Accuracy of Strong and Weak Comparisons for Network of Queues

Quality of performance measure bounds is crucial for an accurate dimensioning of computer network resources. We study stochastic comparisons of multidimensional Markov processes for which quantitative analysis could be intractable if there is no specific solution form. On partially ordered state space, different stochastic orderings can be defined as the strong or the less constrained weak ordering. The goal of the present paper is to compare these two orderings with respect the quality of derived bounds. We propose to study a system similar to a Jackson network except that queues have finite capacity. Different bounding systems are built either in the sense of the strong ordering with hard constraints, or in the sense of the weak ordering with less ones. The proofs of the stochastic comparisons are done using the coupling and the increasing set methods, with an intuitive event based formalism. The qualities of bounding systems are compared regarding to blocking probabilities.