Analysis of the M/G b /1 Queue by the Arrival Time Approach

We analyze bulk service queues using the arrival time approach of Chae et al. (2001). As a result, the decomposition property of the M/G/1 queue with generalized vacations is extended to the queue in which the batch size is exactly a constant b. We also demonstrate that the arrival time approach is useful for relating the time-average queue length PGF to that of the departure time, both for the queue in which the batch size is as big as possible but up to the maximum of constant b. The case that the batch size is a random variable is also briefly mentioned.