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Sample Path Criteria for Weak Majorization

Part of: Special processes

Published online by Cambridge University Press:  01 July 2016

Panayotis D. Sparaggis ,
Don Towsley  and
Christos G. Cassandras
Panayotis D. Sparaggis*
Affiliation:
University of Massachusetts, Amherst
Don Towsley*
Affiliation:
University of Massachusetts, Amherst
Christos G. Cassandras*
Affiliation:
University of Massachusetts, Amherst
*
* Postal address: Department of Electrical and Computer Engineering
** Department of Computer Science, University of Massachusetts, Amherst, MA 01003, USA.
* Postal address: Department of Electrical and Computer Engineering
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Abstract

We present two forms of weak majorization, namely, very weak majorization and p-weak majorization that can be used as sample path criteria in the analysis of queueing systems. We demonstrate how these two criteria can be used in making comparisons among the joint queue lengths of queueing systems with blocking and/or multiple classes, by capturing an interesting interaction between state and performance descriptors. As a result, stochastic orderings on performance measures such as the cumulative number of losses can be derived. We describe applications that involve the determination of optimal policies in the context of load-balancing and scheduling.

Keywords

MAJORIZATIONSTOCHASTIC ORDERINGBLOCKINGROUTINGSCHEDULING

MSC classification

Primary: 60K99: None of the above, but in this section
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 26 , Issue 1 , March 1994 , pp. 155 - 171
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

This work was partly supported by an IBM Graduate Fellowship Award and by NSF under contracts ECS-8801912 and NCR-9116183.

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