### Restricted admissibility of batches into an $M$/$G$/1 type bulk queue with modified Bernoulli schedule server vacations

We investigate the steady state behavior of an $M$/$G$/1 queue with modified Bernoulli schedule server vacations. Batches of variable size arrive at the system according to a compound Poisson process. However, all arriving batches are not allowed into the system. The restriction policy differs when the server is available in the system and when he is on vacation. We obtain in closed form, the steady state probability generating functions for the number of customers in the queue for various states of...