A batch arrival Bernoulli vacation queue with a random setup time under restricted admissibility policy. (1st December 2006)

• Record Type: Journal Article
• Authors: Choudhury, Gautam; Madan, Kailash C.
• Is Part Of: International journal of operational research. Volume 2:Number 1(2007)
• Page Start: 81
• Page End: 97
• Publication Date: 2006-12-01
• Subjects: Mx/G/1 queues -- Bernoulli schedule -- vacation time -- random setup time -- SET -- restricted admissibility policy -- queue size -- operational research -- batch arrivals -- performance measures -- queueing control; Operations research -- Periodicals; 003.05
• Languages: English
• ISSNs: 1745-7645

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.