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Two competing queues with linear costs and geometric service requirements: the μc-rule is often optimal

Published online by Cambridge University Press:  01 July 2016

J. S. Baras ,
A. J. Dorsey  and
A. M. Makowski
J. S. Baras*
Affiliation:
University of Maryland
A. J. Dorsey*
Affiliation:
IBM—Federal Systems Division
A. M. Makowski*
Affiliation:
University of Maryland
*
∗Postal address: Electrical Engineering Department, University of Maryland, College Park, MD 20742, USA.
∗∗ Postal address: IBM—Federal Systems Division, 21 Firstfield Road, Gaithersburg, MD 20748, USA.
∗Postal address: Electrical Engineering Department, University of Maryland, College Park, MD 20742, USA.
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Abstract

A discrete-time model is presented for a system of two queues competing for the service attention of a single server with infinite buffer capacity. The service requirements are geometrically distributed and independent from customer to customer as well as from the arrivals. The allocation of service attention is governed by feedback policies which are based on past decisions and buffer content histories. The cost of operation per unit time is a linear function of the queue sizes. Under the model assumptions, a fixed prioritization scheme, known as the μc-rule, is shown to be optimal for the expected long-run average criterion and for the expected discounted criterion, over both finite and infinite horizons. Two different approaches are proposed for solving these problems. One is based on the dynamic programming methodology for Markov decision processes, and assumes the arrivals to be i.i.d. The other is valid under no additional assumption on the arrival stream and uses direct comparison arguments. In both cases, the sample path properties of the adopted state-space model are exploited.

Keywords

DISCRETE-TIME MODELSINGLE SERVERINFINITE BUFFERFEEDBACKSAMPLE PATHS
Type
Research Article
Information
Advances in Applied Probability , Volume 17 , Issue 1 , March 1985 , pp. 186 - 209
Copyright
Copyright © Applied Probability Trust 1985 

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Footnotes

This work was supported in part by the Department of Energy under Grant DOE-AC01-78ET 29244, A5 and the National Science Foundation under Grant ECS-82-04451.

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