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Optimal pricing for tandem queues with finite buffers

  • Xinchang WangEmail author
  • Sigrún Andradóttir
  • Hayriye Ayhan
Article

Abstract

We consider optimal pricing for a two-station tandem queueing system with finite buffers, communication blocking, and price-sensitive customers whose arrivals form a homogeneous Poisson process. The service provider quotes prices to incoming customers using either a static or dynamic pricing scheme. There may also be a holding cost for each customer in the system. The objective is to maximize either the discounted profit over an infinite planning horizon or the long-run average profit of the provider. We show that there exists an optimal dynamic policy that exhibits a monotone structure, in which the quoted price is non-decreasing in the queue length at either station and is non-increasing if a customer moves from station 1 to 2, for both the discounted and long-run average problems under certain conditions on the holding costs. We then focus on 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 and no holding cost, the optimal static policy produces a gain quite close to the optimal gain even when the buffer at station 1 is small. 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.

Keywords

Tandem queueing systems Markov decision processes Static pricing Dynamic pricing Monotone structure Asymptotic optimality 

Mathematics Subject Classification

60J28 90B22 90C40 

Notes

Supplementary material

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of BusinessMississippi State UniversityMississippi StateUSA
  2. 2.H. Milton Stewart School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

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