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Stochastic majorization of random variables by proportional equilibrium rates

Published online by Cambridge University Press:  01 July 2016

J. George Shanthikumar
J. George Shanthikumar*
Affiliation:
University of California, Berkeley
*
∗Postal address: School of Business Administration, University of California, Berkeley, CA 94720, USA.
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Abstract

The equilibrium rate rY of a random variable Y with support on non-negative integers is defined by rY(0) = 0 and rY(n) = P[Y = n – 1]/P[Y – n], Let (j = 1, …, m; i = 1,2) be 2m independent random variables that have proportional equilibrium rates with (j = 1, …, m; i = 1, 2) as the constant of proportionality. When the equilibrium rate is increasing and concave [convex] it is shown that , …, ) majorizes implies , …, for all increasing Schur-convex [concave] functions whenever the expectations exist. In addition if , (i = 1, 2), then

Keywords

CONVEXITYBIRTH-DEATH QUEUEQUEUEING NETWORKS
Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 4 , December 1987 , pp. 854 - 872
Copyright
Copyright © Applied Probability Trust 1987 

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