An M/G/1 queue with finite population and gated service discipline

A queueing model with finite customer population (an M/G/1//N model), multiple server vacations and gated service policy is considered. For such a model, the steady state probabilities and the customers' waiting time are analyzed. Numerical results for the mean waiting times are obtained and used to draw conclusions on the system performance and to compare the present model with the corresponding model with exhaustive service. The comparison shows that, under variations on the mean vacation period and on the offered load, the two models behave in completely different ways. This is more apparent in case of large vacation periods and seems to be a consequence of the vacation principle.