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Dynamic Pricing and Matching for Two-Sided Queues

Motivated by diverse applications in sharing economy and online marketplaces, we consider optimal pricing and matching control in a two-sided queueing system. We assume that heterogeneous customers and servers arrive to the system with price-dependent arrival rates. The compatibility between servers and customers is specified by a bipartite graph. Once a pair of customer and server are matched, they depart from the system instantaneously. The objective is to maximize the long-run average profits of the system while minimizing average waiting time. We first propose a static pricing and max-weight matching policy, which achieves O(√ n) optimality rate when all of the arrival rates are scaled by n. We further show that a dynamic pricing and modified max-weight matching policy achieves an improved O(n1/3) optimality rate. In addition, we propose a constraint generation algorithm that solves value function approximation of the MDP and demonstrate strong numerical performance of this algorithm.