Bulk arrival queues with server vacations (Q1264088)

The paper considers M/G/1 bulk arrival queues with server vacations. Server vacation queues are those in which the server leaves for a vacation as soon as the system becomes empty, and returns after a vacation of random duration. Two types of vacation policies are considered: (1) if the server finds no customer upon return from a vacation, he immediately leaves for another one, and so on, until he finally finds at least one customer; (2) if the server finds no customer upon return, he waits for the first customer group to arrive. We derive the server idle probabilities, waiting time distributions, and the mean system sizes.