A Diffusion Approximation of ATM Traffic for Statistical Multiplexing

We introduce a diffusion process model to approximately characterize the output process of a statistical multiplexer for a heterogeneous set of traffic sources. Statistical multiplexing is the basic principle for ATM (asynchronous transfer mode) fast packet switching adopted by the B-ISDN (Broadband Integrated Services Digital Networks) architecture. This diffusion process can then be approximated by a multi-dimensional Ornstein-Uhlenbeck process. The packet arrival process is shown to be a Gaussian (but not Markov) process, which adequately captures the correlated nature of packet arrivals and determine the statistical behavior of the buffer content. Some simulated sample paths and estimated correlation functions will be shown to verify the diffusion approximation. We then apply our analytical results to evaluate the multiplexer’s dynamic behavior, i.e., the time-dependent packet loss probabilities and the transient periods at the cell and burst levels.