A Queueing Reward System with Several Customer Classes

Abstract

This paper considers an n-server queueing system with m customer classes distinguished by the reward associated with serving customers of that class. Our objective is to accept or reject customers so as to maximize the expected value of the rewards received over an infinite planning horizon. By making the assumptions of Poisson arrivals and a common exponential service time this problem can be formulated as an infinite horizon continuous time Markov decision problem. In §3 we customize the general algorithm for solving continuous time Markov decision problems to our queueing model. In §4 we obtain qualitative results about the form of the optimal policy. §6 reports the results of simulation tests which compare heuristic policies for our model when the service times associated with each customer class have arbitrary distributions. The “winning” policy is based on a rather intricate theorem whose proof comprises §5.

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