Date of Award

Spring 2002

Document Type

Thesis

Degree Name

Bachelor of Arts

Department

Mathematics

First Advisor

Dr. Lewis Barnett

Abstract

It is critical to properly understand the nature of network traffic in order to effectively design models describing network behavior. These models are usually used to simulate network traffic, which in turn are used to construct congestion control techniques, perform capacity planning studies, and/or evaluate the behavior of new protocols. Using the wrong models could lead to potentially serious problems such as delayed packet transmissions or an increase in packet drop rates.

Traditionally, packet arrivals were assumed to follow a Poisson arrival process. Although Poisson processes have several properties that make them easy to work with, they do not accurately describe certain traits seen in network traffic. Recent studies such as [1] and [2] have shown that LAN and WAN traffic exhibits a different kind of behavior than one would expect to see from Poisson processes. One characteristic that differs is burstiness. A burst, or a period of intense activity[3], has no natural length in network traffic. If network traffic were to be a Poisson process, it would have a "characteristic burst length that would be smoothed by averaging over a long enough period of time" [1]. Instead, network traffic appears to be bursty in all time scales; it exhibits fractal-like behavior, a behavior described statistically by a self-similar process. A self-similar process by definition is one whose correlational structure remains unchanged regardless of the time scale being used. Thus, the burst lengths in a self-similar process will not be smoothed out. Instead, there will be bursty periods which themselves contain bursty periods, etc.

In Section 2 we discuss the related work that has been previously done on the self-similarity of network traffic. After discussing the process used to capture data in Section 3, we will statistically determine the fractal-like behavior in Section 4 and present estimates for this behavior. In Section 5 we will examine the results of our analyses, and then summarize and compare these results to those from previous studies in Section 6. Finally, acknowledgements are made in Section 7 and an Appendix containing more detailed information on the analysis performed (including source code and sample input and output for all the scripts used) is presented in Section 8.

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