Stochastic Bounds Applied to the End to End QoS in Communication Systems

End to end QoS of communication systems is essential for users but their performance evaluation is a complex issue. The abstraction of such systems are usually given by multidimensional Markov processes whose analysis is very difficult and even intractable, if there is no specific solution form. In this study, we propose an algorithm in order to automatically derive aggregated Markov processes providing upper and lower bounds on performance measures. We applied the algorithm to the analysis of an open tandem queueing network with rejection in order to derive performance measure bounds. Parametric aggregation schemes have been proposed in order to compute bounds on loss probabilities and end to end mean delays. Therefore a tradeoff between the accuracy of the bound and the size of considered Markov chains is possible.