The paper is designated to the analysis of queueing systems, arising in the network theory and communications theory (called multiphase queueing systems, tandem queues or series of queueing systems). Also we note that multiphase queueing systems can be useful for modelling practical multi-stage service systems in a variety of disciplines, especially on manufacturing (assembly lines), computer networking (packet switch structures), and in telecommunications (e.g. cellular mobile networks), etc. This research presents heavy traffic limit theorems for the cumulative idle time in multiphase queues. In this work, functional limit theorems are proved for the values of important probability characteristics of the queueing system (a cumulative idle time of a customer).
@article{RO_2005__39_2_75_0,
author = {Minkevi\v{c}ius, Saulius and Stei\v{s}\={u}nas, Stasys},
title = {About the cumulative idle time in multiphase queues},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {75--85},
publisher = {EDP-Sciences},
volume = {39},
number = {2},
year = {2005},
doi = {10.1051/ro:2005008},
mrnumber = {2181792},
zbl = {1092.90017},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ro:2005008/}
}
TY - JOUR AU - Minkevičius, Saulius AU - Steišūnas, Stasys TI - About the cumulative idle time in multiphase queues JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2005 SP - 75 EP - 85 VL - 39 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro:2005008/ DO - 10.1051/ro:2005008 LA - en ID - RO_2005__39_2_75_0 ER -
%0 Journal Article %A Minkevičius, Saulius %A Steišūnas, Stasys %T About the cumulative idle time in multiphase queues %J RAIRO - Operations Research - Recherche Opérationnelle %D 2005 %P 75-85 %V 39 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro:2005008/ %R 10.1051/ro:2005008 %G en %F RO_2005__39_2_75_0
Minkevičius, Saulius; Steišūnas, Stasys. About the cumulative idle time in multiphase queues. RAIRO - Operations Research - Recherche Opérationnelle, Tome 39 (2005) no. 2, pp. 75-85. doi : 10.1051/ro:2005008. http://archive.numdam.org/articles/10.1051/ro:2005008/
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