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On a random interval graph and the maximum throughput rate in the system GI/G/1/0

Published online by Cambridge University Press:  01 July 2016

Wim M. Nawijn*
Affiliation:
University of Twente
*
Postal address: University of Twente, Faculty of Applied Mathematics, P.O. Box 217, 7500 AE Enschede, The Netherlands.

Abstract

The paper gives an explicit expression for the expectation of the maximum attainable fraction of served customers in the long run for the single-server loss system GI/G/1/0, under the assumption of perfect information regarding the sequences {Xi, i = 1, 2, ·· ·} and {Yi, i = 1, 2, ·· ·} of interarrival times and service times, respectively. A heavy traffic result for this fraction is obtained for the system GI/M/1/0. The general result is based on an analysis of the random interval graph corresponding to the random intervals {[Ti, Ti + Yi), i = 1, 2, ·· ·}, in which {Ti} denotes the sequence of arrival epochs.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1991 

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