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SUPPLEMENTARY VARIABLE TECHNIQUE IN STOCHASTIC MODELS

Published online by Cambridge University Press:  01 April 2000

Attahiru Sule Alfa  and
T. S. S. Srinivasa Rao
Attahiru Sule Alfa
Affiliation:
Department of Industrial and Manufacturing Systems Engineering, The University of Windsor, Windsor, Ontario N9B 3P4, Canada, E-mail: alfa@uwindsor.ca
T. S. S. Srinivasa Rao
Affiliation:
Institute for Systems Studies and Analyses, Defence R & D Organisation, Metcalfe House, Delhi-110 054, India, tssr@mailcity.com
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Abstract

In this article, we formalize the framework for the supplementary variable technique in stochastic models. Specifically, we show that the use of remaining or elapsed times (or any metric) as supplementary variables leads to the notion of forward or backward Chapman–Kolmogorov equations, respectively. We further show that for a class of queueing systems, using remaining time as the supplementary variable makes analysis simpler.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 14 , Issue 2 , April 2000 , pp. 203 - 218
Copyright
© 2000 Cambridge University Press

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