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A Batch Arrival Queue with a Random Setup Time Under Bernoulli Vacation Schedule  

Choudhury, Gautam (Mathematical Sciences Division, Institute of Advanced Study in Science and Technology)
Tadj, Lotfi (Department of Management and e-Business, School of Business Administration, American University)
Paul, Maduchanda (Mathematical Sciences Division, Institute of Advanced Study in Science and Technology)
Publication Information
Management Science and Financial Engineering / v.15, no.2, 2009 , pp. 1-21 More about this Journal
Abstract
We consider an $M^x/G/1$ queueing system with a random setup time under Bernoulli vacation schedule, where the service of the first unit at the completion of each busy period or a vacation period is preceded by a random setup time, on completion of which service starts. However, after each service completion, the server may take a vacation with probability p or remain in the system to provide next service, if any, with probability (1-p). This generalizes both the $M^x/G/1$ queueing system with a random setup time as well as the Bernoulli vacation model. We carryout an extensive analysis for the queue size distributions at various epochs. Further, attempts have been made to unify the results of related batch arrival vacation models.
Keywords
$M^x/G/1$ Queue; Setup Time; Vacation Time; Bernoulli Schedule Vacation; Queue Size;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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