Further Analysis of Expected Number of Departures in M/G/1 Queues with Server Vacations

In this paper, the departure processes of M/G/1 queueing systems with single server vacation and multiple server vacations are analyzed. The expressions of the LS transform of the expected number of departures during the time interval (0, t are obtained. It is shown that the LS transform of the expected number of departures during (O, t is invariant under the interchange of arrival and service rates in the initially empty M/M/1 queue in which the server begins vacations at t=0 and the length of each vacation has an exponential distribution. Simultaneously the asymptotic expansions of the expected number of departures during (0, t are also discussed. It is given that the asymptotic formula are convenient in application.