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An M/G/1 queue with second optional service and Bernoulli schedule server vacations

Madan K.C., Abu-Dayyeh W., Saleh M.F.

Systems Science

2002

Vol. 28, nr 3

51-62

We study an M/G/1 queue with second optional service and Bernoulli schedule server vacations. Poisson arrivals with mean arrival rate lambda ([right angle bracket] 0), all demand the first 'essential' service, whereas only some of them demand the second 'optional' service. The service times of the first essential service are assumed to follow a general (arbitrary) distribution with distribution function B( nu ) and that of the second optional service are exponential with mean service time 1/ mu /sub 2/ ( mu /sub 2/ [right angle bracket] 0). We have assumed that after completion of a service, the server takes Bernoulli schedule server vacations. The time-dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results have been derived explicitly in closed form. Some known results have been derived as particular cases.

On M/D/1 queue with deterministic server vacations

Madan K.C., Saleh M.F.

Systems Science

2001

Vol. 27, nr 2

107-118

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.