Geodesic
The M X /M/1 queue with working breakdown
RAIRO - Operations Research - Recherche Opérationnelle, Tome 48 (2014) no. 3, pp. 399-413

Voir la notice de l'article provenant de la source Numdam

In this paper, we consider a batch arrival MX/M/1 queue model with working breakdown. The server may be subject to a service breakdown when it is busy, rather than completely stoping service, it will decrease its service rate. For this model, we analyze a two-dimensional Markov chain and give its quasi upper triangle transition probability matrix. Under the system stability condition, we derive the probability generating function (PGF) of the stationary queue length, and then obtain its stochastic decomposition, which shows the relationship with that of the classical MX/M/ 1 queue without vacation or breakdown. Besides, we also give the Laplace-Stieltjes transform (LST) of the stationary waiting time distribution of an arbitrary customer in a batch. Finally, some numerical examples are given to illustrate the effect of the parameters on the system performance measures.

DOI : 10.1051/ro/2014014
Classification : 68M20, 60K20, 90B22
Keywords: MX/M/1 queue, working breakdown, probability generating function (PGF), Laplace-Stieltjes transform (LST), waiting time distribution, stochastic decomposition 
@article{RO_2014__48_3_399_0,
     author = {Liu, Zaiming and Song, Yang},
     title = {The $M^{X}/M/1$ queue with working breakdown},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {399--413},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {3},
     year = {2014},
     doi = {10.1051/ro/2014014},
     zbl = {1297.90019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2014014/}
}
TY  - JOUR
AU  - Liu, Zaiming
AU  - Song, Yang
TI  - The $M^{X}/M/1$ queue with working breakdown
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2014
SP  - 399
EP  - 413
VL  - 48
IS  - 3
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/ro/2014014/
DO  - 10.1051/ro/2014014
LA  - en
ID  - RO_2014__48_3_399_0
ER  - 
%0 Journal Article
%A Liu, Zaiming
%A Song, Yang
%T The $M^{X}/M/1$ queue with working breakdown
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2014
%P 399-413
%V 48
%N 3
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/ro/2014014/
%R 10.1051/ro/2014014
%G en
%F RO_2014__48_3_399_0
Liu, Zaiming; Song, Yang. The $M^{X}/M/1$ queue with working breakdown. RAIRO - Operations Research - Recherche Opérationnelle, Tome 48 (2014) no. 3, pp. 399-413. doi: 10.1051/ro/2014014

Cité par Sources :