document: 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 -LRB- > 0 -RRB- and deterministic vacations of constant duration d -LRB- > 0 -RRB- 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
doc_bio_tags: O O O O B I I O O O O O O O O B I O B I O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I I O O O O O O O O O O O O O O O B I O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
extractive_keyphrases: deterministic server vacations poisson arrivals deterministic service deterministic vacations steady state probability generation functions mean number mean waiting time
abstractive_keyphrases: m/d/1 queue m/d/d/1 model time-dependent probability generation functions