A stochastic process is said to exhibit long range dependence (LRD) structure when it has a hyperbolically decaying autocorrelation function. Self-similar (or fractal) processes (both exact and asymptotic) are among those LRD processes which are widely used. Traditional traffic models. on the other hand. typically possess some form of Markovian structure and display short range dependence (SRD) only. Several recent papers have shown that traditional traffic models may be inadequate for modeling real traffic. Instead, self-similar stochastic processes were proposed as more accurate models of certain categories of traffic (e.g.. Ethernet traffic, WAN traffic, variable-bit-rate video) which will be transported in ATM networks.

Due to the distinct differences between these two classes of models, their implications for network design and performance estimation will be significantly different. In this thesis. we will start with our work on modeling real traffic based on LRD traffic models. Then we will introduce our fast simulation technique for simulating the behavior of LRD traffic over ATM network. We will show that, some of the congestion control schemes proposed in the literature under the traditional models may fail under LRD models. In the last part, we will propose a new congestion control scheme which may work well under LRD traffic models.