Modeling and solving the optimal allocation-pricing of public parking resources problem in urban-scale network. (July 2020) - Wang, Pengfei; Guan, Hongzhi; Liu, Peng
Highlights: Auction-based mechanisms are proposed to maximize the social surplus through optimizing the allocation-pricing of reservable parking resources. The proposed mechanisms not only simplify the users' bidding procedures but also ensure that users express their preferences truthfully, even in the case of non-optimal allocation of parking permits. It is theoretically demonstrateed that the computational efficiencies of the proposed mechanisms are much higher than that of traditional methods in the worst-case scenario. Some numerical experiments in urban-scale networks are presented to confirm the analytical results about reservable parking resources. For unreservable parking facilities, a region-based optimal dynamic parking pricing is obtained, which results in a "bang-bang control". Abstract: This paper models and solves the optimal allocation-pricing of reservable parking resources and the pricing of unreservable parking resources, respectively. For reservable parking facility, a MP-DGS (modified proxy Demange-Gale-Sotomayor) mechanism and combinatorial system (integration of direct and evolutionary methods) are adopted to maximize the social surplus through optimizing the allocation-pricing of parking permits. As a result, it is found that: (i) the proposed approaches not only simplify the users' bidding procedures but also ensure the users express their preference truthfully even under the situation of non-optimal parking permits allocation; (ii) in homogeneous case (parking periods for all users are the same), it is theoretically demonstrated that the MP-DGS mechanism is more efficient than the traditional mechanisms in the worst-case scenario; (iii) in heterogeneous case (users are heterogeneous in desired parking timing and duration), time-dependent parking permits are taken into account. The ranking of the algorithm time complexity in the worst-case scenario is that direct method = evolutionary method < Leonard mechanism = VCG (Vickrey-Clarke-Groves) mechanism, and the combinatorial system not only solves out the optimal allocation-pricing results effectively but also ensures the optimal results can be obtained in a shorter time. In addition, for unreservable parking facility, we formulate a dynamic social optimum as a stochastic control problem and then obtain a region-based optimal dynamic parking pricing. Through theoretical analysis, it is revealed that depending on the realization of the queue length due to the cruising-for-parking, the region-based optimal dynamic parking pricing can be divided into two patterns, furthermore, each pattern results in a "bang-bang" control.