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Interchange arguments in stochastic scheduling

Published online by Cambridge University Press:  14 July 2016

Philippe Nain ,
Pantelis Tsoucas  and
Jean Walrand
Philippe Nain*
Affiliation:
INRIA
Pantelis Tsoucas
Affiliation:
University of Maryland
Jean Walrand*
Affiliation:
University of California, Berkeley
*
∗Postal address: INRIA-Sophia Antipolis, Av. E. Hugues, 06565 Valbonne, France.
∗∗∗Postal address: EECS and Electronics Research Laboratory, University of California, Berkeley, CA 94720, USA.
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Abstract

Interchange arguments are applied to establish the optimality of priority list policies in three problems. First, we prove that in a multiclass tandem of two ·/M/1 queues it is always optimal in the second node to serve according to the cµ rule. The result holds more generally if the first node is replaced by a multiclass network consisting of ·/M/1 queues with Bernoulli routing. Next, for scheduling a single server in a multiclass node with feedback, a simplified proof of Klimov's result is given. From it follows the optimality of the index rule among idling policies for general service time distributions, and among pre-emptive policies when the service time distributions are exponential. Lastly, we consider the problem of minimizing the blocking in a communication link with lossy channels and exponential holding times.

Keywords

OPTIMAL POLICIESTANDEM QUEUESMULTICLASS NETWORKS
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 4 , December 1989 , pp. 815 - 826
Copyright
Copyright © Applied Probability Trust 1989 

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Footnotes

Work performed while this author was visiting the Systems Research Center, University of Maryland, College Park, supported by the Office of Naval Research through grant number N00014–84-K-0614.

∗∗

Present address: Computer Science, IBM Thomas J. Watson Research Center, P.O. Box 704, Yorktown Heights, NY 10598, USA.

The work of this author was supported in part by the NSF Engineering Research Centers Program NSFD-CDR-88–03012.

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