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Stochastic bounds and deterministic bounds (for instance network calculus) are promising methods to analyze QoS requirements for high speed networks. Indeed, it is sufficient to prove that a bound of the real performance satisfies the guarantee. However, stochastic bounds are quite difficult to prove and often require some sample-path proofs. We present a new method based on stochastic ordering, algorithmic derivation of simpler Markov chains, and numerical analysis of these chains. The performance indices defined by reward functions are stochastically bounded by reward functions computed on much simpler or smaller Markov chains. This leads to an important reduction of numerical complexity.