Chaotic characteristic analysis of network traffic time series at different time scales

Abstract

Abstract Characteristic analysis of network traffic time series is very meaningful for network traffic prediction. The dynamic behavior of network traffic time series is an external manifestation under the combined action of complex non-linear and multi-scale phenomena. Based on the chaotic theory, the chaotic characteristics of network traffic time series collected at different time scales are analyzed and discussed. Firstly, power spectral density analysis and autocorrelation function analysis are introduced. The results show that the power spectral density of network traffic has continuous broad spectrum, which qualitatively explains the chaotic behavior of network traffic. The value of autocorrelation function of network traffic decreases with time delay, which shows its short-term predictability. Calculations on scaling exponent show that network traffic is scale-free at different time scales. Then, Hurst index of network traffic is calculated, and the 0-1 test algorithm for chaos is used to calculate the incremental growth rate of network traffic time series. The variation of chaotic characteristics of network traffic at different time scales is discussed. Further, the phase space of network traffic time series at different time scales is reconstructed, and the correlation dimension, largest Lyapunov exponent, and Kolmogorov entropy are calculated respectively. These chaotic identification indexes are used to analyze the chaotic characteristics of network traffic and their variation with time scales. The results show that the relationship between the time scale and the non-linear characteristics of network traffic time series is not obvious. The incremental growth rate of network traffic time series has no obvious change with the increase of time scale. There is no clear relationship between the change of time scale and embedding dimension and delay time. The largest Lyapunov exponent show that the network traffic at different time scales has different maximum predictable time. At the same time, Kolmogorov entropy increase with the increase of time scale, which means that the chaotic characteristics of network traffic time series become stronger and the predictability becomes worse with the time scale.