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 the
server, the average number of customers as well as their average waiting time in the
queue and the system. Many special cases of interest including complete admissibility,
partial admissibility and no server vacations have been discusssed. Some known
results are derived as particular cases of our model.