基于小波的网络流量的特性刻画与模型建立
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摘要
网络流量的特性刻画与模型建立一直是网络技术研究中的一个热点问题。一个具有精确刻画能力的模型的建立，对分析、理解和仿真网络的动态行为，对指导网络流量均衡控制方案的设计，对相关网络路由、交换和管理设备及其支撑软件的开发都具有基础性的重要意义。
近年来，通信与网络技术得到了飞速发展，其结果是带来了网络流量特征的重大变化，其主要表现为以下几个方面：
(1)、数据量的急剧增长——Internet用户数以及每一个用户所产生的流量均是以指数形式增长。
(2)、服务功能的变化——目前，Internet提供越来越多的个性化服务项目，如：多媒体技术的应用，是Internet为用户提供了诸如视频点播等多种新的应用服务。
(3)、移动及无线网技术的发展——目前，大量的无线用户的接入，改变了原有的Internet流量特性。
网络技术的发展为网络技术的研究提出了诸多新问题，就网络流量的特性刻画与模型建立等方面，主要有以下问题：
(1)、网速的提高以及流量的增大，将对网络流量的特性分析方法带来重大变化，其研究的重点将从大尺度(1s及其以上)转移到小尺度(100ms以下)及其在中尺度(100ms—1s)上来。
(2)、多媒体的广泛应用，为网络流量的特性分析与模型建立提出了新问题。视音频流具有有别于Internet流的自身特点，其特点决定了传统的分析方法和数学模型将无法满足其要求。
(3)、移动性和无线网技术的实施，会带来信号的多径衰落和频率选择性衰落等诸多问题。
小波变换是一种信号的时间——尺度分析方法，它具有多分辨率分析的特点，而且在时频两域都具有表征信号局部特征的能力，是一种窗口大小不变，但其形状可以改变，时间窗和频率窗都可以改变的时频局部化分析方法。即在低频部分具有较高的频率分辨率和较低的时间分辨率，在高频部分具有较高的时间分辨率和较低的频率分辨率，很适合于探测正常信号中夹带的瞬态反常现象并展示其成分，被誉为分析信号的显微镜。
本人基于小波分析的方法和多分形的理论，在网络流量的特性刻画及模型建立等方面进行了以下的研究：
(1)、对诸如聚类方差法等几种常用的网络流量的Hurst参数估值算法的性能、适用范围以及短相关特性对其的影响进行了分析。
(2)、对MPEG-4视频流的特性进行了分析，并基于分析的结果，用多分形小波模型对其进行了仿真，对其仿真性能进行了评估，同时探讨了小波基函数及其消失矩的选择对仿真性能的影响。
(3)、对网络流量特性进行了多尺度分析，对流量在小尺度上的平稳性、泊松性、高斯性、长相关性以及多分形特征进行了全面地分析，并基于Alpha、Beta的流量分解原则，对流量在小尺度上所表现出的非平稳性和非长相关性的原因进行了研究。
其研究成果可以概括为以下几点：
(1)、对五种Hurst参数估值算法的鲁棒性进行了分析，给出了在用Hurst参数估值法对流量的LRD特性进行分析时，应遵循的原则。
(2)、研究了SRD特性对五种Hurst参数估值算法性能的影响，提出了一种有效消除SRD特性的方法——聚类分析法。
(3)、对MPEG-4视频流的LRD特性进行了研究，指出流量的突发性是造成MPEG-4视频流具有LRD特性的主要原因。并基于上述研究结果，用多分形小波模型对MPEG-4视频流进行仿真并对其性能进行了分析，指出多分形小波模型是一个性能较好的MPEG-4视频流的仿真模型，其很好地刻画了流量的全局特性，但随着流量的突发性的增强，其对流量的局部特性的刻画能力减弱。
(4)、对小波基的选择和消失矩的选择对多分形小波模型性能的影响进行了研究，指出小波基函数的选择和消失矩的选择对多分形小波模型的性能均有影响，但小波基函数的选择影响更大。
(5)、对Internet流量在小尺度上(1s及以下)的平稳性、泊松性、高斯性、长相关性和多分形性进行了研究，指出网络流量在小尺度上表现出：非平稳的、非高斯的、非长相关性的泊松分布的特性，同时指出，网络流量的多分形特征具有非一致性，网速为几个kbps的低速网络，其流量表现出多分形的小尺度特性，而网速为几个Gbps的骨干网，其流量表现出单分形的小尺度特性。
(6)、对流量在小尺度上的非平稳性和非LRD特性的原因进行了研究，指出：流量的非LRD特性主要是由Dense流决定的，即由流量的密度决定的。从全局特性来看，流量的非平稳性是由Dense流决定的，即由流量的密度决定的，而从局部特性来看，流量的非平稳性是由Alpha流决定的，即由流量的包字节数的大小决定的。
本论文以小波作为主要分析工具，并结合分形理论，对网络流量的多种特性进行了详实的分析，同时，基于分析的结果，用MWM模型对其进行了仿真，此项研究为网络流量的特性分析和建模工作提供了一种切实可行的方法。特别是本文中，在网络流量的特性分析方面，有别于传统的分析方法(研究流量在中和大尺度即：1s及其以上的尺度上的特性)，将研究的重点集中于流量在小尺度(1s及其以下)上的特性分析，并找出了网络流量在小尺度上表现出的非平稳性和非LRD特性的原因，此项研究对于目前正在发展的高速网的建设，具有一定的现实指导意义。论文最后总结了网络流量特性分析和建模中亟待解决的问题，并指出了下一步研究的重点。
Network traffic analysis and modeling play a major role in charactering network performance, so it has been a focus of many researches. Models that accurately capture the salient characteristics of the traffic is useful for analysis and simulation, and they further our understanding of network dynamics, so it has a fundamental meaning for many network designs and engineering problems, e.g., the traffic balance scheme, router, switcher designing, the manage devices and its support software developing.
Recently, communication and network technologies are developing rapidly, it brings the traffic characteristics to change greatly, and the main changes are shown as follow:
(1) The drastic increasing of the amount of the data-The Internet has beengrowing exponentially. This growth has occurred both in the number of hosts connected to Internet, and the amount of traffic produced by each host.
(2) The changing of the service functions-Recently, more and more.differentiated services such as multi-media and VOD are widely deployed in Internet.
(3) The development of mobile and wireless technology-The access ofmany wireless users has changed the original characteristics of the traffic.
The development of network technology has brought many new problems for the network researches. As for the traffic characterization and modeling, the problems are as follow:
(1) The high link capacity of the network will allow us to zoom into small-time scale (below 100ms) and middle-time scale (100ms—1s) and perform reliable data analysis. This is different from the traditional analysis method at the large-time scale (1s and above).
(2) Video and audio traffic has their own characteristics which are different from the Internet traffic, so the widely deployed multi-media technology will lead new problems to traffic characterization and modeling. The traditional analysis method and models need to be modified.
(3) The access of many mobile and wireless users will lead some new problems such as multi-path shading and frequency selecting.
Wavelet transform is a time-scale analysis method which has a multi-resolution analysis function. It can capture the local behaviors of the signal both in time and frequency fields. The method can change its window's shape while hold the window's size the same, and it can also change the time window and frequency window at the same time. It is a time-frequency localization analysis method, i.e., at the part of low frequency, it has higher frequency resolution and lower time resolution, and at the part of high frequency, it has lower frequency resolution and higher time resolution. So it is suitable for detecting the burst phenomena in the signal. It is a microscope for signal analysis.
Based on wavelet analysis method and multi-fractal theory, we have done some research works on traffic characterization and modeling. They are as follow:
(1) The performance of several Hurst parameter estimate algorithms is studied and the influence of SRD to these algorithms is analyzed.
(2) The behaviors of MPEG-4 video traces are studied, and based on the results, the video traces are simulated using multi-fractal wavelet model. The performance of the model is evaluated and the influence of mother wavelet selection and vanishing moment selection to the performance of the model is also studied.
(3) Multi-scale analysis is done to the network traffic. The stationary, Poisson, Gaussian, LRD, and multi-fractal behaviors of the traffic at the small-time scale are studied in detail. Based on the Alpha, Beta separation scheme, some research works are done to identify the potential causing factors of the non-stationary and non-LRD behavior of the traffic at the small-time scale.
The research results can be summarized in following:
(1) The robustness of 5 Hurst parameter estimate algorithms is studied and the principle which we should obey when using these methods to study the LRD behavior of traffic is presented.
(2) The influence of SRD to the performance of 5 Hurst parameter estimate algorithms is studied and a method which can eliminate this influence is presented. The method is called aggregate analysis method.
(3) The LRD behavior of MPEG-4 video traces is studied and the results show that the burstiness is the main causes. Based on the results, the MPEG-4 video trace is simulated using multi-fractal wavelet model and its performance is evaluated. The results show that multi-fractal wavelet model is a good model for characterizing MPEG-4 video trace. It can capture the global behavior of the traffic perfectly, but its ability to capture the local behavior of the traffic become weaker when the burstiness of the traffic become stronger.
(4) The influence of mother wavelet selection and vanishing moment selection to the performance of the MWM model is studied. The results show that they both have influence to the performance of MWM model. The influence of mother wavelet selection is the bigger.
(5) The stationary, Poisson, Gaussian, LRD, and multi-fractal behaviors of the traffic at the small-time scale are studied. The results show that the traffic exhibits non-stationary, non-Gaussian, non-LRD and Poisson distribution behaviors at the small-time scale. The results also show that the multi-fractal behavior is not uniform, for the relatively low capacity link (several kbps), the traffic exhibits multi-fractal behavior, but for the high capacity link (several Gbps), the traffic exhibits mono-fractal behavior.
(6) The non-stationary and non-LRD causing factors are studied at the small-time scale, the results show that Dense flow is the main causing factor of the non-LRD. From the global view, the Dense flow is the main causing factor of non-stationary, but from the local view, the Alpha flow is the main causing factor of non-stationary.
In this dissertation, combined with the fractal theory, the wavelet is used as a tool, to make a detailed analysis to the traffic. Based on the results, the traffic simulation is made using MWM model. This study provides a useful way for the traffic characterization and modeling. Especially in this dissertation, much more researches are done to the small-time scaling (1s and down) behaviors of the traffic, which is differ from the conventional works which focus on the large-time scaling (1s and above) behaviors, and the non-stationary and non-LRD behaviors causing factors at the small-time scale were found. This study is helpful for the recently construction works of the high-speed network. Finally, the dissertation summarizes the to-be-resolved problems and point out the emphasis of the further research.
近年来，通信与网络技术得到了飞速发展，其结果是带来了网络流量特征的重大变化，其主要表现为以下几个方面：
(1)、数据量的急剧增长——Internet用户数以及每一个用户所产生的流量均是以指数形式增长。
(2)、服务功能的变化——目前，Internet提供越来越多的个性化服务项目，如：多媒体技术的应用，是Internet为用户提供了诸如视频点播等多种新的应用服务。
(3)、移动及无线网技术的发展——目前，大量的无线用户的接入，改变了原有的Internet流量特性。
网络技术的发展为网络技术的研究提出了诸多新问题，就网络流量的特性刻画与模型建立等方面，主要有以下问题：
(1)、网速的提高以及流量的增大，将对网络流量的特性分析方法带来重大变化，其研究的重点将从大尺度(1s及其以上)转移到小尺度(100ms以下)及其在中尺度(100ms—1s)上来。
(2)、多媒体的广泛应用，为网络流量的特性分析与模型建立提出了新问题。视音频流具有有别于Internet流的自身特点，其特点决定了传统的分析方法和数学模型将无法满足其要求。
(3)、移动性和无线网技术的实施，会带来信号的多径衰落和频率选择性衰落等诸多问题。
小波变换是一种信号的时间——尺度分析方法，它具有多分辨率分析的特点，而且在时频两域都具有表征信号局部特征的能力，是一种窗口大小不变，但其形状可以改变，时间窗和频率窗都可以改变的时频局部化分析方法。即在低频部分具有较高的频率分辨率和较低的时间分辨率，在高频部分具有较高的时间分辨率和较低的频率分辨率，很适合于探测正常信号中夹带的瞬态反常现象并展示其成分，被誉为分析信号的显微镜。
本人基于小波分析的方法和多分形的理论，在网络流量的特性刻画及模型建立等方面进行了以下的研究：
(1)、对诸如聚类方差法等几种常用的网络流量的Hurst参数估值算法的性能、适用范围以及短相关特性对其的影响进行了分析。
(2)、对MPEG-4视频流的特性进行了分析，并基于分析的结果，用多分形小波模型对其进行了仿真，对其仿真性能进行了评估，同时探讨了小波基函数及其消失矩的选择对仿真性能的影响。
(3)、对网络流量特性进行了多尺度分析，对流量在小尺度上的平稳性、泊松性、高斯性、长相关性以及多分形特征进行了全面地分析，并基于Alpha、Beta的流量分解原则，对流量在小尺度上所表现出的非平稳性和非长相关性的原因进行了研究。
其研究成果可以概括为以下几点：
(1)、对五种Hurst参数估值算法的鲁棒性进行了分析，给出了在用Hurst参数估值法对流量的LRD特性进行分析时，应遵循的原则。
(2)、研究了SRD特性对五种Hurst参数估值算法性能的影响，提出了一种有效消除SRD特性的方法——聚类分析法。
(3)、对MPEG-4视频流的LRD特性进行了研究，指出流量的突发性是造成MPEG-4视频流具有LRD特性的主要原因。并基于上述研究结果，用多分形小波模型对MPEG-4视频流进行仿真并对其性能进行了分析，指出多分形小波模型是一个性能较好的MPEG-4视频流的仿真模型，其很好地刻画了流量的全局特性，但随着流量的突发性的增强，其对流量的局部特性的刻画能力减弱。
(4)、对小波基的选择和消失矩的选择对多分形小波模型性能的影响进行了研究，指出小波基函数的选择和消失矩的选择对多分形小波模型的性能均有影响，但小波基函数的选择影响更大。
(5)、对Internet流量在小尺度上(1s及以下)的平稳性、泊松性、高斯性、长相关性和多分形性进行了研究，指出网络流量在小尺度上表现出：非平稳的、非高斯的、非长相关性的泊松分布的特性，同时指出，网络流量的多分形特征具有非一致性，网速为几个kbps的低速网络，其流量表现出多分形的小尺度特性，而网速为几个Gbps的骨干网，其流量表现出单分形的小尺度特性。
(6)、对流量在小尺度上的非平稳性和非LRD特性的原因进行了研究，指出：流量的非LRD特性主要是由Dense流决定的，即由流量的密度决定的。从全局特性来看，流量的非平稳性是由Dense流决定的，即由流量的密度决定的，而从局部特性来看，流量的非平稳性是由Alpha流决定的，即由流量的包字节数的大小决定的。
本论文以小波作为主要分析工具，并结合分形理论，对网络流量的多种特性进行了详实的分析，同时，基于分析的结果，用MWM模型对其进行了仿真，此项研究为网络流量的特性分析和建模工作提供了一种切实可行的方法。特别是本文中，在网络流量的特性分析方面，有别于传统的分析方法(研究流量在中和大尺度即：1s及其以上的尺度上的特性)，将研究的重点集中于流量在小尺度(1s及其以下)上的特性分析，并找出了网络流量在小尺度上表现出的非平稳性和非LRD特性的原因，此项研究对于目前正在发展的高速网的建设，具有一定的现实指导意义。论文最后总结了网络流量特性分析和建模中亟待解决的问题，并指出了下一步研究的重点。
Network traffic analysis and modeling play a major role in charactering network performance, so it has been a focus of many researches. Models that accurately capture the salient characteristics of the traffic is useful for analysis and simulation, and they further our understanding of network dynamics, so it has a fundamental meaning for many network designs and engineering problems, e.g., the traffic balance scheme, router, switcher designing, the manage devices and its support software developing.
Recently, communication and network technologies are developing rapidly, it brings the traffic characteristics to change greatly, and the main changes are shown as follow:
(1) The drastic increasing of the amount of the data-The Internet has beengrowing exponentially. This growth has occurred both in the number of hosts connected to Internet, and the amount of traffic produced by each host.
(2) The changing of the service functions-Recently, more and more.differentiated services such as multi-media and VOD are widely deployed in Internet.
(3) The development of mobile and wireless technology-The access ofmany wireless users has changed the original characteristics of the traffic.
The development of network technology has brought many new problems for the network researches. As for the traffic characterization and modeling, the problems are as follow:
(1) The high link capacity of the network will allow us to zoom into small-time scale (below 100ms) and middle-time scale (100ms—1s) and perform reliable data analysis. This is different from the traditional analysis method at the large-time scale (1s and above).
(2) Video and audio traffic has their own characteristics which are different from the Internet traffic, so the widely deployed multi-media technology will lead new problems to traffic characterization and modeling. The traditional analysis method and models need to be modified.
(3) The access of many mobile and wireless users will lead some new problems such as multi-path shading and frequency selecting.
Wavelet transform is a time-scale analysis method which has a multi-resolution analysis function. It can capture the local behaviors of the signal both in time and frequency fields. The method can change its window's shape while hold the window's size the same, and it can also change the time window and frequency window at the same time. It is a time-frequency localization analysis method, i.e., at the part of low frequency, it has higher frequency resolution and lower time resolution, and at the part of high frequency, it has lower frequency resolution and higher time resolution. So it is suitable for detecting the burst phenomena in the signal. It is a microscope for signal analysis.
Based on wavelet analysis method and multi-fractal theory, we have done some research works on traffic characterization and modeling. They are as follow:
(1) The performance of several Hurst parameter estimate algorithms is studied and the influence of SRD to these algorithms is analyzed.
(2) The behaviors of MPEG-4 video traces are studied, and based on the results, the video traces are simulated using multi-fractal wavelet model. The performance of the model is evaluated and the influence of mother wavelet selection and vanishing moment selection to the performance of the model is also studied.
(3) Multi-scale analysis is done to the network traffic. The stationary, Poisson, Gaussian, LRD, and multi-fractal behaviors of the traffic at the small-time scale are studied in detail. Based on the Alpha, Beta separation scheme, some research works are done to identify the potential causing factors of the non-stationary and non-LRD behavior of the traffic at the small-time scale.
The research results can be summarized in following:
(1) The robustness of 5 Hurst parameter estimate algorithms is studied and the principle which we should obey when using these methods to study the LRD behavior of traffic is presented.
(2) The influence of SRD to the performance of 5 Hurst parameter estimate algorithms is studied and a method which can eliminate this influence is presented. The method is called aggregate analysis method.
(3) The LRD behavior of MPEG-4 video traces is studied and the results show that the burstiness is the main causes. Based on the results, the MPEG-4 video trace is simulated using multi-fractal wavelet model and its performance is evaluated. The results show that multi-fractal wavelet model is a good model for characterizing MPEG-4 video trace. It can capture the global behavior of the traffic perfectly, but its ability to capture the local behavior of the traffic become weaker when the burstiness of the traffic become stronger.
(4) The influence of mother wavelet selection and vanishing moment selection to the performance of the MWM model is studied. The results show that they both have influence to the performance of MWM model. The influence of mother wavelet selection is the bigger.
(5) The stationary, Poisson, Gaussian, LRD, and multi-fractal behaviors of the traffic at the small-time scale are studied. The results show that the traffic exhibits non-stationary, non-Gaussian, non-LRD and Poisson distribution behaviors at the small-time scale. The results also show that the multi-fractal behavior is not uniform, for the relatively low capacity link (several kbps), the traffic exhibits multi-fractal behavior, but for the high capacity link (several Gbps), the traffic exhibits mono-fractal behavior.
(6) The non-stationary and non-LRD causing factors are studied at the small-time scale, the results show that Dense flow is the main causing factor of the non-LRD. From the global view, the Dense flow is the main causing factor of non-stationary, but from the local view, the Alpha flow is the main causing factor of non-stationary.
In this dissertation, combined with the fractal theory, the wavelet is used as a tool, to make a detailed analysis to the traffic. Based on the results, the traffic simulation is made using MWM model. This study provides a useful way for the traffic characterization and modeling. Especially in this dissertation, much more researches are done to the small-time scaling (1s and down) behaviors of the traffic, which is differ from the conventional works which focus on the large-time scaling (1s and above) behaviors, and the non-stationary and non-LRD behaviors causing factors at the small-time scale were found. This study is helpful for the recently construction works of the high-speed network. Finally, the dissertation summarizes the to-be-resolved problems and point out the emphasis of the further research.
引文
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