# 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.