Optimal Parking Management of Connected Autonomous Vehicles

In this paper we develop a dynamic model for the parking management of connected autonomous vehicles (CAVs) in a given area with multiple parking lots. Motivated by the well-known Lotka-Volterra equations, a mathematical model is developed to incorporate the interactions among those parking garages. Parking space availability is considered as the system state, while the price of parking is used as the control variable chosen by the parking garage operators from the admissible set. By regulating parking rates, the demand can be properly distributed among the set of parking lots under consideration, which could potentially reduce traffic congestion as well as fuel consumption of CAVs. Further, we formulate an optimal control problem with the objective of maintaining the availability of each parking lot at a desired level. The optimization problem is addressed using Pontryagin's minimum principle which determines the optimum parking pricing policy. A series of numerical experiments is conducted to show the effectiveness of the proposed approach. Since the mathematical model is fairly general and can be easily modified, it is believed that the procedures presented here will be useful for the parking management of CAVs in the near future.