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The Compensation Approach Applied to a 2 × 2 Switch

Published online by Cambridge University Press:  27 July 2009

O. J. Boxma  and
G. J. van Houtum
O. J. Boxma
Affiliation:
CWI, P.O. Box 4079, 1009 AB Amsterdam, The Netherlands, and Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands
G. J. van Houtum
Affiliation:
Eindhoven University of Technology, Department of Mathematics and Computing Science, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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Abstract

In this paper we analyze an asymmetric 2 × 2 buffered switch, fed by two independent Bernoulli input streams. We derive the joint equilibrium distribution of the numbers of messages waiting in the two output buffers. This joint distribution is presented explicitly, without the use of generating functions, in the form of a sum of two alternating series of product-form geometric distributions. The method used is the so-called compensation approach, developed by Adan, Wessels, and Zijm.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 7 , Issue 4 , October 1993 , pp. 471 - 493
Copyright
Copyright © Cambridge University Press 1993

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