Analysis And Modeling Of The Fractal Property Of Wireless Network Traffic

Ever since 1993, when W. E. Leland formally introduced the concept of self-similarity of fractal into the study of network traffic in the field of telecommunication, the further development of applying the fractal theory to studying the network behavior has found a new way for the development of the network-related theories. Furthermore, the fractal theory has a strong impact upon the network performance analysis, QoS control, and network design. Although the following over ten year's traffic researches aim at the wired networks and the complex fractal properties has been discovered in these kinds of network traffic, the wireless-networks take different physical layer transport scheme and MAC compared with wired network. The wireless traffic distribution and its depends on the mobility of wireless stations, the size of packets, the bit ratio of wireless link, network traffic load, the scheduling scheme in access point, handover, and location management. So the fractal characteristics, the corresponding traffic models, and queue performance analysis of wired network traffic can not been applied to the wireless traffic directly. The researches on the wireless traffic properties are still in the initial stage, and the intact and efficient research methods and system are lacking. From the network technologies and engineering practice points of view, the researchers try to select a proper research method from the existing mathematics theories and tools which reflect the wireless traffic properties, and build a whole system of wireless traffic properties analyses, traffic modeling, traffic prediction and network performance evaluation. Our researches aim at the above problems. Based on applying the fractal theory to analyses the wireless traffic and comparing the different traffic mathematics models, this paper introduces the time series analyses, multifractal spectrum, wavelet analyses, queuing theory, and computer simulation into the wireless traffic modeling, wireless traffic forecasting, and network performance evaluation.This paper has taken detailed researches on the required theory, methods, tools, and technologies, including fractal network traffic theories, fractal property identification and estimation, the researches on the properties of merging self-similar traffic flows, fractal traffic modeling and prediction, and the network performance analysis with fractal traffic. Aimed at the fractal property identification and estimation of wireless traffic, traffic merg- ing, traffic modeling and prediction, and network performance evaluation, we've donesome innovated researches.The 2nd chapter of this paper summarizes some concepts and definitions in fractal theories which related to the traffic properties researches. From the monofractal and multifractal views, this chapter studies the theoretical backgrounds, basic principles and the correlation between these concepts and definitions, which forms the theories bases of the further researches.The 3th chapter studies the identification and estimation of fractality. The Hurst parameter estimation methods in time/frequency and wavelet domain are given in identifying the self-similarity, and Holder parameter and multifractal spectrum are used to estimate the multifractal property of the network traffic. The self-similarity and multifractal property of the OPNET-simulating and real wireless traffic are identified through experiment 1 and experiment 2. To overcome the shortcomings of the traditional Hurst parameter estimation methods, an optimal linear regression wavelet model is proposed, and applied to estimate the Hurst parameter of WLAN traffic. The estimation results are compared with the results obtained from the traditional estimation methods. In order to realize the unified identification of the fractal properties in the large and small time scale, a novel fractal dimension-based method is proposed, which can identify the self-similarity in the large time scale and the multifractality in the small time scale at the same time. The validity of this proposed method is validated via experiment.The 4th chapter studies the characteristics of the aggregating self-similar traffic flows. The aggregation operation is a basic network operation, and self-similarity reflects the long term correlation of the network traffic. Based on the theoretic proof of the characteristics of the aggregating exact second-order self-similar, long range dependent, and strong second-order self-similar traffic flows, this chapter detailed study the traffic aggregation process in IEEE 802.11 WLAN under four-way handshaking and backoff schemes. The experiment research utilizes the Sup-FRPP-based node model and WLAN simulation via OPNET to study the aggregating traffic flows.The 5th chapter studies the modeling of fractal wireless traffic based on researches results of the fractal network traffic theories, fractality identification, and the aggregating traffic properties. The traditional traffic models are classed into two trends, i.e., physical model and statistical model. The researches of ON/OFF model are from single ON/OFF source to the multi-traffic sources, and statistical models are summarized via the time-domain short range dependence and long range dependence models. This chapter proposes a FARIMA-based wireless traffic model and gives the model identification process. The experiment utilizes the FARIMA process to model the wireless traffic and validate the proposed model. The GARMA model and its identification are given in this chapter. A stable distribution-based wireless traffic self-similarity model is proposed, which includes the definition and attributes of stable distribution, parameters estimation, and the results of the experiment. Owing to the special virtues of wavelet transform, this chapter proposes a wavelet decomposition-based wireless traffic model. We studies the continuous wavelet transform (CWT), multiresolution analysis (MRA) and the Mallat arithmetics. Based on the research results, the wireless traffic wavelet model is built and the experiment research is conducted.The 6th chapter studies the traffic prediction based on the wireless traffic model built in chapter 5. A FARIMA self-similar wireless network traffic adaptive forecasting method is proposed. This suggested algorithm is applied to predict the future wireless traffic under different time scales. The prediction results are analyzed and validate the proposed algorithm. Due to the wavelet transform has the good dis-correlation property, the scaling coefficients and wavelet coefficients of network traffic trace wavelet decomposition can be modeled by ARMA model. This chapter proposes a regression algorithm based on the wireless traffic wavelet model. This method predict the approximation and detailed parts of the wireless traffic and obtain the predict results of the whole wireless traffic. The prediction results are anal sized.The 7th chapter introduces a class of mixtures of exponential distribution and proof they are heavy-tailed Pareto distributions. By calculating the LST and asymptotic series of the service-time distribution we analyze the steady-state waiting-time probabilities of M/G/1 queue system. We also extend the special caseγ=3/2 to the normal case. The results show that it will be helpful to analyze the heavy-tailed waiting-time distribution of self-similar traffic sources. This chapter also proposes a generalized packets loss method. Analyses of busty network traffic in LAN and WAN have demonstrated that the network traffic exhibits double-fractal property: self-similarity on large time scale and multifractality on small time scale. The traditional Poisson or Markovian short-range dep- endent model is not applicable. The normal and Log-normal distributions are used to model the large and small time scale, respectively. A generalized method is applied to analyze the steady and transient queuing performance. The packets loss is classified into two types: absolute loss and arbitrary loss, and analyzed quantificationally via the generalized method.