In this paper we develop a continuous-time stochastic dynamic model for the optimal parking management of connected autonomous vehicles (CAVs) in the presence of multiple parking lots within a given area. Inspired by the well-known Lotka-Volterra equations, a mathematical model is developed to explicitly incorporate the interactions among those parking garages under consideration. Time-dependent parking space availability is considered as the system state, while the dynamic price of parking is naturally used as the control input which can be properly chosen by the parking garage operators from the admissible set. By regulating parking rates, the total demand for parking can be distributed among the set of parking lots under question. Further, we formulate an optimal control problem (called Bolza problem) with the objective of maintaining the availability (managing the demand) of each parking garage at a desired level, which could potentially reduce traffic congestion as well as fuel consumption of CAVs. Based on the necessary conditions of optimality given by Pontryagin’s minimum principle (PMP), we develop a computational algorithm to address the nonlinear optimization problem and formally prove its convergence. A series of Monte Carlo simulations is conducted under various scenarios and the corresponding optimization problems are solved determining the optimal pricing policy for each parking lot. Since the stochastic dynamic model is general and the control inputs, i.e., parking rates, are easy to implement, it is believed that the procedures presented here will shed light on the parking management of CAVs in the near future.

在本文中，我们开发了一个连续时间随机动力学模型，用于在给定区域内存在多个停车场的情况下，对连接的自动驾驶汽车（CAV）进行最佳停车管理。受著名的Lotka-Volterra方程的启发，开发了一个数学模型，以明确纳入考虑中的那些停车场之间的相互作用。随时间变化的停车位可用性被视为系统状态，而停车的动态价格自然被用作控制输入，停车库操作员可以从允许的集合中正确选择。通过调节停车费率，可以将总停车需求分配到所讨论的那组停车场中。进一步，我们制定了一个最优控制问题（称为Bolza问题），目的是将每个停车场的可用性（管理需求）保持在所需水平，这有可能减少交通拥堵以及CAV的燃料消耗。基于庞特里亚金最小原理（PMP）给出的最优性的必要条件，我们开发了一种计算算法来解决非线性优化问题并正式证明其收敛性。在各种情况下进行了一系列的蒙特卡洛模拟，并解决了相应的优化问题，从而确定了每个停车场的最优定价策略。由于随机动态模型是通用的，并且控制输入（例如停车率）易于实现，