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TWO-CLASS ROUTING WITH ADMISSION CONTROL AND STRICT PRIORITIES

Published online by Cambridge University Press:  13 June 2017

Kenneth C. Chong ,
Shane G. Henderson  and
Mark E. Lewis
Kenneth C. Chong
Affiliation:
E-mail: kcc66@cornell.edu
Shane G. Henderson
Affiliation:
230 Rhodes Hall, Cornell University, Ithaca, NY 14850 E-mail: sgh9@cornell.edu
Mark E. Lewis
Affiliation:
221 Rhodes Hall, Cornell University, Ithaca, NY 14850 E-mail: mark.lewis@cornell.edu
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Abstract

We consider the problem of routing and admission control in a loss 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, lacks structure, 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.

Keywords

Markov decision processesqueueing controlstochastic dynamic programmingtwo-class queue
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 32 , Issue 2 , April 2018 , pp. 163 - 178
Copyright
Copyright © Cambridge University Press 2017 

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