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• W76977664 abstract "Introduction The use of fractal models in computer networking has a strong tradition (see references in ). Most prominently, fractional Brownian motion provides a parsimonious abstraction of aggregate traffic at time scales of a second and beyond, which is found useful for design and management and which explains the occurrence of detrimental traffic bursts in terms of user behavior. At time scales small enough to be relevant for control, queueing and multiplexing, on the other side, multifractal cascades appear to be more accurate than self-similar models. Modeling First reports of multifractal scaling in network traffic traces 2 were quickly followed by models based cascading multiplication such as the Binomial cascade and more recently more general iterative products. Being parsimonious and computationally inexpensive these multifractal models proved accessible to analysis and a welcome alternative to the forbiddingly expensive network simulations. Inference An application as important as simulation is rooted in the fact that networks are stateless and not aware of individual connections. For load balancing and certain rate sensitive applications such as broadcasting, however, a reliable estimate of the available bandwidth is most useful. Inspired by the task of estimating parameters on multiple scales, e.g., the tool pathChirp uses efficient trains of exponentially spaced probe packets. When queued, probes are spaced according to traffic load arriving between probes, thus allowing to infer the free capacity. Alpha-beta decomposition Searching for the causes of multifractal bursts (instances of extreme workload) in traces of aggregate traffic, individual connections with exceptionally large sending rate were found to be the typical culprit, as opposed to a “conspiracy” of an exceptional number of connections as predicted by the classical On-Off model. Only few in number, the high rate alpha connections contrast strongly against the large crowd of average beta connections, similar to the alpha and beta males in the animal kingdom. Notably, there is strong statistical evidence that alpha connections tend to occur over paths of short response time. As a major conclusion, the alpha-beta decomposition of traffic points to the heterogeneity in the network topology as the main cause for the multifractal bursts. Moreover, with only a few connections being potentially harmful and important to monitor, operating a network with relevant state information becomes feasible. Alpha-beta traffic modeling First, let us revisit the celebrated On-Off model for network traffic , a process introduced very early by B. Mandelbrot. In this framework, a traffic source is modelled as being sending traffic at a constant rate (the On state), or as being silent (the Off state) with heavy tailed durations of the On and Off states. It is well known that in the limit of an infinite number of sources the aggregate (sum) of such sources becomes a Gaussian process with LRD," @default.
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• W76977664 date "2004-01-01" @default.
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• W76977664 title "FRACTALS IN NETWORKING: MODELING AND INFERENCE" @default.
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