Discrete-time queues with general service times and general server interruptions

摘要

In this contribution; we investigate a discrete-time single-sever 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 at random slot boundaries. From these results, closed-form expressions for various performance measures, such as mean and variance of the buffer occupancy, can be established. As an application, we show that this model is able to assess performance of low-priority traffic in a two-priority HOL scheduling discipline. We then illustrate our approach with some numerical examples.