Quantitative estimates in an M2/G2/1 priority queue with non-preemptive priority: The method of strong stability

The main purpose of this article is to use the strong stability method to approximate the characteristics of the M2/G2/1 priority system with non-preemptive priority by those of the M/G/1 queue, when the arrival intensity of the priority stream is sufficiently small. This last queue is simpler and more exploitable. For this, we clarify the stability conditions and next obtain stability quantitative estimates with an exact computation of constants. From these theoretical results, we elaborate an algorithm allowing to verify the approximation conditions and to provide the made numerical error. In order to have an idea about the efficiency of this approach, we consider a concrete example whose results are compared with those obtained by our simulator.