On M/D/1 queue with deterministic server vacations

We study a single server vacation queue with Poisson arrivals, deterministic service of constant duration b (> 0) and deterministic vacations of constant duration d (> 0) and designate this model as M/D/D/1. After completion of each service, the server may take a vacation with probability p or may continue working in the system with probability 1 - p. We obtain time-dependent as well as steady state probability generation functions for the number in the system. For the steady state we obtain explicitly the mean number and the mean waiting time for the system and for the queue. All known results of the M/D/1 queue are derived as a special case. Finally, a numerical illustration is discussed.