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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
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.
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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.

Keywords

STABLE SETSINGLE-SERVER LOSS SYSTEMOPTIMISATION
Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 4 , December 1991 , pp. 945 - 956
Copyright
Copyright © Applied Probability Trust 1991 

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