Geodesic
On transient queue-size distribution in the batch-arrivals system with a single vacation policy
Kybernetika, Tome 50 (2014) no. 1, pp. 126-141

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

A queueing system with batch Poisson arrivals and single vacations with the exhaustive service discipline is investigated. As the main result the representation for the Laplace transform of the transient queue-size distribution in the system which is empty before the opening is obtained. The approach consists of few stages. Firstly, some results for a ``usual'' system without vacations corresponding to the original one are derived. Next, applying the formula of total probability, the analysis of the original system on a single vacation cycle is brought to the study of the ``usual'' system. Finally, the renewal theory is used to derive the general result. Moreover, a numerical approach to analytical results is discussed and some illustrative numerical examples are given.
DOI : 10.14736/kyb-2014-1-0126
Classification : 60K25, 90B22
Keywords: batch Poisson arrivals; queue-size distribution; renewal theory; single vacation; transient state 
@article{10_14736_kyb_2014_1_0126,
     author = {Kempa, Wojciech M.},
     title = {On transient queue-size distribution in the batch-arrivals system with a single vacation policy},
     journal = {Kybernetika},
     pages = {126--141},
     publisher = {mathdoc},
     volume = {50},
     number = {1},
     year = {2014},
     doi = {10.14736/kyb-2014-1-0126},
     mrnumber = {3195008},
     zbl = {1288.90011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-1-0126/}
}
TY  - JOUR
AU  - Kempa, Wojciech M.
TI  - On transient queue-size distribution in the batch-arrivals system with a single vacation policy
JO  - Kybernetika
PY  - 2014
SP  - 126
EP  - 141
VL  - 50
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-1-0126/
DO  - 10.14736/kyb-2014-1-0126
LA  - en
ID  - 10_14736_kyb_2014_1_0126
ER  - 
%0 Journal Article
%A Kempa, Wojciech M.
%T On transient queue-size distribution in the batch-arrivals system with a single vacation policy
%J Kybernetika
%D 2014
%P 126-141
%V 50
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-1-0126/
%R 10.14736/kyb-2014-1-0126
%G en
%F 10_14736_kyb_2014_1_0126
Kempa, Wojciech M. On transient queue-size distribution in the batch-arrivals system with a single vacation policy. Kybernetika, Tome 50 (2014) no. 1, pp. 126-141. doi: 10.14736/kyb-2014-1-0126

Cité par Sources :