Detrended fluctuation analysis of IP-network traffic using a two-dimensional topology map

This paper describes an analysis of IP-network traffic in terms of the time variation of self-similarity. To get a comprehensive view of network traffic conditions in analyzing the degree of long-range dependence (LRD) of IP-network traffic, this paper used a self-organizing scheme-based topology map, which provides a way to map high-dimensional data onto a low-dimensional domain. Also, in the LRD-based analysis, this paper employed detrended fluctuation analysis (DFA), which is applicable to the analysis of long-range power-law correlations or LRD in apparently non-stationary time-series signals. Based on sequential measurements of IP-network traffic at a 100-Mbps point of interface between an access provider and the Internet, this paper derived corresponding values for the LRD-related parameter α of the traffic. In training the topology map, this paper used three parameters: the α value, average throughput, and a parameter that reflects the degree of non-stationarity for each measured data set. We visually confirmed that the traffic data could be projected onto the topology map in accordance with the traffic properties, resulting in a combined depiction of the effects of the degree of LRD and other factors. The proposed method can deal with multi-dimensional parameters, projecting its results onto a two-dimensional space in which the positions of the projected data give us with an effective depiction of network conditions at different times.