域间网络流量的延迟相关性
Delayed Correlations in Inter-Domain Network Traffic
摘要：
为了观察网络流量相关性的演变，我们分析了网络流量计数时间序列的延迟相关矩阵的特征值谱和特征向量统计。延迟相关矩阵D由多变量时间序列中的一个变量与另一个变量在时间延迟τ处的相关性组成。D的特征向量的逆参与比（IPR）与等时间相关矩阵C的特征向量的IPR有很大偏差。我们将这一发现的本地化，并讨论其对网络拥塞控制的重要性。网络时间序列之间的时滞相关模式在很长一段时间内保持不变，最长可达100τ，其中τ=300 sec。D的最大本征值λ max和相应的IPR以3τ和6τ两个特征周期振荡。网络时间序列之间的延迟相关性的存在很好地符合网络流量的长程相关（LRD）性质。监视和控制长内存进程的能力至关重要，因为它们会影响网络性能。在非随机相关的时间序列之间注入随机流量计数，我们能够打破λ_{max}的周期性。此外，我们研究了周期性注入对最大特征值和IPR的影响，并解决了这些指标的LRD和网络流量的自相似性的相关性。
英文摘要：
To observe the evolution of network traffic correlations we analyze the eigenvalue spectra and eigenvectors statistics of delayed correlation matrices of network traffic counts time series. Delayed correlation matrix D is composed of the correlations between one variable in the multivariable time series and another at a time delay τ. Inverse participation ratio (IPR) of eigenvectors of D deviates substantially from the IPR of eigenvectors of the equal time correlation matrix C. We relate this finding to the localization and discuss its importance for network congestion control. The time-lagged correlation pattern between network time series is preserved over a long time, up to 100τ, where τ=300 sec. The largest eigenvalue λ_{max} of D and the corresponding IPR oscillate with two characteristic periods of 3τand 6τ. The existence of delayed correlations between network time series fits well into the long range dependence (LRD) property of the network traffic. The ability to monitor and control the long memory processes is crucial since they impact the network performance. Injecting the random traffic counts between non-randomly correlated time series, we were able to break the picture of periodicity of λ_{max}. In addition, we investigated influence of the periodic injections on both largest eigenvalue and the IPR, and addressed relevance of these indicators for the LRD and self-similarity of the network traffic.
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