Two-Class Routing with Admission Control and Strict Priorities. Chong, K. C., Henderson, S. G., & Lewis, M. E. Probability in the Engineering and Informational Sciences, 32(2):163-178, 2018.
Two-Class Routing with Admission Control and Strict Priorities [pdf]Paper  abstract   bibtex   
We consider the problem of routing and admission control in a service system featuring two classes of arriving jobs (high-priority and low-priority jobs) and two types of servers, in which decision-making for high-priority jobs is forced, and rewards influence the desirability of each of the four possible routing decisions. We seek a policy that maximizes expected long-run reward under both the discounted reward and long-run average reward criteria, and formulate the problem as a Markov decision process. When the reward structure favors high-priority jobs, we demonstrate that there exists an optimal monotone switching curve policy with slope of at least −1. When the reward structure favors low-priority jobs, we demonstrate that the value function, in general, is fairly unstructured, which complicates the search for structure in optimal policies. However, we identify conditions under which optimal policies can be characterized in greater detail. We also examine the performance of heuristic policies in a brief numerical study.

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