Transient analysis of fluid model for ATM statistical multiplexer

Abstract

We analyze the transient behavior of a fluid model of ATM multiplexer, in which the input process is generated by a Markov modulated rate process (MMR Process). This model is a natural extension of the on-off-type multi-entry queueing model which has been widely used for modeling ATM multiplexers with bursty inputs. The Laplace transform of the joint distribution of the buffer content and the state of the input process is obtained by solving a system of partial differential equations. The unknown functions included in the solution are determined from the boundary conditions by using eigenvalues and eigenvectors of a key matrix. By taking a limit of the solution, the state probabilities in the steady-state are written explicitly. An effective lower bound of the relaxation time is also presented. In case of an on-off-type input fluid model with phase-type on/off period distributions, the equations for the eigenvalues and eigenvectors of the key matrix are reduced to more concrete ones using the Laplace transforms of the on/off period distributions. The lower bound of the relaxation time is also reduced to the maximum among the relaxation times of phase-type renewal processes governing the on/off periods of the inputs. © 1995.