Analysis of a MX/G(a,b)/1 queueing system with vacation interruption

M. Haridass; R. Arumuganathan

RAIRO - Operations Research - Recherche Opérationnelle (2012)

  • Volume: 46, Issue: 4, page 305-334
  • ISSN: 0399-0559

Abstract

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In this paper, a batch arrival general bulk service queueing system with interrupted vacation (secondary job) is considered. At a service completion epoch, if the server finds at least ‘a’ customers waiting for service say ξ, he serves a batch of min (ξ, b) customers, where b ≥ a. On the other hand, if the queue length is at the most ‘a-1’, the server leaves for a secondary job (vacation) of random length. It is assumed that the secondary job is interrupted abruptly and the server resumes for primary service, if the queue size reaches ‘a’, during the secondary job period. On completion of the secondary job, the server remains in the system (dormant period) until the queue length reaches ‘a’. For the proposed model, the probability generating function of the steady state queue size distribution at an arbitrary time is obtained. Various performance measures are derived. A cost model for the queueing system is also developed. To optimize the cost, a numerical illustration is provided.

How to cite

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Haridass, M., and Arumuganathan, R.. "Analysis of a MX/G(a,b)/1 queueing system with vacation interruption." RAIRO - Operations Research - Recherche Opérationnelle 46.4 (2012): 305-334. <http://eudml.org/doc/275067>.

@article{Haridass2012,
abstract = {In this paper, a batch arrival general bulk service queueing system with interrupted vacation (secondary job) is considered. At a service completion epoch, if the server finds at least ‘a’ customers waiting for service say ξ, he serves a batch of min (ξ, b) customers, where b ≥ a. On the other hand, if the queue length is at the most ‘a-1’, the server leaves for a secondary job (vacation) of random length. It is assumed that the secondary job is interrupted abruptly and the server resumes for primary service, if the queue size reaches ‘a’, during the secondary job period. On completion of the secondary job, the server remains in the system (dormant period) until the queue length reaches ‘a’. For the proposed model, the probability generating function of the steady state queue size distribution at an arbitrary time is obtained. Various performance measures are derived. A cost model for the queueing system is also developed. To optimize the cost, a numerical illustration is provided.},
author = {Haridass, M., Arumuganathan, R.},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {bulk arrival; single server; batch service; vacation; interruption},
language = {eng},
number = {4},
pages = {305-334},
publisher = {EDP-Sciences},
title = {Analysis of a MX/G(a,b)/1 queueing system with vacation interruption},
url = {http://eudml.org/doc/275067},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Haridass, M.
AU - Arumuganathan, R.
TI - Analysis of a MX/G(a,b)/1 queueing system with vacation interruption
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 2012
PB - EDP-Sciences
VL - 46
IS - 4
SP - 305
EP - 334
AB - In this paper, a batch arrival general bulk service queueing system with interrupted vacation (secondary job) is considered. At a service completion epoch, if the server finds at least ‘a’ customers waiting for service say ξ, he serves a batch of min (ξ, b) customers, where b ≥ a. On the other hand, if the queue length is at the most ‘a-1’, the server leaves for a secondary job (vacation) of random length. It is assumed that the secondary job is interrupted abruptly and the server resumes for primary service, if the queue size reaches ‘a’, during the secondary job period. On completion of the secondary job, the server remains in the system (dormant period) until the queue length reaches ‘a’. For the proposed model, the probability generating function of the steady state queue size distribution at an arbitrary time is obtained. Various performance measures are derived. A cost model for the queueing system is also developed. To optimize the cost, a numerical illustration is provided.
LA - eng
KW - bulk arrival; single server; batch service; vacation; interruption
UR - http://eudml.org/doc/275067
ER -

References

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