A diffusion approximation analysis of an ATM statistical multiplexer with multiple types of traffic .II. Time-dependent solutions

We introduce a diffusion model to approximately characterize 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 determine the statistical behavior of the buffer content. Some simulated sample paths and estimated correlation functions (or the correlograms) are 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