| 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 data networks inefficient. These problems make it difficult to predict, quantify, and control data traffic, in contrast to the traditional Poisson-distributed traffic in telephone networks. In this thesis, two analytical methods are used to study fractal network traffic. They are second-order self-similarity analysis and multifractal analysis. Using a number of experiments, the following results towards characterizing and quantifying the network traffic processes have been achieved:; 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 is provided. This view is an improvement over the theory used in most current literature, which assumes that the traffic self-similarity is solely based on the heavy-tailed file-size distribution.; 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 (RTT time) 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 quantify traffic burstiness is derived from the self-similarity property.; Furthermore, studies of fractal traffic with multifractal analysis have given more interesting and applicable results. (1) At large timescales, increasing bandwidth does not improve throughput (or network performance). 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. (2) At small timescales, traffic burstiness varies. In order to improve network efficiency, we need to control bandwidth, TCP window size, and network delay to reduce traffic burstiness. There are the tradeoffs from each other, but the effect is nonlinear. (3) In general, network traffic processes have a Holder exponent alpha ranging between 0.7 and 1.3. Their statistics differ from Poisson processes.; To apply this prior knowledge from traffic analysis and to improve network efficiency, a notion of the efficient bandwidth, EB, is derived to represent the fractal concentration set. 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. |
