网络视频流量的多重分形建模与多步预测研究
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摘要
在网络传输中，网络流量影响现实网络的业务传送质量。网络流量的自相似性（SelfSimilarity，SS）被发现后，利用分形和多重分形理论研究网络流量的测量、建模和控制，成为一个热点研究问题。
由于分形理论揭示了分形整体与局部形态的相似，揭示了介于整体与部分、有序与无序、复杂与简单之间的新形态、新秩序。分形形体中的自相似可以是完全相同，也可以是统计意义上的相似。对于流量的分析经过三阶段，第一阶段是传统的流量模型，如Poisson，Markov和ARMA等模型，第二阶段是自相似特征的流量模型，如FGN模型，FBM模型，FARIMA模型。第三阶段是多重分形特征的流量模型，如MWM、MFM。并给出分割函数S (q)的定义和h (q)的定义，并说明了用S (q)和h(q)函数判断流量的单分形和多重分形，为流量分析提供了有利方法。
在对网络流量的分形特征与估计方法充分分析基础上，对视频流量的图像质量和压缩比YUV、均值X|-、方差系数S x/X|-和峰值/均值X_(max)/X|-参数进行统计，统计数据表明视频流量的质量越高，突发性就越强，这种波动性体现在整体，对于局部却没有发现，说明了方差系数反映的是流量整体的波动性，而不能反映局部的波动性的。
对流量的LRD特性分析中，明确了不同内容的视频流均表现出LRD特性，只是其LRD的程度相差很大；对于不同质量的同一视频内容，它的LRD的程度也不同，一般图像质量越高，其LRD越强；对于相同质量、不同内容视频流，其LRD程度不同，其原因在于YUV越高，而压缩比越小，视频越清晰，同时H也越强，当然LRD也越高。在相同内容中，如果前景与背景相对出现快速变化，形成了流量的突发性，X max/X|-就会变大，LRD也就产生变化。
对视频流量的多重分形特征分析中，明确MPEG-4视频流量中的I、P、B帧相关性，在各尺度系数下，分析了MPEG-4视频流量中的I帧的边缘分布性质和相关性，用较少的数据进行统计参数，达到估计长相关性的目的，奠定了网络视频流量的多重分形模型设计基础。
本论文在相关的理论基础、方法和技术基础上，研究了网络流量的分形特征，对网络流量的单分形和多重分形特征进行分析，确定了基于单分形的Hurst参数估计方法、Holder指数估计和多重分形谱的估计方法；同时研究了具有分形特征的网络流量建模技术，综合分析了传统的网络流量模型、单分形和多重分形的网络流量建模。又由于多媒体技术的广泛应用，网络视频流量在Internet网络流量中占据了很大的比重，本文在针对网络视频流量的分析、多重分形建模和预测开展了一些具有创新意义的工作。
第一分析了多重分形模型的小波基、消失矩和因子等因素对仿真序列的影响，确定了选取各因素的方法和策略。通过选用Haar、Daubechies、Coifets和Symlets小波分别生成多重分形模型的仿真序列，以及对仿真序列的长相关和多重分形特征进行分析，基于Haar小波的多重分形模型仿真序列最接近真实视频流量；通过分析Haar、Daubechies、Coifets和Symlets小波的消失矩，选用Daubechies和Haar小波进行仿真实验，实验表明，由于Haar小波有最短的支集和最小的消失矩，并且它是Daubechies小波的一种，在多重分形模型中，Haar小波是最理想的选择。
针对传统多重分形模型中因子分布的缺陷，选用了β分布、点集（pointmass）分布和pareto分布等因子完成了多重分形建模过程，分析了仿真流量的分布特性、长相关性和多重分形等特征，并通过定义Kullback-Leiblar（KL）方法，判断具有距离最近的因子，实现多重分形模型仿真序列具有最佳分布，使得各尺度上的因子参数具有鲁棒性，因此多重分形模型中β分布就不是唯一的选择，可以依据信号的不同特性选择不同的因子分布。
第二针对视频流量的长相关性（long range dependence, LRD）进行了研究，通过对多重分形的各尺度系数和边缘分布进行了分析，以及对系数间的相关函数进行分析，提出了一个控制LRD的方法，这个方法主要对最粗的尺度系数建模，而这种建模具有自回归的短相关性（short range dependence, SRD），目的是将具有SRD特性的最粗尺度能够与具有LRD特性的最终流量序列建立联系，达到能够精确地控制流量序列的LRD，实验验证了这各方法能够保证了流量序列的LRD，也验证了多重分形模型的有效性。
第三由于多重分形树的分解能力，将时间序列进行分解细化为多层结构，通过对多重分形模型的各尺度系数进行性质分析，由于这个模型保持流量序列自相关函数的主体形状不变，设计了网络视频流量的多步预测方法，针对网络视频流量的多步预测方法，完成了多重分形可预测的分析，详细地设计了预测模型，介绍了尺度系数预测和因子预测方法，仿真表明多步预测模型的视频流量仿真有较好地效果。
第四将视频流量多步预测和流量控制相结合，主要讨论了网络QoS中的一些应用问题。在排队分析中，定义了一种广义尺度参数，并推导用于排队分析的多重分形模型的统计参数，然后利用Norris提出的排队理论，用广义尺度参数定义了长相关和短相关的的控制策略，给出了基于多重分形的预测模型，利用RTT设计了流量控制算法，实现了实际应用中的控制目的仿真实验证明了这个预测算法是有效性的。
In network transmission, network traffic influences the transmission quality of the actualnetwork. With discover of self-similarity, the measurement, modeling and traffic controlbecome an important problem with the fractal and multi-fractal theory.
Since fractal theory reveals the form of the whole and the parts is similar, and it showsthe new form or the new order between he whole and the parts, orderly and disorder, complexand simple.
Self-Similarity of fractal form may be identical, also may be the statistics. The fractalmodel of network traffic shows three phases, the first is the traditional model such as Poisson,Markov and ARMA, the second is self-similarity model such as the FGN, FBM and FARIMA,and the third is multifractal model such as MWM and MFM.
We give the definition of S(q) and h(q) function, it illustrates that use S(q) and h(q)functions to estimate the single or multi-fractal of network traffic, and it provides the goodmethod for traffic analysis.
Based on the analysis of the fractal characteristics and the estimation method of networktraffic, those parameters of the video image were calculated, such as YUV, X, S x/X|-andX max/X|-. The statistical data shows that the video traffic quality is higher, the sudden is stronger.So the volatility of video traffic is only reflected in whole traffic rather than the local, andS x/X|-reflects the volatility of the overall traffic but the local.
In characteristics analysis, all video traffics represent LRD, but its LRD degree is varydifferent. For the different content of the video traffic, its LRD degree is different. For thesame content video of different quality, its LRD degree is different, generally the imagequality is the higher, the LRD is the stronger. For the different content video of the samequality, its LRD degree is also different, its YUV is higher, the compression ratio is smaller,the video is clearer, The H parameter is stronger and the LRD is higher.
In the same content, if the foreground and background rapidly chang, formed the suddenof traffic,X max/X|-can be greater and LRD is also changed.
For the multifractal analysis of MPEG-4video traffic, those I frame, P frame and Bframe are correlation. We analyzed the edge distribution properties and correlation of I framefor the scale factors, and used less statistical parameters to estimate the long correlation, andestablished the basis of the multi-fractal model for network video.
In this paper, we prepare the basic theory, methods and technology, and analyze thefeatures of fractal and multi-fractal of network traffic, so we determined the estimationmethods of the Hurst parameter and spectrum function. And we study the modelingtechnology of network traffic basic on of the fractal features, and analyze the traditionalmodel, single fractal model and multi-fractal network traffic model.
With the wide application of multimedia technology, network video traffic will have alarge proportion in the Internet network flow. Based on previous results, some innovativeworks were carried out for multi-fractal model of network traffic, such as analysis, modeling,predict and control of network video traffic.
Firstly, we discuss the influence reasons of the multi-fractal model for the simulationsequence, such as wavelet base, disappear moment and distribution factor, and decide themethod and strategy of those chosen facts.
We Utilize Haar, Daubechies, Coifets and Symlets wavelet to express the simulationsequences of the multi-fractal model, and analyze those long range dependence (LRD) andmulti-fractal feature. The simulation sequence of multi-fractal model with Haar wavelet is themost close to real video traffic. And we analyze the disappear moment of Haar, Daubechies,Coifets and Symlets wavelet, and chose Daubechies and Haar wavelet to simulate experiment.The results show that Haar wavelet is the most ideal choice with the shortest tight supportedset and the minimum disappear moment, and it is a kind of Daubechies wavelet in themulti-fractal model.
And, we study the defects of traditional model on the factor distribution, and chose theβdistribution, pointmass distribution and pareto distribution to complete the modeling processof multi-fractal model and analyze the long range dependence, distribution characteristics andmulti-fractal. The Kullback-Leiblar (KL) method is defined and utilized to choose the factwith the shortest distance, so we enhance the robustness of estimated parameter with bestdistribution. The results show that theβdistribution is not the best option. According todifferent characteristics of the signal feature, to choose different distribution.
Secondly, we analyze the LRD of network video traffic and relation of edge distributionand the relevance function of the coefficient from the point of theory view, the controllingmethod of the LRD of multi-fractal model is proposed. In the method, the early scalecoefficients is modeled with AR and the connection is constructed on the short rangedependence (SRD) of the early scale coefficients and LRD of finally traffic sequence, realizedthe precise control sequence on LRD. Experiments show, the stability of multi-fractal modeland the consistency of LRD are improved by this method.
Thirdly, we analyze the feature of all scale coefficients in multi-fractal model. Amulti-scale prediction method of network video traffic is made based on multi-fractal model,utilized the ability of multi-fractal model to decompose the time series into more layers. Sothe multi-step prediction model of network video traffic is made and proved by the consistentshape of main relevance function, and consistd of the analysis of predictable, the design ofprediction model such as scale coefficients and factor prediction. The simulations show thatthe prediction model has better effect.
Fourthly, we discuss the application question of network QoS with multi-step predictingof network video traffic and TCP control. In the queuing analysis of multi-fractal model, andcalculate statistical parameters multi-fractal model. The parameters is defined and maydeduce some conclusions of queuing theory with queuing theory of Norris. In the applicationof TCP control mechanism, a predict algorithm of congestion control mechanism is designedand simulated. Experiment shown the validity of the predicting algorithm.
由于分形理论揭示了分形整体与局部形态的相似，揭示了介于整体与部分、有序与无序、复杂与简单之间的新形态、新秩序。分形形体中的自相似可以是完全相同，也可以是统计意义上的相似。对于流量的分析经过三阶段，第一阶段是传统的流量模型，如Poisson，Markov和ARMA等模型，第二阶段是自相似特征的流量模型，如FGN模型，FBM模型，FARIMA模型。第三阶段是多重分形特征的流量模型，如MWM、MFM。并给出分割函数S (q)的定义和h (q)的定义，并说明了用S (q)和h(q)函数判断流量的单分形和多重分形，为流量分析提供了有利方法。
在对网络流量的分形特征与估计方法充分分析基础上，对视频流量的图像质量和压缩比YUV、均值X|-、方差系数S x/X|-和峰值/均值X_(max)/X|-参数进行统计，统计数据表明视频流量的质量越高，突发性就越强，这种波动性体现在整体，对于局部却没有发现，说明了方差系数反映的是流量整体的波动性，而不能反映局部的波动性的。
对流量的LRD特性分析中，明确了不同内容的视频流均表现出LRD特性，只是其LRD的程度相差很大；对于不同质量的同一视频内容，它的LRD的程度也不同，一般图像质量越高，其LRD越强；对于相同质量、不同内容视频流，其LRD程度不同，其原因在于YUV越高，而压缩比越小，视频越清晰，同时H也越强，当然LRD也越高。在相同内容中，如果前景与背景相对出现快速变化，形成了流量的突发性，X max/X|-就会变大，LRD也就产生变化。
对视频流量的多重分形特征分析中，明确MPEG-4视频流量中的I、P、B帧相关性，在各尺度系数下，分析了MPEG-4视频流量中的I帧的边缘分布性质和相关性，用较少的数据进行统计参数，达到估计长相关性的目的，奠定了网络视频流量的多重分形模型设计基础。
本论文在相关的理论基础、方法和技术基础上，研究了网络流量的分形特征，对网络流量的单分形和多重分形特征进行分析，确定了基于单分形的Hurst参数估计方法、Holder指数估计和多重分形谱的估计方法；同时研究了具有分形特征的网络流量建模技术，综合分析了传统的网络流量模型、单分形和多重分形的网络流量建模。又由于多媒体技术的广泛应用，网络视频流量在Internet网络流量中占据了很大的比重，本文在针对网络视频流量的分析、多重分形建模和预测开展了一些具有创新意义的工作。
第一分析了多重分形模型的小波基、消失矩和因子等因素对仿真序列的影响，确定了选取各因素的方法和策略。通过选用Haar、Daubechies、Coifets和Symlets小波分别生成多重分形模型的仿真序列，以及对仿真序列的长相关和多重分形特征进行分析，基于Haar小波的多重分形模型仿真序列最接近真实视频流量；通过分析Haar、Daubechies、Coifets和Symlets小波的消失矩，选用Daubechies和Haar小波进行仿真实验，实验表明，由于Haar小波有最短的支集和最小的消失矩，并且它是Daubechies小波的一种，在多重分形模型中，Haar小波是最理想的选择。
针对传统多重分形模型中因子分布的缺陷，选用了β分布、点集（pointmass）分布和pareto分布等因子完成了多重分形建模过程，分析了仿真流量的分布特性、长相关性和多重分形等特征，并通过定义Kullback-Leiblar（KL）方法，判断具有距离最近的因子，实现多重分形模型仿真序列具有最佳分布，使得各尺度上的因子参数具有鲁棒性，因此多重分形模型中β分布就不是唯一的选择，可以依据信号的不同特性选择不同的因子分布。
第二针对视频流量的长相关性（long range dependence, LRD）进行了研究，通过对多重分形的各尺度系数和边缘分布进行了分析，以及对系数间的相关函数进行分析，提出了一个控制LRD的方法，这个方法主要对最粗的尺度系数建模，而这种建模具有自回归的短相关性（short range dependence, SRD），目的是将具有SRD特性的最粗尺度能够与具有LRD特性的最终流量序列建立联系，达到能够精确地控制流量序列的LRD，实验验证了这各方法能够保证了流量序列的LRD，也验证了多重分形模型的有效性。
第三由于多重分形树的分解能力，将时间序列进行分解细化为多层结构，通过对多重分形模型的各尺度系数进行性质分析，由于这个模型保持流量序列自相关函数的主体形状不变，设计了网络视频流量的多步预测方法，针对网络视频流量的多步预测方法，完成了多重分形可预测的分析，详细地设计了预测模型，介绍了尺度系数预测和因子预测方法，仿真表明多步预测模型的视频流量仿真有较好地效果。
第四将视频流量多步预测和流量控制相结合，主要讨论了网络QoS中的一些应用问题。在排队分析中，定义了一种广义尺度参数，并推导用于排队分析的多重分形模型的统计参数，然后利用Norris提出的排队理论，用广义尺度参数定义了长相关和短相关的的控制策略，给出了基于多重分形的预测模型，利用RTT设计了流量控制算法，实现了实际应用中的控制目的仿真实验证明了这个预测算法是有效性的。
In network transmission, network traffic influences the transmission quality of the actualnetwork. With discover of self-similarity, the measurement, modeling and traffic controlbecome an important problem with the fractal and multi-fractal theory.
Since fractal theory reveals the form of the whole and the parts is similar, and it showsthe new form or the new order between he whole and the parts, orderly and disorder, complexand simple.
Self-Similarity of fractal form may be identical, also may be the statistics. The fractalmodel of network traffic shows three phases, the first is the traditional model such as Poisson,Markov and ARMA, the second is self-similarity model such as the FGN, FBM and FARIMA,and the third is multifractal model such as MWM and MFM.
We give the definition of S(q) and h(q) function, it illustrates that use S(q) and h(q)functions to estimate the single or multi-fractal of network traffic, and it provides the goodmethod for traffic analysis.
Based on the analysis of the fractal characteristics and the estimation method of networktraffic, those parameters of the video image were calculated, such as YUV, X, S x/X|-andX max/X|-. The statistical data shows that the video traffic quality is higher, the sudden is stronger.So the volatility of video traffic is only reflected in whole traffic rather than the local, andS x/X|-reflects the volatility of the overall traffic but the local.
In characteristics analysis, all video traffics represent LRD, but its LRD degree is varydifferent. For the different content of the video traffic, its LRD degree is different. For thesame content video of different quality, its LRD degree is different, generally the imagequality is the higher, the LRD is the stronger. For the different content video of the samequality, its LRD degree is also different, its YUV is higher, the compression ratio is smaller,the video is clearer, The H parameter is stronger and the LRD is higher.
In the same content, if the foreground and background rapidly chang, formed the suddenof traffic,X max/X|-can be greater and LRD is also changed.
For the multifractal analysis of MPEG-4video traffic, those I frame, P frame and Bframe are correlation. We analyzed the edge distribution properties and correlation of I framefor the scale factors, and used less statistical parameters to estimate the long correlation, andestablished the basis of the multi-fractal model for network video.
In this paper, we prepare the basic theory, methods and technology, and analyze thefeatures of fractal and multi-fractal of network traffic, so we determined the estimationmethods of the Hurst parameter and spectrum function. And we study the modelingtechnology of network traffic basic on of the fractal features, and analyze the traditionalmodel, single fractal model and multi-fractal network traffic model.
With the wide application of multimedia technology, network video traffic will have alarge proportion in the Internet network flow. Based on previous results, some innovativeworks were carried out for multi-fractal model of network traffic, such as analysis, modeling,predict and control of network video traffic.
Firstly, we discuss the influence reasons of the multi-fractal model for the simulationsequence, such as wavelet base, disappear moment and distribution factor, and decide themethod and strategy of those chosen facts.
We Utilize Haar, Daubechies, Coifets and Symlets wavelet to express the simulationsequences of the multi-fractal model, and analyze those long range dependence (LRD) andmulti-fractal feature. The simulation sequence of multi-fractal model with Haar wavelet is themost close to real video traffic. And we analyze the disappear moment of Haar, Daubechies,Coifets and Symlets wavelet, and chose Daubechies and Haar wavelet to simulate experiment.The results show that Haar wavelet is the most ideal choice with the shortest tight supportedset and the minimum disappear moment, and it is a kind of Daubechies wavelet in themulti-fractal model.
And, we study the defects of traditional model on the factor distribution, and chose theβdistribution, pointmass distribution and pareto distribution to complete the modeling processof multi-fractal model and analyze the long range dependence, distribution characteristics andmulti-fractal. The Kullback-Leiblar (KL) method is defined and utilized to choose the factwith the shortest distance, so we enhance the robustness of estimated parameter with bestdistribution. The results show that theβdistribution is not the best option. According todifferent characteristics of the signal feature, to choose different distribution.
Secondly, we analyze the LRD of network video traffic and relation of edge distributionand the relevance function of the coefficient from the point of theory view, the controllingmethod of the LRD of multi-fractal model is proposed. In the method, the early scalecoefficients is modeled with AR and the connection is constructed on the short rangedependence (SRD) of the early scale coefficients and LRD of finally traffic sequence, realizedthe precise control sequence on LRD. Experiments show, the stability of multi-fractal modeland the consistency of LRD are improved by this method.
Thirdly, we analyze the feature of all scale coefficients in multi-fractal model. Amulti-scale prediction method of network video traffic is made based on multi-fractal model,utilized the ability of multi-fractal model to decompose the time series into more layers. Sothe multi-step prediction model of network video traffic is made and proved by the consistentshape of main relevance function, and consistd of the analysis of predictable, the design ofprediction model such as scale coefficients and factor prediction. The simulations show thatthe prediction model has better effect.
Fourthly, we discuss the application question of network QoS with multi-step predictingof network video traffic and TCP control. In the queuing analysis of multi-fractal model, andcalculate statistical parameters multi-fractal model. The parameters is defined and maydeduce some conclusions of queuing theory with queuing theory of Norris. In the applicationof TCP control mechanism, a predict algorithm of congestion control mechanism is designedand simulated. Experiment shown the validity of the predicting algorithm.
引文
[1]中国互联网信息中心，http://www.cnnic.cn/
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[30] Rajesh N and Raghuveer M. Discrete-Time Self-Similar systems and stable distributions:Applications to VBR Video Modeling, IEEE SIGNAL PROCESSING LETTERS,2003,10(3):124-134.
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[37] Park K and Willinger W. Self-similar network traffic and performance evaluation. WileyInter-science, New York,2000.
[38] Qijin J I. Can multifractal traffic burstiness be approximated by Markov modulatedPoisson processes. IEEE International Conference on Networks (ICON),2004,1:26-30.
[39] Park K and Tuan T. Performance evaluation of multiple time scale TCP underSelf-Similar traffic conditions. ACM Trans. on Modeling and Computer Simulation,2000,10(2):152-177.
[40] Tuan T and Park K. Multiple time scale congestion control for self-similar networktraffic, Perform. Eval.,1999,36-37(4):359-386.
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[49] Nolan J P. Fitting data and assessing goodness of fit with stable distributions. In theConference on Applications of Heavy Tailed Distributions in Economics, Engineeringand Statistics, Washington, DC, American University,1999.
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[51] Vehel J L and Sikdar B. A multiplicative multifractal model for TCP traffic. The SixthIEEE Symposium on Computers and Communications,2001:714-719.
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[53] Gao J. Superposition of multiplicative multifractal traffic processes. Electronics Letters,2000,36(8):761-763.
[54] Melo C A and Fonseca N L. Statistical multiplexing of multifractal flows. IEEEInternational Conference on Communications,2004,2:1135-1140.
[55] Goncalves P, Reidi R and Baraniuk R. A simple statistical analysis of wavelet basedmultifractal spectrum estimation. Proceedings of the32nd conference on signals, systemsand computers,1998:2110-2114.
[56] Salvadlor P, Nogueira A and Valadas R. Modeling multifractal traffic with stochasticL-systems. IEEE Global Telecommunications Conference,2002,3:2518-2522.
[57] Nikolaos D D, Anastasios D D. Efficient modeling of VBR MPEG-1coded video sources.IEEE Transaction on Circuits and Systems for Video Technology,2000,10(1):93-111
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