Fractal Network Traffic Analysis with Applications

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Liu, Jian
Copeland, John A.
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Today, the Internet is growing exponentially, with traffic statistics that mathematically exhibit fractal characteristics: self-similarity and long-range dependence. With these properties, data traffic shows high peak-to-average bandwidth ratios and causes networks inefficient. These problems make it difficult to predict, quantify, and control data traffic. In this thesis, two analytical methods are used to study fractal network traffic. They are second-order self-similarity analysis and multifractal analysis. First, self-similarity is an adaptability of traffic in networks. Many factors are involved in creating this characteristic. A new view of this self-similar traffic structure related to multi-layer network protocols is provided. This view is an improvement over the theory used in most current literature. Second, the scaling region for traffic self-similarity is divided into two timescale regimes: short-range dependence (SRD) and long-range dependence (LRD). Experimental results show that the network transmission delay separates the two scaling regions. This gives us a physical source of the periodicity in the observed traffic. Also, bandwidth, TCP window size, and packet size have impacts on SRD. The statistical heavy-tailedness (Pareto shape parameter) affects the structure of LRD. In addition, a formula to estimate traffic burstiness is derived from the self-similarity property. Furthermore, studies with multifractal analysis have shown the following results. At large timescales, increasing bandwidth does not improve throughput. The two factors affecting traffic throughput are network delay and TCP window size. On the other hand, more simultaneous connections smooth traffic, which could result in an improvement of network efficiency. At small timescales, in order to improve network efficiency, we need to control bandwidth, TCP window size, and network delay to reduce traffic burstiness. In general, network traffic processes have a Hlder exponent a ranging between 0.7 and 1.3. Their statistics differ from Poisson processes. From traffic analysis, a notion of the efficient bandwidth, EB, is derived. Above that bandwidth, traffic appears bursty and cannot be reduced by multiplexing. But, below it, traffic is congested. An important finding is that the relationship between the bandwidth and the transfer delay is nonlinear.
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