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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.
@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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/articles/10.1051/ro/2014011/
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