Optimal Dynamic Supply of Parking Permits Under Uncertainties: A Stochastic Control Approach

This paper proposes an optimal dynamic supply of parking permits under uncertainties in the mixed traffic environment of regular vehicles (RVs) and autonomous vehicles (AVs). The uncertainties from queuing delay and cruising-for-parking time, respectively, are derived from parking permit holders’ unascertainable early arrival/late departure and the randomness of vehicle speed for cruising-for-parking users. We formulate the dynamic system optimum as a stochastic optimal control problem, aiming to minimize the total time lost for all parking users. On this basis, we express the optimality condition as Hamilton-Jacobi-Bellman equation and propose an optimal control strategy for dynamic supply of parking permits (called optimal parking supply scheme). The proposed scheme is determined by two observable and measurable variables, i.e., queuing time and cruising-for-parking time. We find that the scheme can significantly reduce the total system time lost, especially when the uncertainty from parking permit holders is at a high level or the percentage of AVs is small. Finally, a case study of a selected sample area in Beijing is conducted, which verifies the efficiency of the proposed scheme numerically.