Sankhya: The Indian Journal of Statistics
2004, Volume 66, Pt. 1, 175--193
An $M^X/G/1$ Queue with a Bernoulli Vacation Schedule Under Restricted Admissibility Policy
Kailash C. Madan, Yarmouk University, Irbid, Jordan & Gautam Choudhury, Institute of Advanced Study in Science and Technology, Guwahati, India
SUMMARY. We consider a batch arrival queue with a Bernoulli vacation schedule, where after completion of a service the server either goes for a vacation of random length with probability $\theta(0 \le \theta \le 1)$ or may continue to serve the next unit, if any, with probability $(1 -\theta)$, under a restricted admissibility policy of arriving batches. Unlike the usual batch arrival queueing system, the restricted admissibility policy differs during a busy period and a vacation period and hence all arriving batches are not allowed to join the system at all time. We derive the steady state queue size distribution at a random point of time as well as at a departure epoch. Also we obtain some important performance measures of this model. More over, this paper attempts to unify several classes of related batch arrival queueing systems.
AMS (1991) subject classification}. Primary 60K25; secondary 60J15, 90B10.
Key words and phrases. $M^X/G/1$ queue, bernoulli schedule, vacation time, restricted admissibility policy, queue size.