Optimal Pricing and Admission Control in a Queueing System

with Periodically Varying Parameters


Seunghwan Yoon and Mark E. Lewis
Industrial and Operations Engineering Department
University of Michigan
1205 Beal Avenue
Ann Arbor, MI 48109-2117


We consider congestion control in a non-stationary queueing system. Assuming that the arrival and service rates are measurable, bounded, and periodic functions of time, a Markov decision process (MDP) formulation is developed. We show under infinite horizon discounted and average reward optimality criterion, for each fixed time, optimal pricing and admission

control strategies are non-decreasing in the number of customers in the system. This extends

well-known stationary results to the non-stationary setting. However, even with this insight,

solution of the problem is intractable. We propose an easily implementable pointwise stationary

approximation (PSA) to approximate the optimal policies in each case, and suggest a heuristic

to improve the implementation of the PSA and verify its usefulness via a numerical study.