分数阶Fourier变换域中网络流量的自相似特性分析

doi:10.3969/j.issn.1000-436X.2013.06.005

摘要/Abstract

摘要：

通过分析网络流量数据在FrFT域的统计特性发现，实际网络流量在FrFT域满足自相似性，进一步地，针对网络流量在 FrFT 域的“时域”和“频域”展开，分别给出了基于改进的整体经验模态分解—去趋势波动分析（MEEMD-DFA）的Hurst指数估计法以及基于加权最小二乘回归（WLSR）的Hurst指数自适应估计法。实验结果表明，相比于现有估值算法，MEEMD-DFA法具有较高的估计精度，但计算复杂度高；而FrFT自适应估计法则具有更优的估计顽健性，且计算复杂度较低，可作为一种实时在线估计真实网络数据Hurst指数的方法。

关键词: 自相似特性, 分数阶Fourier变换, Hurst指数, 整体经验模态分解, 去趋势波动分析, 加权最小二乘, 自适应

Abstract:

Statistical characteristics of network traffic data in FrFT domain were analyzed,which indicates the self-simi-larity feature.Further,Hurst parameter estimation methods based on modified ensemble empirical mode decomposi-tion-detrended fluctuation analysis (MEEMD-DFA) and adaptive estimator with weighted least square regression (WLSR) were presented,which aimed at displaying network traffic in “time” or “frequency” domain of FrFT domain separately.Experimental results demonstrate that the MEEMD-DFA method has more accurate estimate precision but higher com-putational complexity than existing common methods.The overall robustness of adaptive estimator is more satisfactory than that of the other methods in simulation,while it has lower computational complexity.Thus,it can be used as a real-time online Hurst parameter estimator for traffic data.

Key words: self-similarity, fractional Fourier transform, Hurst parameter, ensemble empirical mode decomposition, weighted least square regression, adaptive

郭通,兰巨龙,黄万伟,张震. 分数阶Fourier变换域中网络流量的自相似特性分析[J]. 通信学报, 2013, 34(6): 38-48.

Tong GUO,Ju-long LAN,Wan-wei HUANG,Zhen ZHANG. Analysis the self-similarity of network traffic in fractional Fourier transform domain[J]. Journal on Communications, 2013, 34(6): 38-48.

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参考文献 31

[1]	LELAND W E , TAQQU M S , WILLINGER W , et al. On the self-similar nature of Ethernet traffic (extended version)[J]. IEEE/ACM Trans on Networking, 1994,2(1): 1-15.
[2]	BORGNAT P , DAWAELE G , FUKUDA K , et al. Cho seven years and one day: sketching the evolution of Internet traffic[A]. Proc of the 28th Conf on Computer Communications (INFOCOM 2009)[C]. Rio de Janeiro: IEEE, 2009. 711-719.
[3]	GUPTA H , RIBEIRO V J , MAHANTI A . A longitudinal study of small-time scaling behavior of Internet traffic[A]. Networking 2010 Springer Berlin Heidelberg[C]. Ottawa,Canada, 2010. 83-95.
[4]	CIFLIKLI C , GEZER A , ?ZSAHIN A T , et al. Bittorrent packet traffic features over IPv6 and IPv4[J]. Simulation Modelling Practice and Theory, 2010,18(9): 1124-1214.
[5]	CIFLIKLI C , GEZER A , ?ZSAHIN A T , et al. Packet traffic features of IPv6 and IPv4 protocol traffic[J]. Turkish Journal of Electrical Engineering and Computer Sciences, 2012,20(5): 727-749.
[6]	B?RULESCU A , SERBAN C , MAFTEL C . Evaluation of Hurst exponent for precipitation time series[A]. Proceedings of the 14th WSEAS CSCC Multiconference[C]. 2010. 590-595.
[7]	张宾, 杨家海, 吴建平 . Internet流量模型分析与评述[J]. 软件学报, 2011,22(1):115-131. ZHANG B , YANG J H , WU J P . Survey and analysis on the Internet traffic model[J]. Journal of Software, 2011,22(1): 115-131.
[8]	REA W , OXLEY L , REALE M , et al. Estimators for long range dependence: an empirical study[J]. Electronic Journal of Statistics, 2009,3: 1-16.
[9]	陶然, 邓兵, 王越 . 分数阶Fourier变换在信号处理领域的研究进展[J]. 中国科学, 2006,36(2):113-136. TAO R , DENG B , WANG Y . The research evolution of fractional order Fourier transform in signal processing domain[J]. Science in China Ser E Information Sciences, 2006,36(2):113-136.
[10]	CIFLIKLI C , GEZER A . Self similarity analysis via fractional Fourier transform[J]. Simulation Modeling Practice and Theory, 2011,19(3): 986-995.
[11]	SUN R , CHEN Y , ZAVERI N , et al. Local analysis of long-range dependence based on fractional Fourier transform[A]. Proceedings of the 2006 IEEE Mountain Workshop on Adaptive and Learning Systems[C]. 2006. 13-18.
[12]	CHEN Y , SUN R , ZHOU A . An improved Hurst parameter estimator based on fractional Fourier transform[J]. Telecommun System, 2010,43(3-4): 197-206.
[13]	STOEV S , TAQQU M S , PARK C , et al. LASS: a tool for the local analysis of self-similarity[J]. Computational Statistics ＆ Data Analysis, 2006,50(1): 2447-2471.
[14]	BREGNI S , PRIMERANO L . The modified allan variance as time-domain analysis tool for estimating the hurst parameter of long-range dependent traffic[A]. IEEE GLOBECOM '04 Global Telecommunications Conference[C]. 2004. 1406-1410.
[15]	WANG Y G , YU H L , LIANG X Y . Time delay model of fractional Fourier transform and the application in signal filtering[J]. Applied Mechanics and Materials, 2012,121: 3637-3641.
[16]	LAB B . Traces available in the internet traffic archive[EB/OL]. , 1989.
[17]	MAWI working group traffic archive[EB/OL]. , 2011.
[18]	BARDET J M , KAMMOUN I . Asymptotic properties of the detrended fluctuation analysis of long range dependence processes[J]. IEEE Transactions on Information Theory, 2008,54(5): 2041-2052.
[19]	WERON R . Estimation long-range dependence: finite sample properties and confidence intervals[J]. Physica A:Statistical Mechanics and Its Applications, 2002,312(1): 285-299.
[20]	QIAN X Y , ZHOU W X , GU G F . Modified detrended fluctuation analysis based on empirical mode decomposition[J]. Physica A: Statistical Mechanics and Its Applications, 2011,390(23): 4388-4395.
[21]	WU Z , HUANG N E . Ensemble empirical mode decomposition: a noise assisted data analysis method[J]. Advances in Adaptive Data Analysis, 2009,1(1): 1-41.
[25]	LIN J . Improved Ensemble Empirical Mode Decomposition Method and Its Simulation[M]. Advances in Intelligent Systems 2012.
[23]	TARRIO P , BERNARDOS A M , CASAR J R . Weighted least squares techniques for improved received signal strength based localization[J]. Sensors, 2011,11(9): 8569-8592.
[24]	YARDIBI T , LI J , STOICA P , et al. Source localization and sensing: a nonparametric iterative adaptive approach based on weighted least squares[J]. IEEE Transactions on Aerospace and Electaonic Systems, 2010,46(1): 425-433.
[25]	BELSLEY D A , KUH E , WELSCH R E . Regression Diagnostics:Identifying Influential Data and Sources of Collinearity[M]. 2005.
[26]	KUO C C , CHUI L C , CHUNG B L . The comparison of algorithms in change-points problem[J]. Journal of Applied Science and Engineering, 2012,15(1): 11-19.
[27]	BERTRAND P R , FHIMA M , GUILIN A . Fast change point analysis on the Hurst index of piecewise fractional brownian motion[J]. Journée de Statistiques 2011 (JDS 2011), 2011,(3): 1-6.
[28]	HUAT N K , MIDI H . Change point detection with robust control chart[J]. Mathematical Problems in Engineering, 2011,2011: 1-20.
[29]	SHENG H , CHEN Y Q , QIU T . On the robustness of Hurst estimators[J]. IET Signal Process, 2011,5(2): 209-225.
[30]	Stilian stoev's new web page[EB/OL]. , 2011.
[31]	PARK J , PARK C . Robust estimation of the Hurst parameter and selection of an onset scaling[J]. Statistica Sinica, 2009,19(4): 1531-1555.

原始数据	均值(byte·s^?1)/μ₁	方差/σ₁2	延迟5均值	延迟10均值	延迟15均值
BC_pAug89(1)	6.439 8×10⁵	1.303 1×10¹²	6.439 6×10⁵	6.439 5×10⁵	6.439 2×10⁵
MAWI_20030603(1)	2.125 8×10⁶	1.479 1×10¹²	2.125 9×10⁶	2.125 6×10⁶	2.125 4×10⁶

原始数据	时域法		频域法		FrFT域
原始数据	Abs	R/S	Periodogram	Wavelet	FrFT LASS
BC_pAug89(1)	0.848 8	0.834 1	0.843 0	0.912	0.918
MAWI_20030603(1)	0.413 2	0.488 3	0.419 4	0.416	0.796

H				Hurst指数估计方法				[j₁,j₂]
H	R/S	Periodogram	Wavelet	EMD-DFA	FrFT LASS	MEEMD-DFA	FrFT Adaptive	[j₁,j₂]
0.55	0.556	0.523	0.566	0.534	0.584	0.556	0.552	[7,16]
0.60	0.614	0.581	0.607	0.582	0.628	0.586	0.652	[5,16]
0.65	0.659	0.647	0.664	0.669	0.661	0.640	0.652	[5,16]
0.70	0.698	0.701	0.695	0.721	0.682	0.677	0.698	[6,16]
0.75	0.774	0.739	0.756	0.772	0.732	0.741	0.750	[6,16]
0.80	0.799	0.815	0.806	0.824	0.809	0.782	0.805	[5,16]
0.85	0.825	0.849	0.878	0.875	0.835	0.857	0.847	[7,16]
0.90	0.853	0.884	0.942	0.927	0.873	0.909	0.895	[7,16]
0.95	0.907	0.965	0.984	0.978	0.939	0.960	0.953	[5,16]

Hurst指数估计方法	FGN	FGN+余弦周期信号	FGN+高斯白噪声	FGN+趋势项
R/S	0.026 4	0.205 2	0.038 6	0.071 4
Periodogram	0.015 5	0.049 9	0.080 4	0.241 2
Wavelet	0.023 2	0.174 2	0.085 2	0.084 6
EMD-DFA	0.023 9	0.280 6	0.114 1	0.023 9
FrFT LASS	0.022 0	0.031 3	0.032 0	0.028 1
MEEMD-DFA	0.013 7	0.119 8	0.039 7	0.013 7
FrFT Adaptive	0.003 5	0.008 3	0.005 1	0.003 4

Hurst指数估计方法	计算复杂度
R/S	O(N²)
Periodogram	O(NlogN)
Wavelet	O(NlogN)
EMD-DFA	O(N²)
FrFT LASS	O(nNlogN)
MEEMD-DFA	O(mN²)
FrFT Adaptive	O(NlogN)