Quantifying regularity of the Internet Interdomain Routing based on Border Gateway Protocol (BGP) data bases

The time series of border gateway protocol (BGP) updates from 4 autonomous systems (AS) are analyzed. Methods of modern data analysis, such as multifractal detrended fluctuation analysis (MF-DFA) and refined composite multiscale entropy (RCMSE) are used. Analysis is carried out on the entire BGP updates data sets, as well as on their shorter, most regular parts. It is found that the process of BGP updates variability, though reveals general similarity in the dynamics of behavior, all the same is very specific for each of the considered data sets. It is shown that the variability of NTT and Tinet BGP updates is the closest one to monofractal behavior, though the same data sets strictly differ by their extent of complexity. The variability of BGP updates for ATT is the most multifractal one compared to data sets from other AS-es. It is characterized by a lesser extent of complexity compared to BGP updates from Tinet, NTT and IJJ As-es, according to entropy measure calculations. Further analysis, carried out on shorter parts of BGP time series, additionally shows essential differences for different AS-es. Namely, Tinet is characterized by the highest extent of multifractality and a lesser entropy measure, i.e. is the most ordered one compared to BGP updates from other AS-es. A conclusion is made that that BGP updates time series from different AS-es are characterised by a different extent of regularity and multifractality, even if observation is carried out for the same time period. Moreover, for the first time is shown that the dynamical features of variability for different AS-es may strictly differ even for shorter periods when the BGP updates process is most regular over the entire observation period.