A batch arrival Bernoulli vacation queue with a random setup time under restricted admissibility policy (Q885679)

Summary: 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 \(\theta\) (\(0 \leq\theta\leq 1\)) or may continue to serve the next unit, if any, with probability \((1-\theta)\), 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.