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On the optimality of LEPT and μc rules for parallel processors and dependent arrival processes

Part of: Operations research and management science

Published online by Cambridge University Press:  01 July 2016

Arie Hordijk  and
Ger Koole
Arie Hordijk*
Affiliation:
University of Leiden
Ger Koole
Affiliation:
University of Leiden
*
* Postal address: Dept. of Mathematics and Computer Science, University of Leiden P.O. Box 9512, 2300 RA Leiden, The Netherlands.
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Abstract

In this paper we study scheduling problems of multiclass customers on identical parallel processors. A new type of arrival process, called a Markov decision arrival process, is introduced. This arrival process can be controlled and allows for an indirect dependence on the numbers of customers in the queues. As a special case we show the optimality of LEPT and the µc-rule in the last node of a controlled tandem network for various cost structures. A unifying proof using dynamic programming is given.

Keywords

STOCHASTIC SCHEDULINGDYNAMIC PROGRAMMINGDEPENDENT ARRIVALS

MSC classification

Primary: 90B22: Queues and service
Secondary: 90C40: Markov and semi-Markov decision processes
Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 4 , December 1993 , pp. 979 - 996
Copyright
Copyright © Applied Probability Trust 1993 

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Footnotes

**

Present address: CWI, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands.

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