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.
Mots-clés : mathematical models of information systems, performance evaluation, queueing theory, multiserver open queueing network, heavy traffic, limit theorem, queue length of jobs
@article{RO_2014__48_3_349_0,
author = {Minkevi\v{c}ius, Saulius},
title = {Fluid limits for the queue length of jobs in multiserver open queueing networks},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {349--363},
publisher = {EDP-Sciences},
volume = {48},
number = {3},
year = {2014},
doi = {10.1051/ro/2014011},
mrnumber = {3264382},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ro/2014011/}
}
TY - JOUR AU - Minkevičius, Saulius TI - Fluid limits for the queue length of jobs in multiserver open queueing networks JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2014 SP - 349 EP - 363 VL - 48 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2014011/ DO - 10.1051/ro/2014011 LA - en ID - RO_2014__48_3_349_0 ER -
%0 Journal Article %A Minkevičius, Saulius %T Fluid limits for the queue length of jobs in multiserver open queueing networks %J RAIRO - Operations Research - Recherche Opérationnelle %D 2014 %P 349-363 %V 48 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2014011/ %R 10.1051/ro/2014011 %G en %F RO_2014__48_3_349_0
Minkevičius, Saulius. Fluid limits for the queue length of jobs in multiserver open queueing networks. RAIRO - Operations Research - Recherche Opérationnelle, Tome 48 (2014) no. 3, pp. 349-363. doi : 10.1051/ro/2014011. http://archive.numdam.org/articles/10.1051/ro/2014011/
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