Investigating the scaling behavior, crossover and anti-persistence of Internet packet delay dynamics

Relying on the wavelet-based time-scale analysis techniques and a so called height difference correlation function method, we studied the dynamics of the delay traces measured in the Internet with sampling interval ranging from 20 ms to 1 min. Scaling analyses showed that the delay traces have a complicated scaling behavior changing with both the time scales and the sampling intervals. A significant observation of our research was that the nature of the delay traces changes from a long range dependence (LRD) noise-like time series (e.g., fractional Brownian noise) to a self-similar one with an outer cutoff scale when the sampling intervals decrease (we refer this as crossover). It turns out that the delay jitter time series derived from a sampled delay trace with small sampling interval is LRD noise with a Hurst parameter H<0.5 (anti-persistence), indicating that the current Internet works in a controlled state. We also used a wavelet-based partition function method to investigate the possible multifractality of the delay traces, We analyzed the underlying physical mechanisms of the observed scaling behavior, crossover and anti-persistence, and discussed the implications of our findings on several aspects of networking engineering.