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

Institute of Mathematics and Informatics of VU, Akademijos 4, 08663 Vilnius, Lithuania.
minkevicius.saulius@gmail.com

Received: 6 December 2011
Accepted: 7 January 2014

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.