The calculation of the stationary distribution for a stochastic infinite matrix is generally difficult and does not have closed form solutions, it is desirable to have simple approximations converging rapidly to this distribution. In this paper, we use the weak perturbation theory to establish analytic error bounds for the M/G/1 model. Numerical examples are carried out to illustrate the quality of the obtained error bounds.
Accepté le :
DOI : 10.1051/ro/2018027
Mots-clés : Truncation, queueing system, weak stability, algorithm
@article{RO_2018__52_4-5_1411_0,
author = {Issaadi, Badredine and Abbas, Karim and A{\"\i}ssani, Djamil},
title = {A weak perturbation theory for approximations of invariant measures in {M/G/1} model},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {1411--1428},
publisher = {EDP-Sciences},
volume = {52},
number = {4-5},
year = {2018},
doi = {10.1051/ro/2018027},
zbl = {1430.60075},
mrnumber = {3884159},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ro/2018027/}
}
TY - JOUR AU - Issaadi, Badredine AU - Abbas, Karim AU - Aïssani, Djamil TI - A weak perturbation theory for approximations of invariant measures in M/G/1 model JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2018 SP - 1411 EP - 1428 VL - 52 IS - 4-5 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2018027/ DO - 10.1051/ro/2018027 LA - en ID - RO_2018__52_4-5_1411_0 ER -
%0 Journal Article %A Issaadi, Badredine %A Abbas, Karim %A Aïssani, Djamil %T A weak perturbation theory for approximations of invariant measures in M/G/1 model %J RAIRO - Operations Research - Recherche Opérationnelle %D 2018 %P 1411-1428 %V 52 %N 4-5 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2018027/ %R 10.1051/ro/2018027 %G en %F RO_2018__52_4-5_1411_0
Issaadi, Badredine; Abbas, Karim; Aïssani, Djamil. A weak perturbation theory for approximations of invariant measures in M/G/1 model. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 4-5, pp. 1411-1428. doi : 10.1051/ro/2018027. http://archive.numdam.org/articles/10.1051/ro/2018027/
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