Volume 48, Number 3, July-September 2014
|Page(s)||349 - 363|
|Published online||21 March 2014|
Fluid limits for the queue length of jobs in multiserver open queueing networks
Institute of Mathematics and Informatics of VU, Akademijos 4, 08663 Vilnius,
Accepted: 7 January 2014
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.
Mathematics Subject Classification: 60K25 / 60G70 / 60F17
Key words: Mathematical models of information systems / performance evaluation / queueing theory / multiserver open queueing network / heavy traffic / limit theorem / queue length of jobs
© EDP Sciences, ROADEF, SMAI, 2014
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