Doubly dynamics for multi-modal networks with park-and-ride and adaptive pricing

This paper models and controls a multi-region and multi-modal transportation system, given that the travelers can adjust their mode choices from day to day, and the within-day traffic dynamics in the network also evolve over days. In particular, it considers that the city network can be partitioned into two regions (center and periphery). There are park-and-ride facilities located at the boundary between the city center region and the periphery. Travelers can either drive to the city center, or take public transit, or drive to the park-and-ride facilities and then transfer to the public transit. Travelers can “learn” from their travel experience, as well as real-time information about traffic conditions, thus will adjust their choices accordingly. It follows that the dynamic traffic pattern (within-day) in the city network will evolve over (calendar) time (day-to-day). To improve traffic efficiency in the network, an adaptive mechanism, which does not need detailed travelers’ behavioral characteristics, is developed to update parking pricing (or congestion pricing) from period to period (e.g., one period can be one month). The developed doubly dynamics methodological framework coupled with a feedback pricing mechanism unfolds and influences equilibrium system characteristics that traditional static day-to-day models cannot observe. The proposed adaptive pricing approach is practical for implementation in large-scale networks as the variables involved can be observed in real life with monitoring techniques. Also, it can contribute to reduce total social cost effectively, as shown in the numerical experiments.