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

RAIRO - Operations Research - Recherche Opérationnelle (2014)

- Volume: 48, Issue: 3, page 349-363
- ISSN: 0399-0559

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topMinkevičius, Saulius. "Fluid limits for the queue length of jobs in multiserver open queueing networks." RAIRO - Operations Research - Recherche Opérationnelle 48.3 (2014): 349-363. <http://eudml.org/doc/275089>.

@article{Minkevičius2014,

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.},

author = {Minkevičius, Saulius},

journal = {RAIRO - Operations Research - Recherche Opérationnelle},

keywords = {mathematical models of information systems; performance evaluation; queueing theory; multiserver open queueing network; heavy traffic; limit theorem; queue length of jobs; queue-length of jobs},

language = {eng},

number = {3},

pages = {349-363},

publisher = {EDP-Sciences},

title = {Fluid limits for the queue length of jobs in multiserver open queueing networks},

url = {http://eudml.org/doc/275089},

volume = {48},

year = {2014},

}

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

PB - EDP-Sciences

VL - 48

IS - 3

SP - 349

EP - 363

AB - 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.

LA - eng

KW - mathematical models of information systems; performance evaluation; queueing theory; multiserver open queueing network; heavy traffic; limit theorem; queue length of jobs; queue-length of jobs

UR - http://eudml.org/doc/275089

ER -

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