On transient queue-size distribution in the batch-arrivals system with a single vacation policy

Wojciech M. Kempa

Kybernetika (2014)

  • Volume: 50, Issue: 1, page 126-141
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Kempa, Wojciech M.. "On transient queue-size distribution in the batch-arrivals system with a single vacation policy." Kybernetika 50.1 (2014): 126-141. <http://eudml.org/doc/261130>.

@article{Kempa2014,
abstract = {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.},
author = {Kempa, Wojciech M.},
journal = {Kybernetika},
keywords = {batch Poisson arrivals; queue-size distribution; renewal theory; single vacation; transient state; batch Poisson arrivals; queue-size distribution; renewal theory; single vacation; transient state},
language = {eng},
number = {1},
pages = {126-141},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On transient queue-size distribution in the batch-arrivals system with a single vacation policy},
url = {http://eudml.org/doc/261130},
volume = {50},
year = {2014},
}

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
PB - Institute of Information Theory and Automation AS CR
VL - 50
IS - 1
SP - 126
EP - 141
AB - 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.
LA - eng
KW - batch Poisson arrivals; queue-size distribution; renewal theory; single vacation; transient state; batch Poisson arrivals; queue-size distribution; renewal theory; single vacation; transient state
UR - http://eudml.org/doc/261130
ER -

References

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