Modelling and analysis of LRD in packet networks: Tsallis entropy framework

Abstract

The phenomenon of long range dependence (LRO) in network traffic is ubiquitous and newlineis being increasingly observed in a variety of networks like BISON, broadband wireless newlineand ad hoc. These networks generally carry various types of traffic comprising data, video newlineand voice which pose challenging problems for designers of these networks. To facilitate newlineunderstanding of these networks, one needs to develop models to study performance measures. newlineThese models essentially have been proposed in the context of queueing systems newlinewith input traffic exhibiting self-similar, fractal, long range dependence and service process newlinedepicting Pareto like tail requiring specification of both arrival and service rates. Such a newlinestudy in turn will lead to development of traffic control algorithms. newlineNoting that Tsallis entropy has been successfully employed to study non-extensive newlinesystems which exhibit multi-fractal structure, an alternative framework based on Tsallis newlineentropy is proposed to investigate the effects of LRO on network traffic characteristics. newlineThe framework is based upon the maximization of Tsallis entropy subject to availability newlineof partial information in the form of constraints. The detailed analysis of models provide newlineclosed form expressions for various performance measures like overflow probability, newlineutilization, loss probability etc. The thesis begins with an overview of queueing models newlineemployed to study networks. Salient features of Tsallis entropy and Jaynes maximum entropy newlineprinciple are described in the first chapter. The second chapter deals with the study newlineof queue length distribution of number of packets by maximizing Tsallis entropy subject to newlinex newlinexi newlineavailability of fractional moments. For appropriate range of the Tsallis entropy parameter newlineq, it is found though probability distribution of number of packets exists, first moment newlineof number of packets mayor may not exist. In the limiting case as q tends to 1, one newlinerecovers the known asymptotic results for buffer overflow probability depicting Weibull-like tail.