Stochastic Poisson game for an online decentralized and coordinated parking mechanism

• Develop stochastic Poisson game based online decentralized coordinated parking guidance.
• Prove the existence and the uniqueness of the equilibrium of the stochastic Poisson game.
• Develop distributed algorithms and prove its convergence to the equilibrium.

This paper proposes a decentralized and coordinated online parking mechanism (DCPM), which seeks to reduce parking congestion at multiple parking facilities in a central business district (CBD) through guiding the parking decisions of a parking coordination group. To establish this DCPM, this study develops a stochastic Poisson game to model the competitions among parking vehicles en route at multiple parking facilities. The equilibrium condition for the proposed stochastic Poisson game is formulated through involving travelers’ parking choice behavior described by multinomial logit model. Furthermore, we prove that the stochastic Poisson game is a potential game with a unique equilibrium. A simultaneously updating distributed algorithm is developed to search the equilibrium solution of the DCPM. Its convergence is proved by both mathematical analysis and numerical experiments. The numerical experiments are conducted to test the efficiency of the DCPM, based on a real-world CBD covering Guicheng Community, Nanhai District at Foshan in China. The performance of the DCPM is compared to three greedy strategies following the nearest first, cheapest first, and least cruise first policies, respectively. The experimental results demonstrate that the DCPM significantly reduces cruise vehicles and average cruise distance per vehicle from all other three greedy strategies; the least cruise first strategy, which takes advantage of the real-time open spots information at parking facilities, performs better than the nearest first and the cheapest first strategies without the access to real-time information. The DCPM can further improve the benefit of the real-time information. Additionally, in terms of walking distance and parking cost, the DCPM provide a trade-off solution between the nearest first and the cheapest first strategies.