Analysis of Multi-Server Queueing Systems with Station and Server Vacation

This paper deals with finite-population, single and multi-server queueing systems with two classes of vacation mechanisms : station vacation and server vacation. In the first one, all the servers take vacation simultaneously whenever the system becomes empty, and they also return to the system at the same time, i.e., station vacation is group vacation for all servers. For the second class of vacation, each server takes its own vacation whenever it completes a service and finds no customers waiting in the queue. We show a method for modeling theses queueing systems using Generalized Stochastic Petri Nets. We develop the general form of the underlying CTMCs, and we give two algorithms for computing the infinitesimal generator Q for systems with s servers (s≥1). Hence, several quantitative performance measures can be obtained for queueing systems with station or server vacation. this work. Key-Words. Multi-server Queueing systems, Server vacation, Station vacation, Generalized Stochastic Petri nets, Performance Analysis.