Performance Evaluation of Telecommunication Systems with Repeated Attempts and Two Servers Classes

摘要

Repeated attempts and servers heterogeneity arise in various practical areas as telecommunications, computer systems and cellular mobile networks. In this paper, we propose a numerical approach for evaluating performances of telecommunication systems with finite population, repeated attempts of users whose request was refused due to the lack of available servers (resources) and two servers classes, using the Generalized Stochastic Petri Nets (GSPNs) model as a support. One of the major drawbacks of the use of this high-level formalism in performance evaluation of large systems is the state space explosion problem which increases when considering repeated attempts and several servers classes. Hence, this paper aims to present an approach which allows a direct computing of the infinitesimal generator describing the users behavior and servers allocation, without generating nor storing the reachability set In addition, we develop the formulas of the main stationary performance indices as a function of the system parameters, the stationary probabilities and independently of the reachability set markings. Through numerical examples, we discuss the effect of retrials and servers heterogeneity on the systems performances.