摘要
网络通信量测量与建模是网络体系结构设计及性能分析的基础,其测量的精确性和模型描述的准确性对于所设计网络的正常运行并使网络性能达到最优化是非常重要的。很长时间以来,网络通信量都被认为只具有Markov性,并在此基础上建立了以Poisson过程为主的通信量数学描述模型。这种模型具有短程相关结构,长期以来在网络性能分析,尤其是以语音业务为主的传统电信网和以数据为主的计算机网络性能分析中发挥了重要作用。但是近年来对各种网络的大量实际测量发现网络通信量不仅具有短程相关性,而且还具有自相似性(也就是长程相关性)。长程相关性与短程相关性的不同之处在于其相关结构在多个时间尺度上存在,并且在大时间尺度上这种性质对网络延时、抖动以及吞吐量等网络性能具有短程相关性所没有的极大影响,所以自相似网络通信量及其性能分析受到国内外学者的极大重视并被广泛研究。
本文对自相似网络通信量及其网络排队性能分析进行了仔细的研究。首先讨论了自相似网络通信量的参数估计问题,同时还研究了自相似通信量的预测问题。然后我们从不同角度利用不同方法讨论了自相似网络通信量对于网络排队性能的影响,并得到了一些有用的结论。本文研究的主要创新和结论可概括为以下几个方面。
首先,因为自相似过程与Markov过程的区别,也就是其影响网络性能的主要性质是其在多个时间尺度上的长程相关性(二阶自相似性),所以自相似网络通信量的二阶参数估计对于实际网络通信量的建模与性能分析就显得非常重要。我们以分形高斯过程为模型讨论了自相似网络通信量的自相关估计问题,从而得到了一个快速估计通信量自相关值的公式。该公式较精确的描述了自相关估计精度、样本数据长度以及Hurst参数之间的关系。实验分析表明该公式不仅对于分形高斯过程是正确的,而且对于其他自相似过程的自相关估计也可以提供很强的参考价值。
其次,发现了自相似网络通信量的一个新性质,也就是在H=0.75左右其自相关估计的方差会有一个大的跳变,我们称为“jumping burstiness”。“jumping burstiness”表明自相似网络通信量的突发性和H值之间具有非线性关系,这一关系对于分析自相似网络通信量对网络性能的影响以及利用通信量的长程相关性进行网络控制具有很强的指导性意义。同时我们对这一现象的产生原因及其对网络性能的影响也做了分析。
对于自相似通信量的预测,利用同时具有长程相关和短程相关性质的FARIMA(Fractional Auto-Regression Integrated Moving Average)模型提出了一种通过自适应估计模型参数来进行通信量预测的算法。该算法能够很好的反映通信量中的
长程相关性,并且可以逐步自适应的调整预测参数到最优值,从而保证了预测模型与实际通信量的良好拟合性。仿真模拟实验证明了这种算法的收敛性,从而也就保证了预测的精确性。同时根据这一预测算法设计了一个较为有效的多媒体实时传输协议。
因为自相似网络通信量对网络排队系统的作用直接影响到整个网络的QoS(Quality of Service),所以我们先讨论了分形布朗运动通信量模型输入下排队系统的延迟和抖动特性;然后在这一输入模型下提出了缓存溢出带宽的上界以及基于此上界的带宽分配策略和接纳控制策略;另外,我们还考虑了自相似通信量输入对系统性能产生影响的时间尺度问题。研究发现通信量长程相关性发生作用的时间尺度不仅与短程相关参数有关,而且还与系统缓存以及信道容量等参数有关。这一研究克服了分形布朗运动模型不能在小时间尺度上描述通信量的缺点,这对于资源分配等与尺度密切相关的问题具有很强的实际参考意义。
在广泛分析进入网络节点的IP数据包大小和到达时间间隔等统计性质的基础上,提出了一种混合Pareto分布通信量模型,并探讨了基于该模型的合成通信量生成。然后,我们采用补充变量和嵌入式Markov链结合的方法来分析了成批达到成批服务的单服务台有限等待空间的FCFS(First Come First Service)排队系统GIX/MY/1/N。通过使用补充变量得到了用户到达前时刻和任意时刻系统状态概率之间的闭式关系,而通过嵌入式Markov链的方法则得到了到达前时刻的系统状态概率。并基于此得到了部分拒绝和全部拒绝情况下的系统平均队长和等待时间等性能参数。
最后,我们在数据包级对高速路由器性能进行了分析。利用混合Pareto分布通信量模型来描述进入系统的通信量,然后通过GIX/MY/1/N模型来研究了高速路由结构的包级性能,并进行了数值实验分析。研究发现通过这一模型得到的结果较利用大偏差技术所得到的结果的精度大为提高,可以很好的满足系统的包级性能分析要求。
由于自相似网络通信量的发现还不长,并且其影响也涉及网络系统的各个方面,要能够提出一种考虑自相似网络通信量的实际应用也必然要在很多方面进行充分的研究;同时任何研究要应用于实践都不可能一蹴而就,而需要一个漫长的过程。
但是随着研究工作的不断继续和深入,新技术的提出和理论的发展将会对网络系统的研究提供极大的推动作用,所以我们相信我们终将实现这一目标。
Measuring and modeling of network traffic are the fundament of network architecture design and performance analysis, the accuracy of measurement and the fitness of model are very important for an operational network to achieve the optimization of system performance.
For a long time, network traffic has been only regarded as a Markov chain, and mainly modeled by Poisson process. These kinds of models have a short-range dependence structure and play an important role in network analysis, especially in traditional telecommunication network that was mainly designed to provide voice service. However it was found that besides short-range dependence, self-similarity (i.e. long-rang dependence) exists in actual measured network traffic. This character has a great influence on network performance and control scheme at large time scales, such as delay, jitter, congestion control, and so on, which is much different from Markov process. So self-similar network traffic and its performance evaluation attract much attention and are studied world widely.
In this thesis, the self-similar network traffic and its performance evaluation are studied extensively. Firstly, we discuss the second-order parameter estimation and the prediction of self-similar network traffic. Then the impact of self-similar network traffic on queueing performance is discussed at different points of view with different methods and some useful results are obtained. The main research results are presented as follows.
We know that self-similar process is mainly different from Markov process with its long-range dependence (i.e. second-order self-similarity) at multiple time scales, so it is very important to estimate its second-order parameter in practical traffic model and performance evaluation. With fractional Gauss process, we analysis the estimation of autocorrelation and obtain an evaluating formula, in which the relation of the accuracy of estimated autocorrelation, sampled data length and Hurst parameter is accurately described. Experiments confirm that our result is not only correct for fractional Gauss process, but also a perfect reference to other self-similar process.
Meanwhile, a sharply variety in the accuracy of estimated autocorrelation we called “jumping burstiness” is discovered around H=0.75. It is a very interesting phenomenon that hadn’t been reported before. This “jumping burstiness” shows that there is a
non-linear relationship between Hurst parameter and traffic burstiness, which can be a good instruction for the utilization of second-order self-similar character. It also shows that all the traffic varieties cannot be captured only with Hurst parameter.
Afterward, a traffic predicting algorithm based on FARIMA (Fractional Auto- Regression Integrated Moving Average) model is proposed, which estimates the self-similar parameters explicitly. This algorithm considers the character of long-range dependence of network traffic. Simulation result confirms the convergence of estimated parameter, which guarantees the predicting accuracy of this algorithm.
The effect of self-similar network traffic on queueing system relates directly to the whole network performance. Packet delay and jitter in a FCFS (First Come First Service) queueing system with fractional Brown motion input are discussed. Then, the upper bound of buffer overflow probability is obtained with this model. An effective bandwidth allocation and admission control scheme is also proposed. Furthermore, the onset time scale that self-similar traffic begins to affect system performance is discussed. It is found that the onset time scale is not only related to short-range dependence, but also related to the system parameters, such as buffer, bandwidth and so on. This result remedies the defect of fractional Brown motion that cannot be operated at little time scale and it is a good reference to the time scale related problems.
Based on the extensive analysis of the inputting IP packet size and inter-arrival time, a mixture Pareto traffic model is proposed from the point of v
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