Numerical investigation of finite-source multiserver systems with different vacation policies

Systems with vacations are usually modeled and analyzed by queueing theory, and almost all works assume that the customer source is infinite and the arrival process is Poisson. This paper aims to present an approach for modeling and analyzing finite-source multiserver systems with single and multiple vacations of servers or all stations, using the Generalized Stochastic Petri nets model. We show how this high level formalism, allows a simple construction of detailed and compact models for such systems and to obtain easily the underlying Markov chains. However, for real vacation systems, the models may have a huge state space. To overcome this problem, we give the algorithms for automatically computing the infinitesimal generator, for the different vacation policies. In addition, we develop the formulas of the main exact stationary performance indices. Through numerical examples, we discuss the effect of server number, vacation rate and vacation policy on the system’s performances.