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The Equilibrium Distribution for a Clocked Buffered Switch

Published online by Cambridge University Press:  27 July 2009

Steven Jaffe
Steven Jaffe*
Affiliation:
Department of Mathematics University of Southern California Los angeles, California 90089-1113
*
Current address: Department of Mathematics, Vassar College, Poughkeepsie, New York 12601.
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Abstract

A 2-by-2 buffered switch is the basic element of certain parallel data-processing networks. For a switch fed by two independent Bernoulli input streams, we find the joint distribution of the number of messages waiting in the two buffers at equilibrium, in the form of a bivariate generating function. The derivation uses complex-variable techniques developed by Kingman and by Flatto and McKean for the “shortest queue problem.” A number of asymptotic results are given, the principal one being the variance of the total number of waiting messages in the heavy-traffic limit.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 6 , Issue 4 , October 1992 , pp. 425 - 438
Copyright
Copyright © Cambridge University Press 1992

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