Optimal pricing policies for tandem queues: Asymptotic optimality

Abstract

We study the optimal pricing problem for a tandem queueing system with an arbitrary number of stations, finite buffers, and blocking. The problem is formulated using a Markov decision process model with the objective to maximize the long-run expected time-average revenue or gain of the service provider. Our interest lies in comparing the performances of static and dynamic pricing policies in maximizing the gain. We show that the optimal static pricing policies perform as well as the optimal dynamic pricing policies when the buffer size at station 1 becomes large and the arrival rate is either small or large. More importantly, we propose two specific static pricing policies for systems with small and large arrival rates, respectively, and show that each proposed policy produces a gain converging to the optimal gain with an approximately exponential rate as the buffer size before station 1 becomes large. We learn from numerical results that the proposed static policies perform as well as optimal dynamic policies even for a moderate-sized buffer at station 1. We also learn that there exist cases where optimal static pricing policies are, however, neither optimal nor near-optimal.

Keywords:

• Tandem queueing system
• optimal pricing
• static and dynamic policies
• asymptotic optimality
• convergence rate
• Markov decision process

Acknowledgments

We would like to thank the Department Editor, the Associate Editor, and the two referees for their comments that have helped substantially improve this article.

Additional information

Notes on contributors

Tonghoon Suk

Tonghoon Suk received his PhD in operations research from Georgia Institute of Technology in 2016. He is a research scientist in IBM Thomas J. Watson Research Center. His research interests lie in optimization, applied probability, and optimal controls with applications to resource and revenue management in cloud system, communication networks, and automated AI services. His research works have appeared in journals such as Mathematics of Operations Research and Advances in Applied Probability, and conferences such as ACM SIGMETRICS, IFIP WG 7.3 Performance, IEEE Cloud, International Symposium on Computer Architecture and High Performance Computing, and American Control Conference.

Xinchang Wang

Xinchang Wang is an assistant professor of operations management in the Department of Finance and Management Science at the Carson College of Business, Washington State University (WSU). Xinchang received his PhD in operations research from Georgia Institute of Technology in 2015 and another PhD in civil engineering from the National University of Singapore in 2011. His primary research interest falls within the area of pricing and revenue management with applications to queueing service systems, logistics, and supply chain management. His research works have appeared in OR/OM-focused journals such as Queueing Systems: Theory and Applications, Naval Research Logistics, European Journal of Operational Research, and IEEE Transactions on Automatic Control, and transportation-focused journals such as Transportation Research Part B: Methodological and Transportation Research Part E: Logistics and Transportation Review.