大尺度IP流量矩阵估计关键技术研究
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摘要
随着IP网络规模指数式增长而带来的对网络管理和维护的迫切需求，流量矩阵估计已成为当前的热点研究问题。IP网络的快速发展，迫使网络操作员需要知道网络中不同节点间数据包的转发情况，以便更好地进行负载均衡、流量检测、路由最优化、网络维护、网络设计和网络规划等网络活动。流量矩阵作为网络活动的重要输入参数，已受到国内外研究人员的广泛关注，现已成为IP网络的重要研究内容。流量矩阵表示网络中源目的(Original-Destination，OD)节点之间流动的网络流量(即OD流大小)，流量矩阵的维数等于网络中所有OD流的数目，它从全局的观点来描述整个网络的数据流动情况，是网络操作员决策的重要依据。然而，尽管流量矩阵很重要，但是要通过直接测量的方式来获得流量矩阵非常困难，有时甚至是不可能的。而流量矩阵估计采用间接测量的方式来获得流量矩阵，可避免直接测量流量矩阵所遇到的困难。正是由于这一优点，本文研究大尺度IP骨干网络中的流量矩阵(即大尺度IP流量矩阵)估计问题，主要集中在以下几个方面：大尺度IP流量矩阵的最优化估计、基于Fratar模型的大尺度IP流量矩阵估计、基于回归模型的大尺度IP流量矩阵估计、基于递归神经网络的大尺度IP流量矩阵估计和基于前馈神经网络的大尺度IP流量矩阵估计等关键技术的研究。
网络流量根据路由矩阵在网络上流动，并在网络各条链路上汇聚而形成链路负载，因此流量矩阵、路由矩阵和链路负载间具有确定的约束关系。然而，在IP网络中，特别是大尺度IP骨干网络中，OD流的数目远远大于IP网络中的链路数，这导致流量矩阵估计问题具有高度病态特性，如何克服这一问题的病态特性是当前流量矩阵估计面对的主要挑战。针对大尺度IP流量矩阵估计问题的高度病态特性，第二章基于数值最优化理论，探索寻找解决大尺度IP流量矩阵估计过程中解的不稳定性和不唯一性问题的思路，主要包括两方面的工作：(1)基于单纯形方法来估计流量矩阵。通过将流量矩阵估计问题描述为约束条件下的线性规划，然后结合分辨率矩阵和单纯形方法来解决该线性规划，从而获得满足要求的流量矩阵估计值。(2)基于模拟退火方法来求解流量矩阵估计问题。通过将流量矩阵估计问题描述为模拟退火过程，随着温度的不断降低，估计值逐步逼近真实值，从而克服该问题的病态特性，然后利用欧氏距离(Euclid distance)和马氏距离(Mahalanobisdistance)作为最优化尺度来进一步克服该问题的病态特性，并通过迭代反演来获得时变网络条件下的流量矩阵最优化估计值。
以前的文献大多基于统计模型来研究流量矩阵估计问题，但是当前的研究表明流量矩阵具有空间的和时间的相关性，统计模型很难捕获流量矩阵的这些特征。第三章基于Fratar模型来估计大尺度IP流量矩阵，主要包括两方面的工作：(1)利用Fratar模型来建模大尺度IP骨干网络中的OD流。通过Fratar模型，能准确捕获流量矩阵的空间时间相关性，从而能获得精确的流量矩阵初始值，然后通过迭代过程来获得流量矩阵的估计值。(2)由于(1)的迭代过程计算复杂，因而需要时间长。基于Fratar模型，本文利用代数重构技术(Algebraic Reconstruction Technique，ART)来估计流量矩阵。ART是图像重构的重要技术，它基于投影和迭代来完成求解过程，需要的计算简单，计算时间短，因此ART能快速获得流量矩阵的估计结果。
随着对网络流量的深入研究，研究人员发现网络流量不仅具有空间时间相关性，而且具有重尾分布(Heavy-tailed distributions)、自相似(Self-similarity)、短相关(Short-Range Dependence，SRD)和长相关(Long-Range Dependence，LRD)特性，传统的网络流量模型不能准确地捕获这些特征。第四章基于回归模型来估计大尺度IP流量矩阵，主要包括两方面的研究：(1)为了描述网络流量的时间相关性，将OD流建模为自回归滑动平均(Autoregressive Moving Average，ARMA)模型，并利用马氏距离的优点，将流量矩阵估计问题描述为马氏距离下的最优化过程，通过迭代寻优来获得流量矩阵的精确估计。(2)网络流量的自相关函数表示网络流量是非平稳的，它是一种时变非平稳流量。在时变非平稳情况下，本文用广义自回归条件异方差(Generalized Autoregressive Conditional Heteroscedasticity，GARCH)模型来建模OD流。不同于传统的模型，GARCH模型认为网络流量的方差不再是常量，而是随时间的变化而变化。通过GARCH模型，本文能很好地描述网络流量的重尾分布、自相似和LRD特性，从而能精确估计流量矩阵。
尽管流量矩阵的建模方法很多，但是由于流量矩阵的时变非平稳特性、空间时间相关性、重尾分布、自相似、SRD和LRD等特征，要建立精确描述流量矩阵的模型非常困难。递归神经网络具有自学习和归纳的能力，能进行线性和非线性建模，具有强大的建模功能。第五章基于递归神经网络的强大建模功能来估计大尺度IP流量矩阵，主要包括两方面的工作：(1)基于回归多层感知器(RecurrentMultiplayer Perceptron，RMLP)网络来建立流量矩阵估计模型。通过对大尺度IP骨干网络中的每一条OD流用RMLP来建模，然后构建一个多输入多输出的流量矩阵估计模型，获得在满足线性约束条件下的流量矩阵估计值。(2)研究在Elman神经网络下的大尺度IP流量矩阵估计。不同于RMLP，Elman神经网络被用来对所有OD流同时建模。本文通过修改传统的Elman神经网络来更准确地捕获流量矩阵的空间时间相关性，从而获得流量矩阵的精确估计。
与传统的建模方法相比，递归神经网络避免了复杂的数学计算，很好地解决了流量矩阵估计的建模问题，但是递归神经网络具有反馈连接结构，因此计算开销大，训练时间长。第六章讨论利用前馈神经网络来估计大尺度IP流量矩阵，主要包括三方面的工作：(1)在BP(Backpropagation)神经网络下，本文将流量矩阵估计问题建模为一个多输入多输出估计模型。通过输入输出数据对训练BP神经网络，就可快速建立该估计模型，然后通过寻找约束条件下的最优解来快速获得流量矩阵的估计值。(2)基于广义回归神经网络(Generalized Regression NeuralNetwork，GRNN)收敛于基本的回归面和能用于处理任何回归问题的特性，本文利用GRNN来研究大尺度IP流量矩阵估计问题。(3) RBF(Radial Basis Function)神经网络是另一种新的建模工具，它在逼近能力、分类能力和学习速度等方面，均优于BP神经网络。本文利用RBF神经网络来讨论大尺度IP流量矩阵的估计问题，通过修改传统的RBF神经网络模型来更准确地捕获流量矩阵的特征，并在欧氏距离和马氏距离下，通过迭代寻优来获得流量矩阵的精确估计。
最后，第七章总结全文，回顾了前面所述的研究工作，并根据目前的研究情况对未来的研究方向作了展望。
With the exponential increase in the size of the IP network and the urgent demands in network management and maintenance, traffic matrix estimation has currently become an interesting topic. As the IP network fast advances, network operators need to know how data packets among the nodes in a network are forwarded so that they can well make many network activities. These activities include load balancing, traffic detecting, route optimization, network maintenance, network designing, network planning and so on. As a key input of network activities, traffic matrix is extensively paid attention to by the researchers at home and abroad. It becomes an important research topic of the IP network at present. Traffic matrix denotes the volume of network traffic flowing among the Original-Destination (OD) nodes in a network (namely the volume of traffic for OD flows). Its dimension amounts to the number of all the OD flows in the network. It describes, from a global perspective, how the data in the whole network flow. And it is used by network operators to make many decisions. However, though traffic matrix is significantly important, it is very difficult to obtain it by the direct measurement and even is not practical sometimes. Traffic matrix estimation obtains the value of traffic matrix by the indirect measurement. It can avoid the problems met with the direct measurement. Due to this merit, this dissertation investigates the estimation problem of traffic matrix in the large-scale IP backbone network (namely large-scale IP traffic matrix), including: the optimal estimation of large-scale IP traffic matrix, large-scale IP traffic matrix estimation based on Fratar model, large-scale IP traffic matrix estimation based on regressive model, large-scale IP traffic matrix estimation based on recurrent neural network, and large-scale IP traffic matrix estimation based on feedforward neural network.
According to router matrix, network traffic flows in a network and is aggregated into link loads on links. Thus there exist the constraints among traffic matrix, router matrix and link loads. However, the number of OD flows is much more than that of links in the IP network, especially in large-scale IP backbone network. This leads to the highly ill-posed nature that traffic matrix estimation problem holds. How to overcome the ill-posed nature of this problem is the main challenge faced currently. Therefore, based on the numerical optimal theory, Chapter 2 seeks the methods to overcome the problems, which is that the results of large-scale IP traffic matrix estimation are not stable or unique, from two perspectives. (1) The simplex method is used to estimate traffic matrix. Firstly, traffic matrix estimation problem is described into the linear programming process under the constraints. Then the simplex method is combined with resolution matrix to handle this linear programming process. As a result, traffic matrix estimation is obtained. (2) The simulated annealing method is used to estimate traffic matrix. Firstly, traffic matrix estimation problem is described into the simulated annealing process. With temperature dropping, the estimation results of traffic matrix approach slowly to the real value with the result that the ill-posed nature of this problem is overcome. And then to overcome further the ill-posed nature of this problem, Euclid distance and Mahalanobis distance is used as the optimal metric. The optimal estimation of traffic matrix in the time-varying context can be attained by iterative process.
Previous works study traffic matrix estimation mostly based on the statistic models. Current research shows that traffic matrix holds spatio-temporal correlations. It is difficult of statistic models to capture these characteristics. Based on Fratar model, Chapter 3 estimates large-scale IP traffic matrix from two perspectives. (1) Fratar model is used to model the OD flows in large-scale IP backbone networks. By Fratar model, the spatio-temporal correlations of traffic matrix can be captured and its prior value can be obtained accurately. Then by iterative process, we can attain the estimation of traffic matrix. (2) Because the iterative process in (1) needs the complex computations, it takes long time. Based on Fratar model, this dissertation uses algebraic reconstruction technique (ART) to estimate traffic matrix. ART is a key technique in the image reconstruction. By the process of projecting and iterating, it seeks the solution without the complex computations and long time. Thus ART can fast attain the estimation results of traffic matrix.
When network traffic is investigated in details, the researchers find that it does not only hold spatio-temporal correlations, but also hold heavy-tailed distribution, self-similarity, short-range dependence (SRD), and long-range dependence (LRD) nature. Conventional models about network traffic can not accurately capture these characteristics. Chapter 4 uses regressive model to estimate large-scale IP traffic matrix from two perspectives. (1) To capture the temporal correlations of network traffic, OD flows are modeled as autoregressive moving average (ARMA) model. At the same time, traffic matrix estimation problem is described into the optimal process under Mahalanobis distance by taking the advantage of Mahalanobis distance. Then we can obtain the accurate estimation of traffic matrix by iterative process. (2) Autocorrelation function denotes that network traffic is nonstationary. And thus it is a time-varying and nonstationary traffic. In the time-varying and nonstationary context, this dissertation models OD flows into the generalized autoregressive conditional heteroscedasticity (GARCH) model. Unlike conventional model, GARCH model does not regard the variance of network traffic as constant value, but thinks that it changes with time. By GARCH model, this dissertation can well capture the heavy-tailed distribution, self-similarity, and LRD nature and thus can accurately estimate traffic matrix.
Though there are many modeling methods about traffic matrix, it is significantly difficult to build the accurate model about traffic matrix because it holds the time-varying and nonstationary nature, spatio-temporal correlations, heavy-tailed distribution, self-similarity, SRD, and LRD nature. Recurrent neural network can make the learning and generalization. It can be used to model the linear and nonlinear systems. Thus it holds the powerful modeling ability. Chapter 5 exploits the powerful modeling ability of recurrent neural network to estimate large-scale IP traffic matrix from two perspectives. (1) Recurrent multiplayer perceptron (RMLP) network is used to build the estimation model of traffic matrix. By modeling every OD flow in large-scale IP backbone network with RMLP network, a multi-input and multi-output estimation model of traffic matrix is built. Then the estimation results of traffic matrix satisfied with linear constraints is obtained. (2) This dissertation also investigates large-scale IP traffic matrix estimation based on Elman neural network. Unlike RMLP network, Elman neural network is used to model simultaneously all OD flows. By modifying conventional Elman neural network, spatio-temporal correlations of traffic matrix can be captured more accurately. Then the accurate estimation of traffic matrix is obtained.
In contrast to the conventional modeling methods, recurrent neural network avoids complex computations and well handle the modeling problem of traffic matrix estimation. However, because recurrent neural network holds feedback connections, it will take long time to train it with complex computations needed. Chapter 6 uses feedforward neural network to estimate large-scale IP traffic matrix from three perspectives. (1) Based on backpropagation (BP) neural network, this dissertation models traffic matrix estimation problem as a multi-input and multi-output estimation model. By using the input-output data pairs to train BP neural network, this estimation model can quickly be built Then traffic matrix estimation is fast obtained by seeking the optimal solution under the constraints. (2) Based on the characteristics that the generalized regression neural network (GRNN) converges to the underlying regression surface and can be used for any regression problem, this dissertation exploits GRNN to investigate large-scale IP traffic matrix estimation problem. (3) Radial basis function (RBF) neural network is another new modeling tool. It is better than BP neural network in terms of approximate capability, classification ability, and learning speed. This dissertation uses RBF neural network to discuss large-scale IP traffic matrix estimation problem. By modifying conventional RBF neural network, the characteristics of traffic matrix can be captured accurately. Then under Euclid distance and Mahalanobis distance, the accurate estimation of traffic matrix can be obtained by iterative process.
Finally, Chapter 7 summarizes the dissertation, reviews the above research work, and presents the future research directions.
网络流量根据路由矩阵在网络上流动，并在网络各条链路上汇聚而形成链路负载，因此流量矩阵、路由矩阵和链路负载间具有确定的约束关系。然而，在IP网络中，特别是大尺度IP骨干网络中，OD流的数目远远大于IP网络中的链路数，这导致流量矩阵估计问题具有高度病态特性，如何克服这一问题的病态特性是当前流量矩阵估计面对的主要挑战。针对大尺度IP流量矩阵估计问题的高度病态特性，第二章基于数值最优化理论，探索寻找解决大尺度IP流量矩阵估计过程中解的不稳定性和不唯一性问题的思路，主要包括两方面的工作：(1)基于单纯形方法来估计流量矩阵。通过将流量矩阵估计问题描述为约束条件下的线性规划，然后结合分辨率矩阵和单纯形方法来解决该线性规划，从而获得满足要求的流量矩阵估计值。(2)基于模拟退火方法来求解流量矩阵估计问题。通过将流量矩阵估计问题描述为模拟退火过程，随着温度的不断降低，估计值逐步逼近真实值，从而克服该问题的病态特性，然后利用欧氏距离(Euclid distance)和马氏距离(Mahalanobisdistance)作为最优化尺度来进一步克服该问题的病态特性，并通过迭代反演来获得时变网络条件下的流量矩阵最优化估计值。
以前的文献大多基于统计模型来研究流量矩阵估计问题，但是当前的研究表明流量矩阵具有空间的和时间的相关性，统计模型很难捕获流量矩阵的这些特征。第三章基于Fratar模型来估计大尺度IP流量矩阵，主要包括两方面的工作：(1)利用Fratar模型来建模大尺度IP骨干网络中的OD流。通过Fratar模型，能准确捕获流量矩阵的空间时间相关性，从而能获得精确的流量矩阵初始值，然后通过迭代过程来获得流量矩阵的估计值。(2)由于(1)的迭代过程计算复杂，因而需要时间长。基于Fratar模型，本文利用代数重构技术(Algebraic Reconstruction Technique，ART)来估计流量矩阵。ART是图像重构的重要技术，它基于投影和迭代来完成求解过程，需要的计算简单，计算时间短，因此ART能快速获得流量矩阵的估计结果。
随着对网络流量的深入研究，研究人员发现网络流量不仅具有空间时间相关性，而且具有重尾分布(Heavy-tailed distributions)、自相似(Self-similarity)、短相关(Short-Range Dependence，SRD)和长相关(Long-Range Dependence，LRD)特性，传统的网络流量模型不能准确地捕获这些特征。第四章基于回归模型来估计大尺度IP流量矩阵，主要包括两方面的研究：(1)为了描述网络流量的时间相关性，将OD流建模为自回归滑动平均(Autoregressive Moving Average，ARMA)模型，并利用马氏距离的优点，将流量矩阵估计问题描述为马氏距离下的最优化过程，通过迭代寻优来获得流量矩阵的精确估计。(2)网络流量的自相关函数表示网络流量是非平稳的，它是一种时变非平稳流量。在时变非平稳情况下，本文用广义自回归条件异方差(Generalized Autoregressive Conditional Heteroscedasticity，GARCH)模型来建模OD流。不同于传统的模型，GARCH模型认为网络流量的方差不再是常量，而是随时间的变化而变化。通过GARCH模型，本文能很好地描述网络流量的重尾分布、自相似和LRD特性，从而能精确估计流量矩阵。
尽管流量矩阵的建模方法很多，但是由于流量矩阵的时变非平稳特性、空间时间相关性、重尾分布、自相似、SRD和LRD等特征，要建立精确描述流量矩阵的模型非常困难。递归神经网络具有自学习和归纳的能力，能进行线性和非线性建模，具有强大的建模功能。第五章基于递归神经网络的强大建模功能来估计大尺度IP流量矩阵，主要包括两方面的工作：(1)基于回归多层感知器(RecurrentMultiplayer Perceptron，RMLP)网络来建立流量矩阵估计模型。通过对大尺度IP骨干网络中的每一条OD流用RMLP来建模，然后构建一个多输入多输出的流量矩阵估计模型，获得在满足线性约束条件下的流量矩阵估计值。(2)研究在Elman神经网络下的大尺度IP流量矩阵估计。不同于RMLP，Elman神经网络被用来对所有OD流同时建模。本文通过修改传统的Elman神经网络来更准确地捕获流量矩阵的空间时间相关性，从而获得流量矩阵的精确估计。
与传统的建模方法相比，递归神经网络避免了复杂的数学计算，很好地解决了流量矩阵估计的建模问题，但是递归神经网络具有反馈连接结构，因此计算开销大，训练时间长。第六章讨论利用前馈神经网络来估计大尺度IP流量矩阵，主要包括三方面的工作：(1)在BP(Backpropagation)神经网络下，本文将流量矩阵估计问题建模为一个多输入多输出估计模型。通过输入输出数据对训练BP神经网络，就可快速建立该估计模型，然后通过寻找约束条件下的最优解来快速获得流量矩阵的估计值。(2)基于广义回归神经网络(Generalized Regression NeuralNetwork，GRNN)收敛于基本的回归面和能用于处理任何回归问题的特性，本文利用GRNN来研究大尺度IP流量矩阵估计问题。(3) RBF(Radial Basis Function)神经网络是另一种新的建模工具，它在逼近能力、分类能力和学习速度等方面，均优于BP神经网络。本文利用RBF神经网络来讨论大尺度IP流量矩阵的估计问题，通过修改传统的RBF神经网络模型来更准确地捕获流量矩阵的特征，并在欧氏距离和马氏距离下，通过迭代寻优来获得流量矩阵的精确估计。
最后，第七章总结全文，回顾了前面所述的研究工作，并根据目前的研究情况对未来的研究方向作了展望。
With the exponential increase in the size of the IP network and the urgent demands in network management and maintenance, traffic matrix estimation has currently become an interesting topic. As the IP network fast advances, network operators need to know how data packets among the nodes in a network are forwarded so that they can well make many network activities. These activities include load balancing, traffic detecting, route optimization, network maintenance, network designing, network planning and so on. As a key input of network activities, traffic matrix is extensively paid attention to by the researchers at home and abroad. It becomes an important research topic of the IP network at present. Traffic matrix denotes the volume of network traffic flowing among the Original-Destination (OD) nodes in a network (namely the volume of traffic for OD flows). Its dimension amounts to the number of all the OD flows in the network. It describes, from a global perspective, how the data in the whole network flow. And it is used by network operators to make many decisions. However, though traffic matrix is significantly important, it is very difficult to obtain it by the direct measurement and even is not practical sometimes. Traffic matrix estimation obtains the value of traffic matrix by the indirect measurement. It can avoid the problems met with the direct measurement. Due to this merit, this dissertation investigates the estimation problem of traffic matrix in the large-scale IP backbone network (namely large-scale IP traffic matrix), including: the optimal estimation of large-scale IP traffic matrix, large-scale IP traffic matrix estimation based on Fratar model, large-scale IP traffic matrix estimation based on regressive model, large-scale IP traffic matrix estimation based on recurrent neural network, and large-scale IP traffic matrix estimation based on feedforward neural network.
According to router matrix, network traffic flows in a network and is aggregated into link loads on links. Thus there exist the constraints among traffic matrix, router matrix and link loads. However, the number of OD flows is much more than that of links in the IP network, especially in large-scale IP backbone network. This leads to the highly ill-posed nature that traffic matrix estimation problem holds. How to overcome the ill-posed nature of this problem is the main challenge faced currently. Therefore, based on the numerical optimal theory, Chapter 2 seeks the methods to overcome the problems, which is that the results of large-scale IP traffic matrix estimation are not stable or unique, from two perspectives. (1) The simplex method is used to estimate traffic matrix. Firstly, traffic matrix estimation problem is described into the linear programming process under the constraints. Then the simplex method is combined with resolution matrix to handle this linear programming process. As a result, traffic matrix estimation is obtained. (2) The simulated annealing method is used to estimate traffic matrix. Firstly, traffic matrix estimation problem is described into the simulated annealing process. With temperature dropping, the estimation results of traffic matrix approach slowly to the real value with the result that the ill-posed nature of this problem is overcome. And then to overcome further the ill-posed nature of this problem, Euclid distance and Mahalanobis distance is used as the optimal metric. The optimal estimation of traffic matrix in the time-varying context can be attained by iterative process.
Previous works study traffic matrix estimation mostly based on the statistic models. Current research shows that traffic matrix holds spatio-temporal correlations. It is difficult of statistic models to capture these characteristics. Based on Fratar model, Chapter 3 estimates large-scale IP traffic matrix from two perspectives. (1) Fratar model is used to model the OD flows in large-scale IP backbone networks. By Fratar model, the spatio-temporal correlations of traffic matrix can be captured and its prior value can be obtained accurately. Then by iterative process, we can attain the estimation of traffic matrix. (2) Because the iterative process in (1) needs the complex computations, it takes long time. Based on Fratar model, this dissertation uses algebraic reconstruction technique (ART) to estimate traffic matrix. ART is a key technique in the image reconstruction. By the process of projecting and iterating, it seeks the solution without the complex computations and long time. Thus ART can fast attain the estimation results of traffic matrix.
When network traffic is investigated in details, the researchers find that it does not only hold spatio-temporal correlations, but also hold heavy-tailed distribution, self-similarity, short-range dependence (SRD), and long-range dependence (LRD) nature. Conventional models about network traffic can not accurately capture these characteristics. Chapter 4 uses regressive model to estimate large-scale IP traffic matrix from two perspectives. (1) To capture the temporal correlations of network traffic, OD flows are modeled as autoregressive moving average (ARMA) model. At the same time, traffic matrix estimation problem is described into the optimal process under Mahalanobis distance by taking the advantage of Mahalanobis distance. Then we can obtain the accurate estimation of traffic matrix by iterative process. (2) Autocorrelation function denotes that network traffic is nonstationary. And thus it is a time-varying and nonstationary traffic. In the time-varying and nonstationary context, this dissertation models OD flows into the generalized autoregressive conditional heteroscedasticity (GARCH) model. Unlike conventional model, GARCH model does not regard the variance of network traffic as constant value, but thinks that it changes with time. By GARCH model, this dissertation can well capture the heavy-tailed distribution, self-similarity, and LRD nature and thus can accurately estimate traffic matrix.
Though there are many modeling methods about traffic matrix, it is significantly difficult to build the accurate model about traffic matrix because it holds the time-varying and nonstationary nature, spatio-temporal correlations, heavy-tailed distribution, self-similarity, SRD, and LRD nature. Recurrent neural network can make the learning and generalization. It can be used to model the linear and nonlinear systems. Thus it holds the powerful modeling ability. Chapter 5 exploits the powerful modeling ability of recurrent neural network to estimate large-scale IP traffic matrix from two perspectives. (1) Recurrent multiplayer perceptron (RMLP) network is used to build the estimation model of traffic matrix. By modeling every OD flow in large-scale IP backbone network with RMLP network, a multi-input and multi-output estimation model of traffic matrix is built. Then the estimation results of traffic matrix satisfied with linear constraints is obtained. (2) This dissertation also investigates large-scale IP traffic matrix estimation based on Elman neural network. Unlike RMLP network, Elman neural network is used to model simultaneously all OD flows. By modifying conventional Elman neural network, spatio-temporal correlations of traffic matrix can be captured more accurately. Then the accurate estimation of traffic matrix is obtained.
In contrast to the conventional modeling methods, recurrent neural network avoids complex computations and well handle the modeling problem of traffic matrix estimation. However, because recurrent neural network holds feedback connections, it will take long time to train it with complex computations needed. Chapter 6 uses feedforward neural network to estimate large-scale IP traffic matrix from three perspectives. (1) Based on backpropagation (BP) neural network, this dissertation models traffic matrix estimation problem as a multi-input and multi-output estimation model. By using the input-output data pairs to train BP neural network, this estimation model can quickly be built Then traffic matrix estimation is fast obtained by seeking the optimal solution under the constraints. (2) Based on the characteristics that the generalized regression neural network (GRNN) converges to the underlying regression surface and can be used for any regression problem, this dissertation exploits GRNN to investigate large-scale IP traffic matrix estimation problem. (3) Radial basis function (RBF) neural network is another new modeling tool. It is better than BP neural network in terms of approximate capability, classification ability, and learning speed. This dissertation uses RBF neural network to discuss large-scale IP traffic matrix estimation problem. By modifying conventional RBF neural network, the characteristics of traffic matrix can be captured accurately. Then under Euclid distance and Mahalanobis distance, the accurate estimation of traffic matrix can be obtained by iterative process.
Finally, Chapter 7 summarizes the dissertation, reviews the above research work, and presents the future research directions.
引文
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