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On an M/G/1 queue with optional server vacations based on exhaustive service and single vacation policy

Madan K. C.

Systems Science

2009

Vol. 35, no 4

21-25

We analyze a single server queue with optional server vacations based on exhaustive service. Unlike other vacation policies, we assume that only at the completion of service of the last customer in the system, the server has the option to take a vacation or to remain idle in the system waiting for the next customer to arrive. The service times of the customers as well as the vacation times of the server have been assumed to be arbitrary (general). We use the supplementary variable technique and obtain explicit steady state results for the probability generating functions of the queue length, the expected number of customers in the queue and the expected waiting time of the customer. Some known results of the M/G/1 queue have been derived as a particular case.

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.