The treatment of non-Poisson fractal-like time-series describing packet traffic featuring a bursty behaviour and a high variability over a range of time scales is a hot topic, both from the practical point of view of the design of network apparatus and from the theoretical point of view of queuing theory. One-dimensional chaotic maps have been shown to be able to reproduce such intermittent processes and the construction of simple models for realistic traffic sources can be considered a substantial contribution of the theory of complex dynamics to a field which is felt to have reached the necessary maturity to address design and implementation of new network control units. In this chapter, we aim at establishing the theoretical ground for the formal development behind the chaos-based modeling of network traffic and other similar phenomena. More specifically, we develop a set of tools to statistically characterize the process generated by iecewise-affine Markov maps with a possibly infinite, but countable number of Markov intervals. Since, in doing so, we keep the dimensionality of the space of the observables finite, such a description will be possible in terms of a finite-dimensional tensor-based framework. Nevertheless, the increased complexity of the model forces the use of tensors of functions whose handling is greatly simplified by extensive z transformation. With this, a systematic procedure is devised to write analytical expressions for the tensors that take into account the joint probability assignments needed to compute any-order expectations. As an example of use, this machinery is applied to the study of self-similarity of quantized processes both in the analysis of higher order phenomena as well as in the analysis and design of second-order self-similar sources suitable for artificial network traffic generation.
Chaos-Based Generation of Artificial Self-Similar Traffic
SETTI, Gianluca;MAZZINI, Gianluca
2005
Abstract
The treatment of non-Poisson fractal-like time-series describing packet traffic featuring a bursty behaviour and a high variability over a range of time scales is a hot topic, both from the practical point of view of the design of network apparatus and from the theoretical point of view of queuing theory. One-dimensional chaotic maps have been shown to be able to reproduce such intermittent processes and the construction of simple models for realistic traffic sources can be considered a substantial contribution of the theory of complex dynamics to a field which is felt to have reached the necessary maturity to address design and implementation of new network control units. In this chapter, we aim at establishing the theoretical ground for the formal development behind the chaos-based modeling of network traffic and other similar phenomena. More specifically, we develop a set of tools to statistically characterize the process generated by iecewise-affine Markov maps with a possibly infinite, but countable number of Markov intervals. Since, in doing so, we keep the dimensionality of the space of the observables finite, such a description will be possible in terms of a finite-dimensional tensor-based framework. Nevertheless, the increased complexity of the model forces the use of tensors of functions whose handling is greatly simplified by extensive z transformation. With this, a systematic procedure is devised to write analytical expressions for the tensors that take into account the joint probability assignments needed to compute any-order expectations. As an example of use, this machinery is applied to the study of self-similarity of quantized processes both in the analysis of higher order phenomena as well as in the analysis and design of second-order self-similar sources suitable for artificial network traffic generation.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
