Experimental queueing analysis with long-range dependent packettraffic

Traffic measurement studies from a wide range of working packet networks have convincingly established the presence of significant statistical features that are characteristic of fractal traffic processes, in the sense that these features span many time scales. Of particular interest in packet traffic modeling is a property called long-range dependence (LRD), which is marked by the presence of correlations that can extend over many time scales. We demonstrate empirically that, beyond its statistical significance in traffic measurements, long-range dependence has considerable impact on queueing performance, and is a dominant characteristic for a number of packet traffic engineering problems. In addition, we give conditions under which the use of compact and simple traffic models that incorporate long-range dependence in a parsimonious manner (e.g., fractional Brownian motion) is justified and can lead to new insights into the traffic management of high speed networks     

基于FrFT的网络流量Hurst参数估计器

实际的网络流量模型采用自相似模型,Hurst参数是序列长相关程度的度量。为方便工程上对网络流量的长相关性进行估计,介绍了网络流量自相似模型和Hurst参数小波分析法,建立了分数阶傅里叶变换（FrFT）与小波分析之间的联系,在此基础上介绍了一种新的基于FrFT的网络流量Hurst参数估计方法,并运用此方法设计了网络流量Hurst参数估计器。通过对白噪声和已知Hurst参数的实际网络流量数据进行估计,本方法可以有效估计随机时间序列的Hurst参数。     

长相关业务流经成形器后的输出特性研究

网络中业务流的自相似性正日益受到重视，因为它的网络性能有着很大的影响，本文采用计算机仿真的方法，对输入长相关（ＬＲＤ－Ｌｏｎｇ－ＲａｎｇｅＤｅｐｅｎｄｅｎｔ）业务的成形器的输出序列的特性进行了研究。当长相关业和使用分形布朗运动（ＦＢＭ－ＦｒａｎｃｔａｌＢｒｏｗｎａｉｎＭｏｔｉｏｎ）模型时，我们的研究表明，在不同的信元丢失率（ＣＬＲ－ＣｅｌｌＬｏｓｓＲａｔｅ）下，成形器输出序列的自相关特性与输入序更     

结合多重分形的网络流量非线性预测

通过分析树型多重分形结构的相关性发现，多重分形可以把非平稳且具有长相关（LRD）和分形特性的网络流量序列转化为可用短相关（SRD）模型表示的序列组。利用多重分形这种将时间序列分解为多层的能力，提出了一种结合多重分形的FIR神经网络流量预测模型（MF-FIR，multifractal FIR network）。MF-FIR合理地利用了流量序列的LRD信息，具有很好的多步预测性能，可以满足通信系统在线预测的要求。     

基于FBM模型的自相似流量建模仿真

网络流量建模是网络规划与性能评价的重要基础,传统的业务模型大多基于泊松模型和马尔可夫排队模型,只具有短程相关性,随着网络业务的不断研究发现,实际网络业务流在很长的时间范围内都具有长程相关性,即一种自相似性。本文采用RMD算法和Fourier变换法对网络流量的自相似模型-FBM模型进行了建模及仿真研究,生成了所需的自相似流量序列。然后分别采用R/S法和方差时间图法对其进行自相似参数检测。结果验证了仿真算法所产生的序列存在着自相似性,并同时对RMD算法和Fourier变换法的优缺点进行了分析。     

WPANFIS: combine fuzzy neural network with multiresolution for network traffic prediction

A novel methodology for prediction of network traffic,WPANFIS,which relies on wavelet packet transform(WPT)for multi-resolution analysis and adaptive neuro-fuzzy inference system(ANFIS)is proposed in this article.The widespread existence of self-similarity in network traffic has been demonstrated in earlier studies,which exhibits both long range dependence(LRD)and short range dependence(SRD).Also,it has been shown that wavelet decomposition is an effective tool for LRD decorrelation.The new method uses WPT as extension of wavelet transform which can decoorrelate LRD and make more precisely partition in the high-frequency section of the original traffic.Then ANFIS which can extract useful information from the original traffic is implemented in this study for better prediction performance of each decomposed non-stationary wavelet coefficients.Simulation results show that the proposed WPANFIS can achieve high prediction accuracy in real network traffic environment.     

Modeling heterogeneous network traffic in wavelet domain

Heterogeneous network traffic possesses diverse statistical properties which include complex temporal correlation and non-Gaussian distributions. A challenge to modeling heterogeneous traffic is to develop a traffic model which can accurately characterize these statistical properties, which is computationally efficient, and which is feasible for analysis. This work develops wavelet traffic models for tackling these issues. We model the wavelet coefficients rather than the original traffic. Our approach is motivated by a discovery that although heterogeneous network traffic has the complicated short- and long-range temporal dependence, the corresponding wavelet coefficients are all “short-range” dependent. Therefore, a simple wavelet model may be able to accurately characterize complex network traffic. We first investigate what short-range dependence is important among the wavelet coefficients. We then develop the simplest wavelet model, i.e., the independent wavelet model for Gaussian traffic. We define and evaluate the (average) autocorrelation function and the buffer loss probability of the independent wavelet model for fractional Gaussian noise (FGN) traffic. This assesses the performance of the independent wavelet model, and the use of which for analysis. We also develop (low-order) Markov wavelet models to capture additional dependence among the wavelet coefficients. We show that an independent wavelet model is sufficiently accurate, and a Markov wavelet model only improves the performance marginally. We further extend the wavelet models to non-Gaussian traffic through developing a novel time-scale shaping algorithm. The algorithm is tested using real network traffic and shown to outperform FARIMA in both efficiency and accuracy. Specifically, the wavelet models are parsimonious, and have a computational complexity O(N) in developing a model from a training sequence of length N, and O(M) in generating a synthetic traffic trace of length M     

Contradictory relationship between Hurst parameter and queueing performance (extended version)

Long Range Dependent (LRD) network traffic does not behave like the traffic generated by the Poisson model or other Markovian models. From the network performance point of view, the main difference is that LRD traffic increases queueing delays due to its burstiness over many time scales. LRD behavior has been observed in different types and sizes of networks, for different applications (e.g., WWW) and different traffic aggregations. Since LRD behaviour is not rare nor isolated, accurate characterization of LRD traffic is very important in order to predict performance and to allocate network resources. The Hurst parameter is commonly used to quantify the degree of LRD and the burstiness of the traffic. In this paper we investigate the validity and effectiveness of the Hurst parameter. To this end, we analyze the UCLA Computer Science Department network traffic traces and compute their Hurst parameters. Queueing simulation is used to study the impact of LRD and to determine if the Hurst parameter accurately describes such LRD. Our results show that the Hurst parameter is not by itself an accurate predictor of the queueing performance for a given LRD traffic trace.     

自相似模型下的交换式网络仿真

传统模式下的网络仿真,报文到达均服从的是一种具有短相关特性的泊松分布。而经过大量业务流量监测表明,网络流量实际呈现出的确是一种具有长相关特性的自相似分布,这种特性对网络流量建模、性能分析、接纳控制等产生了重要影响。在对自相似特性深入分析的基础上,利用分型布朗运动模型的RMD算法产生自相似序列来模拟网络业务,并对该业务流特性下的交换式以太网进行了仿真实验。结果表明业务量的自相似性对交换式网络的各项性能影响很大,这与传统流量模型形成鲜明对比。     

基于离散小波变换的网络流量多重分形模型

网络流量过程中所蕴含的分形尺度特性对网络性能有显著的影响。因此研究能全面准确地刻画网络流量过程在小时间／空间尺度上的复杂奇异性特征和大时间／空间尺度上的长程依赖性特征的流量模型对Internet网络工程有重要的意义。本文对实测的流量数据(从著名的校园网和国内著名的ISP)进行了分析，利用小波技术构建了一个新的网络流量的多重分形模型，通过模拟验证，发现该新模型能以较简洁的形式捕捉实际网络流量特性，并具有刻画真实流量数据中的多重分形特征的能力。     

Recurrence Plot-Based Approach to the Analysis of IP-Network Traffic in Terms of Assessing Nonstationary Transitions Over Time

This paper presents a recurrence plot scheme approach to the analysis of nonstationary transition patterns of IP-network traffic. In performing a quantitative assessment of dynamical transition patterns of IP-network traffic, we used the values of determinism (DET) defined by the recurrence quantification analysis (RQA). Also, in evaluating fractal-related properties of IP-network traffic, we employed the detrended fluctuation analysis (DFA), which is applicable to the analysis of long-range dependence (LRD) in nonstationary time-series signals. Furthermore, to obtain a comprehensive view of network traffic conditions, we used a self-organizing map, which provides a way to map high-dimensional data onto a low-dimensional domain. When applying this method to traffic analysis, we performed two kinds of traffic measurement in Tokyo, Japan, and derived values of DET and the LRD-based scaling parameter$alpha$of IP-network traffic. Then, we found that the characteristic with respect to DET and self-similarity seen in the measured traffic fluctuated over time, with different time variation patterns for two measurements. In training the self-organizing map, we used three parameters: average throughput, variation ratio of DET, and$alpha$value. As a result, we visually confirmed that the traffic data could be projected onto the map in accordance with traffic properties, resulting in a combined depiction of the effects of the DET and network utilization rates on the time-variations of LRD.     

Analysis of a random-access protocol under long-range-dependent traffic

ALOHA-type random-access protocols have been used as access-control protocols in wireline and wireless, fixed and mobile, multiple-access communications networks. They are frequently employed by the control and signaling subsystem of demand-assigned multiple-access protocols to regulate the sharing of a multi-access communications channel. The correct design and sizing of the random-access operated control/signaling channel is critical in determining the performance of these networks. Excessive delays in the transport of signaling messages (due to too many collisions and retransmissions) lead to unacceptable session-connection setup times. This is of particular concern when the message traffic is highly bursty. We investigate the performance behavior of a random-access protocol when loaded by bursty traffic processes. The latter often exhibit long-range dependence (LRD). We model the LRD traffic flows as multiplicative multifractal processes. The random-access protocol is modeled as an ALOHA channel with blocking. The burstiness of the traffic processes, rather than their LRD character, is the essential element determining the performance behavior of the protocol. When the loading-traffic process is not very bursty, the performance of the random-access channel can be even better than that exhibited under Poisson traffic loading; otherwise, performance degradation is noted. We demonstrate the impact of the selection of the protocol-operational parameters in determining the effective performance behavior of the random-access protocol.     

VBR视频流多重分形建模

该文在小波域多重分形基础上,研究了基于分布、点集(PM)分布的多重分形小波模型(MWM)的性能,并提出了一种具有更好的逼近性能的混合PM-分布形式;同时,针对VBR视频流的I,P,B帧周期分布特性,充分利用异种帧相关性,建立了考虑帧间相关性的混合多重分形小波VBR视频流量模型CMWM(Composite MWM)。仿真试验表明,与传统的短相关和长相关模型相比,具有多重分形特性的CMWM能更加精确地描述MPEG视频业务的统计特性和排队性能。     

Correlation matching method for the weak stationarity test of LRD traffic

The stationarity test of long-range dependent (LRD) traffic remains a challenge problem in the field of traffic engineering. Due to the importance of traffic theory in the Internet, to find a solution to that problem is greatly desired. This paper presents a method of the weak stationarity test of a single history LRD traffic series of finite length. How to apply this method to testing the stationarity of real traffic is demonstrated. The results in this paper suggest that there may be no general conclusion that traffic is either stationary or non-stationary since the stationarity of traffic is observation-scale dependent. Some of the investigated real-traffic traces that are stationary in an observation scale may be non-stationary in a larger observation scale.     

Assessing the accuracy of using aggregated traffic traces in network engineering

Aggregated traffic traces are commonly used in network engineering for QoS or performance parameters evaluation. Many performance models come from such aggregated traces. However, real traffic is a marked point process combining two processes: one for the arrival times of packets and the other for their size in bytes. This paper deals with assessing whether aggregated traces are a good representation of real traffic. Based on the analysis of many traffic traces, and focusing only on loss probability, it is shown that the packet drop probability obtained for the aggregated traffic traces can significantly differ from the real packet drop probability obtained for the real traffic traces. Then, a solution which enables one to obtain correct loss probability based on aggregated traffic traces is proposed by determining the correct aggregation scale and traffic parameters to be applied.     

An improved Hurst parameter estimator based on fractional Fourier transform

A fractional Fourier transform (FrFT) based estimation method is introduced in this paper to analyze the long range dependence (LRD) in time series. The degree of LRD can be characterized by the Hurst parameter. The FrFT-based estimation of Hurst parameter proposed in this paper can be implemented efficiently allowing very large data set. We used fractional Gaussian noises (FGN) which typically possesses long-range dependence with known Hurst parameters to test the accuracy of the proposed Hurst parameter estimator. For justifying the advantage of the proposed estimator, some other existing Hurst parameter estimation methods, such as wavelet-based method and a global estimator based on dispersional analysis, are compared. The proposed estimator can process the very long experimental time series locally to achieve a reliable estimation of the Hurst parameter.     

Modeling and analysis of self-similar traffic source based on fractal-binomial-noise-driven Poisson process

~~Modeling and analysis of self-similar traffic source based on fractal-binomial-noise-driven Poisson process1. Will E L, Murad S T, Walter W, et al. On the self-similarity nature of Ethernet traffic (extended version). IEEE/ACM Transactions on Networking…     

q-Exponential product-form solution of packet distribution in queueing networks: maximization of Tsallis entropy

A maximum Tsallis entropy solution is presented to examine the effect of long-range dependence (LRD) of packet traffic on network of queues. An important finding is that usual product form solution of queueing networks does not hold. However, it is possible to preserve the product like structure in terms of q-product of q-exponential functions. A special case is considered when normalized q-expectation values of first moment and queue utilization at each node are available as the constraint. The joint state probability distribution is shown to depict asymptotically power law behavior.     

Generation of Gaussian Self-similar series via Wavelets for Use in Traffic Simulations

Measurements have shown that network traffic has fractal properties such as self-similarity and long memory or long-range dependence. Long memory is characterized by the existence of a pole at the origin of the power spectrum density function (1/f shape). It was also noticed that traffic may present short-range dependence at some time scales. The use of a “realistic” aggregated network traffic generator, one that synthesizes fractal time series, is fundamental to the validation of traffic control algorithms. In this article, the synthesis of approximate realizations of a kind of self-similar random process named fractional Gaussian noise is done via wavelet transform. The proposed method is also capable of synthesizing Gaussian time series with more generic spectra than 1/f, that is, time series that also have short-range dependence. The generation is done in two stages. The first one generates an approximate realization of fractional Gaussian noise via discrete Wavelet transform. The second one introduces short-range dependence through IIR (Infinite Impulse Response) filtering at the output of the first stage. A detailed characterization of the resulting series was done, using statistical moments of first, second, third and fourth orders, as well as specific statistical tests for self-similar series. It was verified that the Whittle estimator of the Hurst parameter is more robust than the periodogram method for series that simultaneously present short-range and long-range dependence.     

基于EMD及ARMA的自相似网络流量预测

提出了一种基于ARMA(自回归滑动平均)模型的经验模式分解预测自相似网络流量的方法,进行了理论证明和仿真验证.结果表明,经验模式分解对长相关流量有去相关的作用,采用ARMA模型即可对自相似网络流量准确刻画,不但降低了算法的复杂度,而且预测精度高于径向基函数神经网络的预测精度.