The vacation model studied is an M/G/1 queueing system in which the server attends iteratively to ‘secondary’ or ‘vacation’ tasks at ‘primary’ service completion epochs, when the primary queue is exhausted. The time-dependent and steady-state distributions of the backlog process are obtained via their Laplace transforms. With this as a stepping stone, the ergodic distribution of the depletion time is obtained. Two decomposition theorems that are somewhat different in character from those available in the literature are demonstrated. State space methods and simple renewal-theoretic tools are employed.
