M^X/G/1 queueing system with server breakdown, Bernoulli vacation schedule under restricted admissibility policy

In this paper, we analyze a model which deals with the aspects concerning the control of the arrival process with second optional repair and Bernoulli vacation schedule. The paper deals with M^x/G/1 queueing system where after completion of a service the server either goes for a vacation of random length with probability θ(o<θ<1) or may continue to serve the next customer with probability (1-θ) if any. Both service time and vacation time follow general distribution. Unlike the usual batch arrivals queueing model, there is restriction over the admissibility of batch arrivals in which not all the arriving batches are allowed to join the queue at all times. The restricted admissibility policy differs during a busy period and a vacation period. We obtain the time dependent probability generating functions in terms of their Laplace transforms and corresponding steady state results explicitly.