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Product Forms for Stochastic Interference Systems

Published online by Cambridge University Press:  27 July 2009

N.M. Van Dijk  and
J.P. Veltkamp
N.M. Van Dijk
Affiliation:
Department of Econometrics The Free University Amsterdam, The Netherlands
J.P. Veltkamp
Affiliation:
Twente University, The Netherlands
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Abstract

Systems are studied that consist of interfering components which are alternatively active (busy) and passive (idle) for random periods. Such systems naturally arise from the performance evaluation of computer models. A concrete invariance condition is imposed on the interferences allowed. Under this condition, the steady-state vector of active components is shown to be of product form as well as to be robust to distributional forms of active and passive periods. The proof is simple and self-contained. A number of concrete and generic examples is provided. These include resource sharing mechanisms, hierarchical circuit switchings, parallel processing, priorities, and breakdowns.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 2 , Issue 3 , July 1988 , pp. 355 - 376
Copyright
Copyright © Cambridge University Press 1988

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