Stochastic Ordering based Markov process aggregations: applications to tandem queues

We present a general algorithm based on the stochastic ordering theory to provide a bounding aggregation for a given Markov process. Our main goal is to provide bounds on the performance measures of interest by considering the aggregated process without computing the exact values which are in general numerically difficult or intractable due to the well-known state space explosion. The stochastic comparison has been largely applied in performance evaluation however the state space is generally assumed to be totally ordered which provides less accurate bounds for multidimensional Markov processes. The algorithm is proposed by assuming a preorder on the state space, and it is applied in this paper to an open tandem queues system, in order to compute loss probabilities bounds.ou