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Optimal service-rate control of M/G/1 queueing systems using phase methods

Published online by Cambridge University Press:  01 July 2016

Kyung Y. Jo  and
Shaler Stidham Jr
Kyung Y. Jo*
Affiliation:
George Mason University
Shaler Stidham Jr*
Affiliation:
North Carolina State University
*
∗Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, U.S.A.
∗∗Department of Industrial Engineering and Graduate Program in Operations Research, North Carolina State University, Box 5511, Raleigh, NC 27650, U.S.A.
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Abstract

A new approach to the optimal control of the service rate in M/G/1 queues is introduced using the method of phases. Each customer's work requirement is approximated by a random number of exponential phases with (possibly) different parameters (a generalized hyper-Erlang distribution). Using a semi-Markov decision-process formulation, we establish monotonicity properties of optimal policies for the finite-horizon problem, by induction on the horizon length. The analysis is then extended to the discounted infinite-horizon and the long-run average-return problems. In contrast to the models in previous papers, our model is appropriate for situations where the system controller has partial information about the work requirement of a customer, specifically the number of phases (tasks) to be performed. Because it requires a multidimensional state description, the analysis of the phase-type control model may be viewed as a first step toward the solution of control models for networks of queues.

Keywords

M/G/1 QUEUECONTROL OF QUEUESSERVICE-RATE CONTROLSEMI-MARKOV DECISION PROCESSDYNAMIC PROGRAMMINGPHASE-TYPE DISTRIBUTION
Type
Research Article
Information
Advances in Applied Probability , Volume 15 , Issue 3 , September 1983 , pp. 616 - 637
Copyright
Copyright © Applied Probability Trust 1983 

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