A batch arrival Bernoulli vacation queue with a random setup time under restricted admissibility policy

Gautam Choudhury and Kailash C. Madan

International Journal of Operational Research, 2007, vol. 2, issue 1, 81-97

Abstract: We consider a batch arrival queue with a Bernoulli vacation bschedule, where, after completion of a service, the server either goes for a vacation of random length with probability θ(0 ≤ θ ≤ 1) or may continue to serve the next unit, if any, with probability (1−θ), under a Restricted Admissibility (RA) policy of arriving batches with a random Setup Time (SET). Unlike the usual batch arrival queueing system, the RA-policy differs during a busy period and a vacation period and hence all arriving batches are not allowed to join the system at all times. We derive the steady state queue size distributions at a random point of time as well as at a departure epoch. Also, we obtain some important performance measures of this model. Further, we demonstrate the existence of stochastic decomposition result for this type of model.

Keywords: M x /G/1 queues; Bernoulli schedule; vacation time; random setup time; SET; restricted admissibility policy; queue size; operational research; batch arrivals; performance measures; queueing control. (search for similar items in EconPapers)
Date: 2007
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