An approximate analysis of a stochastic fluid flow model applied to an Asynchronous Transfer Mode multiplexer

In this paper, we propose a new approach to solve stochastic fluid flow models applied to the analysis of cell loss of an ATM multiplexer. Existing stochastic fluid flow models have been analyzed by using linear differential equations. In case of large state space, however, analyzing stochastic fluid flow model without numerical errors is not easy. To avoid these numerical errors and to analyze stochastic fluid flow model with large state space, we develop a new computational algorithm. Instead of solving differential equations directly, this approach uses iterative and numerical method without calculating eigenvalues, eigenvectors and boundary coefficients. As a result, approximate solutions and upper and lower bounds are obtained. This approach can be applied to stochastic fluid flow model having general Markov chain structure as well as to the superposition of heterogeneous ON–OFF sources. It can be extended to Markov process having non-exponential sojourn times.