Discrete-time queueing systems with vacations

Dieter Fiems

INRIA Sophia Antipolis and Ghent University


In this talk, we focus on single server queueing systems where the server is unavailable to waiting customers from time to time. In queueing parlance, one says that the server leaves for a vacation and these models are therefore referred to as vacation models. Such abstract models turn out to be useful in the performance assessment of multi-class queueing systems and of queueing systems with unreliable servers. In particular, the vacations models under consideration here share the property that vacations can interrupt customers in service. After the vacation, the server then either continues the service of the interrupted customer, repeats the service from the start, ... . Using a classical queueing theory approach based on the extensive use of probability generating functions, various performance measures are obtained. We then use a vacation model to assess the performance of the low-priority customers in a multi-class preemptive priority system.

[Dieter Fiems]
[INRIA Sophia Antipolis and Ghent University]