Optimal Pricing for Tandem Queues with Finite Buffers

Abstract

We consider optimal pricing for a two-station tandem queueing system with finite buffers and price-sensitive customers. The service provider quotes prices to customers using either static or dynamic pricing. The objective is to maximize either the infinite-horizon discounted profit or the long-run average profit of the provider. We show that there exists an optimal dynamic policy that exhibits an interesting monotone structure, in which the quoted prices have greater dependency on the queue length at station 1 than at station 2, for both the discounted and long-run average problems. We then study the long-run average problem and show that the optimal static policy performs as well as the optimal dynamic policy when the buffer size at station 1 becomes large, there are no holding costs, and the arrival rate is either small or large. We learn from numerical results that for systems with small arrival rates, the optimal static policy is near optimal even when the buffer at station 1 is small and there are positive holding costs. On the other hand, for systems with arrival rates that are not small, there are cases where the optimal dynamic policy performs much better than the optimal static policy.