无线网络流量分形特性分析与建模
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摘要
自从1993年W. E. Leland等人将分形学中“自相似(self-similarity)”概念引入通信领域的网络流量研究中，由此而发展起来的用分形(fractal)理论来研究网络流量行为的思路为网络理论的发展开辟了新的途径，同时也对网络性能分析、服务质量(QoS)控制以及网络设计产生了深远影响。但十余年的大量研究和探索主要针对有线环境下的网络流量而进行，揭示的是有线网络流量在不同时间尺度上所呈现出的复杂分形特性，而无线网络在物理层传输机制和介质访问控制上与有线网络有较大差异，网络中流量的分布及其参数取决于用户移动性、分组大小、无线链路的比特率、网络负载、无线接入点的调度、越区切换、位置管理等因素，因此，有线网络环境中流量所呈现的分形特性以及据此建立的流量模型和进行的排队性能分析不能直接照搬到无线网络中。目前，对无线网络流量特性的相关研究尚处于起步阶段，还缺乏一套完整有效的研究方法和体系，这就要求研究者从网络技术和工程实际的角度出发，从现有数学理论和工具中选择适用于无线网络流量特性研究的方法，建立一个包括无线网络流量特性分析、流量建模、流量预测以及网络性能评价的体系。本论文的主要研究工作就是围绕上述问题而进行。论文在利用分形理论分析无线网络流量特性、比较多种不同的网络流量数学模型的基础上，引入了时间序列分析、多重分形谱理论、小波分析法、排队论、计算机仿真等研究方法，对无线网络流量建模、流量预测以及网络性能评价进行了较为系统的研究。
本论文对研究所必需的理论基础、方法工具和技术手段做了详实的基础工作，主要有：分形网络流量理论、分形特性检验与估计、自相似业务流合成特性研究、分形特性流量建模及预测和分形流量的网络性能分析等。在研究过程中，针对无线网络流量的分形特性检测、业务流合成、流量建模及预测和网络性能评价，开展了一些具有创新意义的工作。
本文第二章对分形理论中与流量研究相关的概念以数学定义和解释的方式做出全面总结，从单分形(monofractal)和多重分形(multifractal)的视角出发，探究概念和定义的理论依据、本质内涵和相互关系，为后续进一步的研究工作打下理论基础。
第三章研究分形特性的检验与估计。本章从自相似和多重分形两条主线出发给出常用的时／频域和小波域内自相似性检验的Hurst参数估计方法，以及利用H(?)lder指数和多重分形谱进行多重分形检验和估计的算法。通过实验一和实验二分别对OPNET仿真所得以及真实无线网络环境中的流量数据序列的自相似性和多重分形特性进行检验和估计。针对传统Hurst参数估计方法所存在的不足，在本章中提出了一种基于最优化线性回归模型的小波域内Hurst参数估计方法，并对无线局域网的网络流量利用所提出的方法和传统Hurst参数估计方法进行比较分析。为实现对大、小时间尺度上分形特性的统一检验与估计，本章还提出了一种基于分形维数的分形特性统一检测方法，能同时对网络流量在大时间尺度上的自相似性和小时间尺度上的多重分形性进行判定，并通过实验验证该方法的有效性。
由于自相似反映了网络流量在较长时间周期上的相关性，而合成操作又是网络中的一种基本操作，因此，第四章对自相似业务流的合成特性进行研究。本章在对N(N∈Z_+，N＞3)个严格二阶自相似、长程相关和强二阶自相似输入流合成后的流量分形特性进行理论推导的基础上，以IEEE 802.11无线局域网(WLAN)为研究对象，详细分析研究了其在四向握手机制、退避机制下的业务流具体汇聚过程，并在OPNET中基于Sup-FRPP节点模型和WLAN环境对自相似业务合成流特性进行实验研究。
第五章基于分形网络流量理论、分形特性检验与估计和自相似业务流合成特性的研究结果，进行分形特性无线网络流量建模的研究。对传统的流量模型从物理模型和统计模型两条主线加以概括，对物理模型中的ON／OFF模型从单一业务源到多业务源组进行研究，而对统计模型则从时域内的短相关和长相关模型进行归纳总结。本章提出了一种基于分形自回归综合滑动平均(FARIMA)过程的无线网络流量模型，给出模型辨识过程，通过实验研究利用该过程对无线网络流量的建模，并对模型有效性进行验证。给出GARMA模型的构建及其模型辨识算法。本章还提出了一种基于稳定分布的无线网络流量自相似模型，包括稳定分布的定义和属性、参数估计和验证，并给出实验与结论。由于小波变换的一些独有优点，本章还提出了基于小波分解的无线网络流量模型，对连续小波变换(CWT)、多解析度分析(MRA)和小波变换的Mallat算法进行研究，并由此建立无线网络流量的小波模型并进行实验研究。
第六章基于第五章所提出的分形网络流量模型进行流量预测。提出了基于FARIMA模型的自相似无线网络流量自适应预测，并对真实无线网络流量在不同时间尺度上的流量数据序列进行预测，对预测结果进行分析以验证预测算法和评估预测性能。由于小波变换具有很好的去相关性，因此对无线网络流量trace进行小波分解所得的尺度系数和小波系数可利用短相关模型ARMA进行建模。本章基于小波分解的无线网络流量模型，提出自回归预测算法，对不同时间尺度上无线网络流量的近似分量和细节分量进行预测，进而得到对整个网络流量的预测结果，并对预测性能进行分析。
第七章在流量建模及流量预测的基础上进行网络性能分析。本章第一部分通过引入一类混合指数分布并证明此类分布服从Pareto重尾分布，得到相应的LST变换闭合形式及服务时间渐进级数，同时将形状参数γ=3/2时的服务时间及其LST变换推广到更一般的情形，较为有效地解决了重尾分布的信源排队等待时间分析问题。此外，本章还提出了一种通用的分组丢失率分析方法，在对流量过程的平稳增量过程利用normal分布和Log-normal分布进行大、小时间尺度建模的基础上，定量分析研究稳态和瞬态时网络性能，将排队系统中发生的分组丢失划分为绝对丢失和随机丢失，分别对相应的分组绝对丢失率和随机丢失率进行定量分析研究，并通过实验研究真实无线网络环境中流量在大、小时间尺度上的分形特性带给网络性能的影响。
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.
本论文对研究所必需的理论基础、方法工具和技术手段做了详实的基础工作，主要有：分形网络流量理论、分形特性检验与估计、自相似业务流合成特性研究、分形特性流量建模及预测和分形流量的网络性能分析等。在研究过程中，针对无线网络流量的分形特性检测、业务流合成、流量建模及预测和网络性能评价，开展了一些具有创新意义的工作。
本文第二章对分形理论中与流量研究相关的概念以数学定义和解释的方式做出全面总结，从单分形(monofractal)和多重分形(multifractal)的视角出发，探究概念和定义的理论依据、本质内涵和相互关系，为后续进一步的研究工作打下理论基础。
第三章研究分形特性的检验与估计。本章从自相似和多重分形两条主线出发给出常用的时／频域和小波域内自相似性检验的Hurst参数估计方法，以及利用H(?)lder指数和多重分形谱进行多重分形检验和估计的算法。通过实验一和实验二分别对OPNET仿真所得以及真实无线网络环境中的流量数据序列的自相似性和多重分形特性进行检验和估计。针对传统Hurst参数估计方法所存在的不足，在本章中提出了一种基于最优化线性回归模型的小波域内Hurst参数估计方法，并对无线局域网的网络流量利用所提出的方法和传统Hurst参数估计方法进行比较分析。为实现对大、小时间尺度上分形特性的统一检验与估计，本章还提出了一种基于分形维数的分形特性统一检测方法，能同时对网络流量在大时间尺度上的自相似性和小时间尺度上的多重分形性进行判定，并通过实验验证该方法的有效性。
由于自相似反映了网络流量在较长时间周期上的相关性，而合成操作又是网络中的一种基本操作，因此，第四章对自相似业务流的合成特性进行研究。本章在对N(N∈Z_+，N＞3)个严格二阶自相似、长程相关和强二阶自相似输入流合成后的流量分形特性进行理论推导的基础上，以IEEE 802.11无线局域网(WLAN)为研究对象，详细分析研究了其在四向握手机制、退避机制下的业务流具体汇聚过程，并在OPNET中基于Sup-FRPP节点模型和WLAN环境对自相似业务合成流特性进行实验研究。
第五章基于分形网络流量理论、分形特性检验与估计和自相似业务流合成特性的研究结果，进行分形特性无线网络流量建模的研究。对传统的流量模型从物理模型和统计模型两条主线加以概括，对物理模型中的ON／OFF模型从单一业务源到多业务源组进行研究，而对统计模型则从时域内的短相关和长相关模型进行归纳总结。本章提出了一种基于分形自回归综合滑动平均(FARIMA)过程的无线网络流量模型，给出模型辨识过程，通过实验研究利用该过程对无线网络流量的建模，并对模型有效性进行验证。给出GARMA模型的构建及其模型辨识算法。本章还提出了一种基于稳定分布的无线网络流量自相似模型，包括稳定分布的定义和属性、参数估计和验证，并给出实验与结论。由于小波变换的一些独有优点，本章还提出了基于小波分解的无线网络流量模型，对连续小波变换(CWT)、多解析度分析(MRA)和小波变换的Mallat算法进行研究，并由此建立无线网络流量的小波模型并进行实验研究。
第六章基于第五章所提出的分形网络流量模型进行流量预测。提出了基于FARIMA模型的自相似无线网络流量自适应预测，并对真实无线网络流量在不同时间尺度上的流量数据序列进行预测，对预测结果进行分析以验证预测算法和评估预测性能。由于小波变换具有很好的去相关性，因此对无线网络流量trace进行小波分解所得的尺度系数和小波系数可利用短相关模型ARMA进行建模。本章基于小波分解的无线网络流量模型，提出自回归预测算法，对不同时间尺度上无线网络流量的近似分量和细节分量进行预测，进而得到对整个网络流量的预测结果，并对预测性能进行分析。
第七章在流量建模及流量预测的基础上进行网络性能分析。本章第一部分通过引入一类混合指数分布并证明此类分布服从Pareto重尾分布，得到相应的LST变换闭合形式及服务时间渐进级数，同时将形状参数γ=3/2时的服务时间及其LST变换推广到更一般的情形，较为有效地解决了重尾分布的信源排队等待时间分析问题。此外，本章还提出了一种通用的分组丢失率分析方法，在对流量过程的平稳增量过程利用normal分布和Log-normal分布进行大、小时间尺度建模的基础上，定量分析研究稳态和瞬态时网络性能，将排队系统中发生的分组丢失划分为绝对丢失和随机丢失，分别对相应的分组绝对丢失率和随机丢失率进行定量分析研究，并通过实验研究真实无线网络环境中流量在大、小时间尺度上的分形特性带给网络性能的影响。
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.
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