A diffusion approximation analysis of an ATM statistical multiplexer with multiple types of traffic. - I. Equilibrium state solutions

A multi-dimensional diffusion model is introduced to characterize the "on-off" sources behavior in an asynchronous transfer mode (ATM) statistical multiplexer, where multiple types of traffic are concentrated. Under a reasonable set of assumptions, this diffusion process can then be approximated by a multi-dimensional Ornstein-Uhlenbeck process, which is a Gaussian Markov process. The packet arrival process is shown to be a Gaussian (but not Markov) process, and this process determines the statistical behavior of the buffer content. An expression is derived for the joint probability distribution of the buffer content and "on-off" sources in the equilibrium state. The final solution form is given in terms of the eigenfunctions of Weber´s equation.