Steady-state analysis of ATM multiplexer with variable input rate through diffusion approximation

We propose an approximation formula for the stationary distribution of the buffer content Qt of a fluid model for an ATM multiplexer in which the input rate process Rt is given as a Gaussian process of the form Rt = m + ∝t−∞ h(t − s) dws, where ws is a standard Wiener process. To derive the approximation formula, we approximate the behavior of Qt by a diffusion process on R(−∞, ∞) having no reflecting barrier. Simulation results show that the formula provides good approximate values. The formula is similar to the one derived by H. Kobayashi and Q. Ren for multiple On-Off types of traffic, but probabilistically it seems more reasonable. Our model is fairly general and it covers almost all variable input rate processes proposed so far for ATM multiplexer. In this sense, the new approximation formula provides a useful tool to analyse and estimate the congestion in the buffer of the ATM multiplexer.