An algorithm approach to bounding aggregations of multidimensional Markov chains

We analyze transient and stationary behaviors of multidimensional Markov chains defined on large state spaces. In this paper, we apply stochastic comparisons on partially ordered state which could be very interesting for performance evaluation of computer networks. We propose an algorithm for bounding aggregations in order to derive upper and lower performance measure bounds on a reduced state space. We study different queueing networks with rejection in order to compute blocking probability and end to end mean delay bounds. Parametric aggregation schemes are studied in order to propose an attractive solution: given a performance measure threshold, we vary the parameter values to obtain a trade-off between the accuracy of bounds and the computation complexity.