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Fluid limits for the queue length of jobs in multiserver open queueing networks

Published online by Cambridge University Press:  21 March 2014

Saulius Minkevičius
Saulius Minkevičius*
Affiliation:
Institute of Mathematics and Informatics of VU, Akademijos 4, 08663 Vilnius, Lithuania.. minkevicius.saulius@gmail.com
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Abstract

The object of this research in the queueing theory is a theorem about the Strong-Law-of-Large-Numbers (SLLN) under the conditions of heavy traffic in a multiserver open queueing network. SLLN is known as a fluid limit or fluid approximation. In this work, we prove that the long-term average rate of growth of the queue length process of a multiserver open queueing network under heavy traffic strongly converges to a particular vector of rates. SLLN is proved for the values of an important probabilistic characteristic of the multiserver open queueing network investigated as well as the queue length of jobs.

Keywords

Mathematical models of information systemsperformance evaluationqueueing theorymultiserver open queueing networkheavy trafficlimit theoremqueue length of jobs
Type
Research Article
Information
RAIRO - Operations Research , Volume 48 , Issue 3 , July 2014 , pp. 349 - 363
Copyright
© EDP Sciences, ROADEF, SMAI, 2014

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