Stochastic performance bounds by state space reduction

In this work, we present a methodology to derive stochastic bounds on discrete-time Markov chains. It is well known that the state space explosion problem of Markovian models may make them numerically intractable. We propose to evaluate bounding models with reduced size state spaces, in order to be able to analyze considered systems for larger values of parameters. Moreover, these bounding models are comparable in the sense of sample-path (strong) ordering with the underlying model. Obviously, this method does not provide exact values, however, it has the following advantages: the errors are stochastically bounded, and it is suitable to analyze transient behaviors, and the stationary ones, as well. We present how this methodology may be applied to evaluate cell loss rates in ATM switches.