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     

The extended alternating fractal renewal process for modelingtraffic in high-speed communication networks

Extensive studies indicate that traffic in high-speed communication networks exhibits long-range dependence (LRD) and impulsiveness, which pose new challenges in network engineering. While many models have appeared for capturing the traffic LRD, fewer models exist that account for impulsiveness as well as LRD. One of the few existing constructive models for network traffic is the celebrated on/off model or the alternating fractal renewal process (AFRP). However, although the AFRP results in aggregated traffic with LRD, it fails to capture impulsiveness, yielding traffic with Gaussian marginal distribution. A new constructive model, namely the extended AFRP (EAFRP), is proposed here, which overcomes the limitations of the AFRP model. We show that for both single-user and aggregated traffic, it results in impulsiveness and long-range dependence, the LRD being defined here in a generalized sense. We provide queueing analysis of the proposed model, which clearly demonstrates the implications of the impulsiveness in traffic engineering, and validate all theoretical findings based on real traffic data     

自相似VBR视频源业务流的建模和仿真

该文在对实际VBR MPEG视频源统计特性分析的基础上,参照分形高斯噪声自相似(Fractional Gaussian Noise Self-Similar)模型产生方法,实现了对ATM网络中最主要业务流VBR视频源流的建模,提出了改进方法,使得对实际源的仿真不仅考虑到了长期相关性,同时也兼顾到了短期相关性。仿真结果表明,经改进的自相似VBR视频源模型是一种较理想的模型。     

Multiscale Fitting Procedure Using Markov Modulated Poisson Processes

This paper proposes a parameter fitting procedure using Markov Modulated Poisson Processes (MMPPs) that leads to accurate estimates of queuing behavior for network traffic exhibiting long-range dependence behavior. The procedure matches both the autocovariance and marginal distribution of the counting process. A major feature is that the number of states is not fixed a priori, and can be adapted to the particular trace being modeled. The MMPP is constructed as a superposition of L 2-MMPPs and one M-MMPP. The 2-MMPPs are designed to match the autocovariance and the M-MMPP to match the marginal distribution. Each 2-MMPP models a specific time-scale of the data. The procedure starts by approximating the autocovariance by a weighted sum of exponential functions that model the autocovariance of the 2-MMPPs. The autocovariance tail can be adjusted to capture the long-range dependence characteristics of the traffic, up to the time-scales of interest to the system under study. The procedure then fits the M-MMPP parameters in order to match the marginal distribution, within the constraints imposed by the autocovariance matching. The number of states is also determined as part of this step. The final MMPP with M2 ^L states is obtained by superposing the L 2-MMPPs and the M-MMPP. We apply the inference procedure to traffic traces exhibiting long-range dependence and evaluate its queuing behavior through simulation. Very good results are obtained, both in terms of queuing behavior and number of states, for the traces used, which include the well-known Bellcore traces.     

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。     

一种基于瑞利分布的VBR视频流的小波模型

本文提出了一种新型的视频业务流模型,以Haar小波的多分辨率分析为基础,在尺度空间和小波空间分别建模,然后通过小波反变换得出仿真业务流.在最"粗"的尺度空间里,我们根据视频流的概率分布特点,采用基于瑞利(Rayleigh)分布的AR模型对尺度系数建模;在各个小波空间里,采用一般的高斯不相关小波模型(WIG,Wavelet Independent Guassian)建模.由于在尺度空间和小波空间针对各自的特点作了不同的处理,本文模型不但能较好拟合复杂业务流在各个时间尺度的概率分布特性,也能拟合其长时相关的特性.另外,在多尺度排队分析(MSQ,MultiScale Queue)的框架下,我们还推导出了基于本文模型的排队分析的理论结果.最后,通过对实际视频业务流数据仿真实验与排队分析验证了本文模型的有效性.     

A shifted gamma distribution model for long-range dependent Internet traffic

It is important to characterize the distributional property and the correlation structure of traffic arrival processes in modeling internet traffic. The conventional fractional Gaussian noise (fGn) model fails in characterizing the distributional property when the distribution of the input traffic rates is nongaussian. We propose a shifted gamma distribution model which can solve this problem. A linear-time generation algorithm is also given.     

基于非平稳型流量队列模型的Internet流量测量研究

针对大规模细粒度网络流量测量的现实困难,本文引入一种非平稳型流量队列模型NTT,直接对粗粒度的流量采样进行建模.NTT模型是大量活跃的流量队列的迭加,每个队列内部的流量变化过程用分形高斯噪声过程FGN描述,队列的到达过程形成非同构的泊松过程,队列的生存周期服从指数分布.对CERNET主干网的实际流量测量分析验证了NTT模型的有效性,证实了NTT模型可用于基于各种粒度的流量测量的网络行为研究.     

ATM网上一种简单通用的业务模型

对于ＡＴＭ网,业务建模是一个很重要的问题。鉴于ＡＴＭ网上的业务特性的多样性,而目前所在的各种业务模型在反映业务统计特性这一方面都有自己的适用范围。为此,本文提出了一种新的简单的业务模型。该模型的输出不但可以满足任意的边缘概率分布,而且其相关性也可长可短,因此,该模型更具有普遍适用性。通过仿真实验,我们对本文所给的业务模型加以了验证。     

A sampling technique for variance estimation of long-range dependent traffic

Due to the long-range dependence of Internet traffic, the sampling distribution of the variance is very hard to obtain and, as a result, confidence intervals cannot be provided. Nevertheless, we show that the r-decimated variance sampling distribution can be approximated by a /spl chi//sup 2/ distribution. This sampling technique can be used to provide a confidence interval for the variance, with significant benefits for many applications in Internet dimensioning, traffic forecasting and control.     

A novel approach to the estimation of the long-range dependence parameter

A new method to estimate the Hurst parameter of certain classes of random processes is presented. This method applies to Gaussian processes that are either exactly second-order self-similar or fractional ARIMA. The case of the former is of special interest because local area network traffic is well-known to be of this form. Confidence intervals and bias are obtained for the estimates using the new method. The new method is then applied to pseudo-random data and to real traffic data. The performance of the new method is compared to that of the widely-used wavelet method, which demonstrates that the former is much faster and produces much smaller confidence intervals of the long-range dependence parameter.     

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     

一种基于扩展自相似过程的VBR视频业务新模型

本文在扩展自相似过程的基础上 ,提出了一种简单的视频业务新模型。该模型的边缘分布近似Gamma分布 ,且其具有长或短的相关性。在许多时间尺度上 ,这些特性可以很好地匹配众多实际变比特率视频业务的一、二阶统计特征。仿真实验中 ,通过利用该模型模拟实际视频信号 ,我们证明它也能很好地反映实际视频业务的排队性能     

In-service monitoring for cell loss quality of service violationsin ATM networks

A new method for in-service cell loss ratio (CLR) QoS estimation for asynchronous transfer mode (ATM) networks has been developed. For a typical CLR, a large number of cells must be observed before statistically meaningful results can be achieved. These results may be obsolete resulting in ineffective network management reactions. For a variety of arrival processes, many analyses have shown there exists a relationship between the logarithm of the cell loss probability and buffer size. For models that do not possess long-range dependence, this relationship is often linear. On the other hand, for the fractional Brownian motion model that captures long-range dependent traffic behavior, this relationship has a polynomial form. The proposed method uses these relationships and observations of cell loss for several small pseudo-buffers to characterize the behavior of the actual system. Specifically, a real-time technique to dynamically detect the failure of meeting a cell loss quality of service (QoS) objective has been developed. The method requires a short observation period and is suitable for in-service monitoring of CLR QoS. Simulation studies show the effectiveness of this method for both modeled traffic and measured network trace data     

Analysis of an ATM multiplexer under self-similar traffic

Recent empirical studies of the real traffic measurement show that the traditional traffic models cannot capture the character of long-range dependence of the traffic. And many computer simulations said that this character has large influences on the network performance. So fractal or self-similar models are more suitable to describe the modern traffic. But there is still little known about the performance of the multiplexer under self-similar traffic. In this paper, a quasi-self-similar traffic model (QSSP) is proposed. Using this model, the upper bond of the cell loss rate and multiplexing gain of the multiplexer are gotten when there are N i.i.d. QSSP inputs. If the sources have different parameters, an efficient numerical algorithm to get, this bond is proposed. Simulations indicate that our analysis is correct and accurate.     

Asymptotic Properties of the Detrended Fluctuation Analysis of Long-Range-Dependent Processes

In the past few years, a certain number of authors have proposed analysis methods of the time series built from a long-range dependence noise. One of these methods is the detrended fluctuation analysis (DFA), frequently used in the case of physiological data processing. The aim of this method is to highlight the long-range dependence of a time series with trend. In this paper, asymptotic properties of the DFA of the fractional Gaussian noise (FGN) are provided. Those results are also extended to a general class of stationary long-range-dependent processes. As a consequence, the convergence of the semiparametric estimator of the Hurst parameter is established. However, several simple examples also show that this method is not at all robust in the case of trends.     

论业务量相关性对排队性能的影响

探讨业务量的相关性对排队系统性能究竟会带来什么样的影响,对于高速网络中流量控制机制和资源分配算法具有非常重要的意义。该文采用了一种独特的方法,来分析业务量的相关性在一定的网络环境下对于排队系统性能的影响。仿真的结果显示:一定时间尺度范围内的长期相关性导致排队性能的恶化,而且这种影响对于增加缓冲区的大小并不十分敏感。而且,业务量序列的边际分布和Hurst参数仍不足以充分决定排队性能的好坏。     

A Nonstationary Offered-Load Model for Packet Networks

Motivated by the desire to appropriately account for complex features of network traffic revealed in traffic measurements, such as heavy-tail probability distributions, long-range dependence, self similarity and nonstationarity, we propose a nonstationary offered-load model. Connections of multiple types arrive according to independent nonhomogeneous Poisson processes, and general bandwidth stochastic processes (not necessarily Markovian) describe the individual user bandwidth requirements at multiple links of a communication network during their connections. We obtain expressions for the moment generating function, mean and variance of the total required bandwidth of all customers on each link at any designated time. We justify Gaussian approximations by establishing a central limit theorem for the offered-load process. We also obtain a Gaussian approximation for the time-dependent buffer-content distribution in an infinite-capacity buffer with constant processing rate. The offered-load model can be used for predicting future bandwidth requirements; we then advocate exploiting information about the history of connections in progress.