| The study of the statistical aspects of network traffic and congestion control are central and critical fields of research in the area of high-speed computer communication networks. The findings in these domains have an immediate practical impact on the design and implementation of future telecommunications infrastructure. In the last decade, the telecommunication industry has undergone extraordinarily rapid development and technological changes. In the first part of this dissertation, we focus on the problem of self-similarity in a network traffic. Specifically, we study the effect of routing policies on the propagation of self-similarity in a nonblocking packet switching network. We show that the degree of self-similarity of the offered traffic remains unchanged as it traverses through switches in a networking environment under different routing policies. This is shown through the analysis of the departure process of the switch. In addition, our results establish that routing policies can have a dramatic influence on the extent to which self-similarity in the arrival process impacts the performance and the design of high-speed computer networks.; In the second part of the dissertation, we turn our attention to an important congestion control problem in TCP/IP networks. Namely, we focus on the Random Early Detection (RED) algorithm. We develop a stochastic approach to model and study the behavior of RED gateways. We present an analytical framework that takes into account the feedback effect and the essential performance measures not only for RED with packet drops but also for an alternate mode in which packets are marked, instead of being dropped for Explicit Congestion Notification. Through our analytical approach, we quantify the benefits of RED and provide an insight into the performance of RED in wide variety of situations. |
