Discrete‐time queueing systems with Markovian preemptive vacations

In this contribution we investigate discrete‐time queueing systems with vacations. A framework is constructed that allows for studying numerous different vacation systems, including a.o. classical vacation systems like the exhaustive and limited vacation systems as well as queueing systems with service interruptions. Using a probability generating functions approach, we obtain steady‐state performance measures such as moments of queue content at different epochs and of customer delay. The usefulness of vacation models in teletraffic is then illustrated by means of some more practical applications (priority queueing, CSMA/CD).