Guaranteed bounds for steady state performance measures of a Markov chain with applications to high speed data networks

A method for approximation of a discrete Markov chain by a chain of considerably smaller dimension which is based on the duality theory of optimization is proposed. A novel feature of the approach is that it provides guaranteed upper and lower bounds for the performance indices defined on the steady state distribution of the original system. Several families of guaranteed bounds are defined, and the algorithms for their computation are developed. The properties of suggested bounds are illustrated by applying the approach to the problem of the statistical multiplexer dimensioning in asynchronous transfer mode (ATM) networks