Error bounds on practical approximation for two tandem queue with blocking and non-preemptive priority

Real life queueing network problems are often very complicated and are usually solved only through approximations. It is therefore very important to justify these approximations and estimate the resulting error. In this work, we approximate the characteristics of the model [M2/G2/1→⋅/G/1/1][M2/G2/1→⋅/G/1/1] tandem queue, with non-preemptive priority, by those of the classical model [M/G/1→⋅/G/1/1][M/G/1→⋅/G/1/1] tandem queue, when the arrival intensity of the priority stream is sufficiently small. This classical queueing network is simpler and more exploitable. Using the strong stability approach, we obtain explicit upper bounds for the error of the approximation. From these theoretical results, we develop an algorithm which allows us to verify the approximation conditions and provide the error made. Finally, numerical examples and simulation studies are presented to illustrate the efficiency of the proposed algorithm.