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On Maxima and Minima of Partial Sums of Strongly Interchangeable Random Variables

Published online by Cambridge University Press:  27 July 2009

Teunis J. Ott  and
J. George Shanthikumar
Teunis J. Ott
Affiliation:
Belicore Morristown, New Jersey 07960
J. George Shanthikumar
Affiliation:
University of California at Berkeley, Berkeley, California 94720
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Abstract

We introduce the concept of “strong interchangeability” of random vectors. Strongly interchangeable random vectors arise naturally in packetized voice channels, M/G/1 queues, symmetric queueing networks, and other standard symmetric distributions. We study some properties of strongly interchangeable random vectors. We show that if (X1, …, XN) is a strongly interchangeable random vector, then even though there is no Markov property, taboo probabilities can be used to compute the joint distribution of ŽN = min1≤n≤N σnk=IXk and ZN = max1≤n≤N σnk=1Xk. For a special instance of this problem that arises in packetized voice communication, it is shown that the resulting algorithm essentially has a complexity of order N4. When ( σnk=1Xk, n = 1,… N) is an associated random vector bound for the joint distribution of ŽN and ZN are obtained and applied to the packetized voice communication problem.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 4 , Issue 3 , July 1990 , pp. 319 - 332
Copyright
Copyright © Cambridge University Press 1990

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References

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