Discrete-time queues with generally distributed service times and renewal-type server interruptions

In this contribution, we investigate a discrete-time single-server queue subjected to server interruptions. Server interruptions are modeled as an on/off process with geometrically distributed on-periods and generally distributed off-periods. As message lengths can exceed one time-slot, different operation modes are considered, depending on whether service of an interrupted message continues, partially restarts or completely restarts after an interruption. For all alternatives, we establish expressions for the steady-state probability generating functions (pgf) of the buffer contents at message departure times and random slot boundaries, of the unfinished work at random slot boundaries, the message delay, and the lengths of the idle and busy periods. From these results, closed-form expressions for various performance measures, such as mean and variance of the buffer occupancy and message delay, can be established. As an application, we show that this model is able to assess performance of a multi-class priority scheduling system. We then illustrate our approach with some numerical examples.