Data network traffic modeling and engineering using stable and fractal processes

One key property of modern network traffic is the presence of fractal behavior or self-similarity, i.e., the fact that the data “looks statistically similar” on all time-scales (highly correlated), as well as heavy-tailness (highly variable or “bursty”). Although the above features have serious implications for analysis, design, and control of data networks, they are inadequately described by classical traffic models such as: Markov, Poisson or Gaussian models. This thesis proposes a family of self-similar and Stable (heavy-tailed) processes for modeling and engineering of data networks traffic, as well as several results applicable to queuing theory. The main objective of this research, is to improve the performance of high-speed networks, using new approaches and techniques. The first contribution of the thesis is the development of a traffic engineering framework for Fractional Brownian Motion (FBM) traffic streams. A comparative study of three call admission control schemes is provided, based on analytic results for the buffer overflow probability in a multiplexer. However, the main interest is on more general, i.e., non-Gaussian, processes, which better characterize real network traffic. The thesis extends existing work on FBM, using the Fractional Lèvy Motion (FLM). The probability density function of the process is introduced first. Next, a further elaboration of all the well-known fractal queuing results obtained for Gaussian processes, is performed. The scaling expressions and the asymptotic lower bound for the buffer overflow probability that are derived, encompass all results in the literature related to ordinary Lèvy motion and FBM. In order to better manage and engineer data traffic, the “S4 Traffic” model, which was the first self-similar Stable model proposed in the literature, is employed. Using this model, the effect of shaping on input traffic is studied, via simulation. It is shown that: (a) the self-similarity property is unaffected; and (b) traffic can be made less heavy-tailed, with the cost of performance degradation. To further engineer the loss curve in a statistical multiplexer, the overflow probabilities are calculated, relying on large deviations techniques, analytical results and measuring techniques. Finally, the Fractionally Autoregressive Integrated Moving Average (FARIMA) process with totally skewed Stable innovations, is considered for traffic modeling. The Stable FARIMA is a powerful linear traffic model which captures short and long range dependences in real traffic as well as heavy-tailed behavior, in a parsimonious manner. In addition, a three-step algorithm for parameter estimation and system identification is proposed and tested. Experimental results based on real traces are used to exhibit the merits of those models and confirm theoretical results. The experiments are performed for link capacities and buffer sizes that are typical for data networks. The traces included MPEG compressed video traffic, Internet Wide Area Network (WAN) traffic, and Local Area Network (LAN) traffic.

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