An M~X/G/1 Queue with a Bernoulli Vacation Schedule Under Restricted Admissibility Policy

摘要

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 θ(0 ≤ θ ≤ 1) or may continue to serve the next unit, if any, with probability (1 - θ), 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.