Optimal Pricing and Admission Control in a Queueing System with Periodically Varying Parameters

Authors:
Seunghwan Yoon;Mark E. Lewis
Affiliations:
Department of Industrial and Operations Engineering, University of Michigan, 1205 Beal Avenue, Ann Arbor, MI 48109-2117, USA syoon@engin.umich.edu;Department of Industrial and Operations Engineering, University of Michigan, 1205 Beal Avenue, Ann Arbor, MI 48109-2117, USA melewis@engin.umich.edu
Venue:
Queueing Systems: Theory and Applications
Year:
2004

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Abstract

We consider congestion control in a nonstationary queueing system. Assuming that the arrival and service rates are bounded, periodic functions of time, a Markov decision process (MDP) formulation is developed. We show under the infinite horizon discounted and average reward optimality criteria, for each fixed time, optimal pricing and admission control strategies are nondecreasing in the number of customers in the system. This extends stationary results to the nonstationary setting. Despite this result, the problem still seems intractable. We propose an easily implementable pointwise stationary approximation (PSA) to approximate the optimal policies, suggest a heuristic to improve the implementation of the PSA and verify its usefulness via a numerical study.