Approximate analysis of an GI/M/∞ queue using the strong stability method

In this work, we are interested in the approximation of the stationary characteristics of the GI/M/∞ system by those of an M/M/∞ system. In other words, we propose to study the strong stability of the M/M/∞ system (ideal system) when the arrivals flow is subject to a small perturbation (the GI/M/∞ is the resulting perturbed system). For this purpose, we first determine the approximation conditions of the characteristics of the perturbed queuing system, and under these conditions we obtain the stability inequalities of the stationary distribution of the queue size. To evaluate the performance of the proposed method, we develop an algorithm which allows us to compute the various theoretical results and which is executed on some systems (Coxian2/M/∞ and E2/M/∞) in order to compare its output results with those of simulation.