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

Abstract

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

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.

Figures/Tables 9

References 31

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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)

Analysis the self-similarity of network traffic in fractional Fourier transform domain

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流量数据	尺度/s	Wavelet	MEEMD-DFA	FrFT Adaptive
	1	0.834	0.847	0.848
BC_pAug89.TL	5	0.855	0.858	0.854
	10	0.887	1.026	0.858
	1	0.804	0.926	0.947
BC_pOct89.TL	5	0.877	0.931	0.952
	10	0.963	1.061	0.957
	1	0.905	0.886	0.917
BC_Oct89Ext.TL	5	0.921	0.907	0.921
	10	0.954	0.919	0.926
	1	0.861	0.913	0.942
BC_Oct89Ext4.TL	5	0.909	0.927	0.946
	10	0.965	0.976	0.948

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