A DISCRETE MAP PH/1 QUEUE WITH VACATIONS AND EXHAUSTIVE TIME-LIMITED SERVICE/

We consider a single-server queue in which the server attends to a que ue only for a limited period of time and then goes on to other queues, in which case we say it proceeds on a vacation. We obtain results for the probability densities of the number of customers in the system at an arbitrary time, during vacation, and during service; the customer waiting time distribution; and the amount of work in the system at pol ling instants and at the start of a vacation. The results are extended to the case of multiple vacations during a cycle. We show that the le ngth of a visit to a time-limited service system has a phase type dist ribution. The work is carried out in discrete time.