode usage equilibrium

This study examines the flow, behavior, and credit dynamics under a credit charge-cum-reward (CCR) scheme that operates periodically. In this scheme, travelers incur an end-of-period credit cost, determined by their periodic mode usage patterns, in addition to regular mode-specific time and monetary costs. As such, travelers are incentivized to make decisions minimizing individual periodic travel costs rather than focusing solely on daily cost minimization. To formulate a CCR-scheme-based dynamic system, we analyze travelers’ intra-period and inter-period learning behaviors and propose two adaptation rules—myopic and forward-looking—for travelers making day-to-day choices. We provide optimal strategies for each traveler under these two rules and derive stability conditions for the dynamic system. Our findings demonstrate that, under mild conditions, both rules, along with travelers’ learning behaviors, lead the dynamic system to converge to a periodic mode usage equilibrium (PUE), where each traveler minimizes their periodic travel costs. Numerical examples illustrate the variations in system performance and traveler behavior across two adaptation rules. This study not only explores the evolution of a CCR-scheme-based dynamic mobility system toward the PUE but also highlights the distinct adaptation behaviors under periodic mobility management policies.