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A new ordering for stochastic majorization: theory and applications

Part of: Distribution theory - Probability Special processes

Published online by Cambridge University Press:  01 July 2016

Cheng-Shang Chang
Cheng-Shang Chang*
Affiliation:
IBM Thomas J. Watson Research Center
*
∗Postal address: IBM Research Division, T. J. Watson Research Center, P.O. Box 704, Yorktown Heights, NY 10598, USA.
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Abstract

In this paper, we develop a unified approach for stochastic load balancing on various multiserver systems. We expand the four partial orderings defined in Marshall and Olkin, by defining a new ordering based on the set of functions that are symmetric, L-subadditive and convex in each variable. This new partial ordering is shown to be equivalent to the previous four orderings for comparing deterministic vectors but differs for random vectors. Sample-path criteria and a probability enumeration method for the new stochastic ordering are established and the ordering is applied to various fork-join queues, routing and scheduling problems. Our results generalize previous work and can be extended to multivariate stochastic majorization which includes tandem queues and queues with finite buffers.

Keywords

LOAD BALANCINGSTOCHASTIC CONVEXITYMAJORIZATION ORDERINGROUTINGSCHEDULINGFORK-JOIN QUEUES

MSC classification

Primary: 60E05: Distributions
Secondary: 60K25: Queueing theory
Type
Research Article
Information
Advances in Applied Probability , Volume 24 , Issue 3 , September 1992 , pp. 604 - 634
Copyright
Copyright © Applied Probability Trust 1992 

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