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

Published online by Cambridge University Press:  08 November 2012

M. Haridass  and
R. Arumuganathan
M. Haridass
Affiliation:
Department of Mathematics, PSG College of Technology, 641 004 Coimbatore, Tamil Nadu, India. [email protected]; [email protected]
R. Arumuganathan
Affiliation:
Department of Mathematics, PSG College of Technology, 641 004 Coimbatore, Tamil Nadu, India. [email protected]; [email protected]
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Abstract

In this paper, a batch arrival general bulk service queueing system with interruptedvacation (secondary job) is considered. At a service completion epoch, if the server findsat least ‘a’ customers waiting for service say ξ, heserves a batch of min (ξ, b) customers, whereb ≥ a. On the other hand, if the queue length is atthe most ‘a-1’, the server leaves for a secondary job (vacation) ofrandom length. It is assumed that the secondary job is interrupted abruptly and the serverresumes for primary service, if the queue size reaches ‘a’, during thesecondary job period. On completion of the secondary job, the server remains in the system(dormant period) until the queue length reaches ‘a’. For the proposedmodel, the probability generating function of the steady state queue size distribution atan arbitrary time is obtained. Various performance measures are derived. A cost model forthe queueing system is also developed. To optimize the cost, a numerical illustration isprovided.

Keywords

Bulk arrivalsingle serverbatch servicevacationinterruption
Type
Research Article
Information
RAIRO - Operations Research , Volume 46 , Issue 4 , October 2012 , pp. 305 - 334
Copyright
© EDP Sciences, ROADEF, SMAI, 2012

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