The authors introduce a diffusion model to characterize approximately a statistical multiplexer for a heterogeneous set of traffic sources, which is a basis for ATM (asynchronous transfer mode) fast packet switching in the future B-ISDN (Broadband Integrated Services Digital Networks). 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, which adequately captures the correlated nature of packet arrivals and determines the statistical behavior of the buffer content. Analytical results are applied to evaluate the multiplexer's dynamic behavior, i.e., the transient packet loss probabilities at the cell and burst levels.
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