A novel stochastic dynamic programming model for park-and-ride autonomous vehicles

The park-and-ride service is an effective way to alleviate traffic congestion and parking pressure in urban central areas. Existing park-and-ride facilities are typically designed for human-driven vehicles (HVs), failing to account for autonomous vehicle (AVs) operations. The occupant-free relocation capability of AVs enhances the flexibility of park-and-ride systems; however, more complex park-and-ride options for AVs also present managerial challenges. In this paper, we propose a bi-level dynamic optimization model to obtain the regulation scheme for both HVs and AVs under the park-and-ride scenario. There are four options for AVs: (a) Single-mode driving and parking (the same as HVs), where users travel directly to their destination by vehicle; (b) single-mode driving and parking elsewhere, where users take AVs to destinations and then AVs drive away to a farther parking lot; (c) standard park-and-ride (the same as HVs), where AVs arrive at the transfer station and users transfer to public transportation; (d) ride and parking elsewhere, where AVs arrive at the transfer station and then drive away to a farther parking lot, and users transfer to public transportation. Considering the uncertainty of park-and-ride demand and user choices, a bi-level stochastic dynamic programming model is developed. In this framework, the lower-level model determines the regulation scheme with the system optimization objective, whereas the upper-level model revises this scheme according to the user equilibrium principle. To cope with the curse of dimensionality in stochastic dynamic programming models, we propose a sequentially nested iterative algorithm that linearizes the optimal value function to solve an approximate optimal scheme efficiently. Numerical examples are conducted based on a real-world problem-scale dataset. The results demonstrate that our method can provide optimal park-and-ride schemes for HVs and AVs in real time. The stochastic dynamic programming model can provide a more foresighted and reliable solution. As the proportion of AVs increases, the performance advantage of our method becomes more significant over the benchmark methods. In contexts with high parking pressure, a subsidy scheme can be implemented to optimize the park-and-ride service and enhance system resilience.