“Nonparametric Statistical Methods to Analyze the Internet Connectivity Reliability”
Dimitri Papadimitriou, Alcatel-Lucent Bell Labs, Belgium; Davide Careglio, Technical University of Barcelona, Spain
Abstract—Facing computational complexity when modeling network reliability by means of parametric models and corresponding statistical methods, in the present study, we apply nonparametric statistical methods, such as the Kaplan-Meier survival probability estimator and the mean cumulative function, to characterize the dynamic properties (in particular, the stability properties) of the Internet routing paths and their relationship with the corresponding forwarding path(s). Providing systematic methodology for quantifying these properties aims at enabling reliability assessment of the Internet connectivity (also referred to as reachability in computer networking). The motivation for studying the dynamic properties (in particular, the stability properties) of the Internet routing paths and their relationship to forwarding paths stems from three main reasons. The first translates the fact that transient but frequent changes in the spatio-temporal properties of routing paths may affect the performance and operating conditions of the corresponding forwarding paths; hence, their reliability. The second reason is that frequent instabilities when observed for the same (subset of) path(s) that can be attributed to a spatially localized portion(s) of the Internet may reveal that the underlying physical topology is more prone to failures; hence, showing limited reliability. The third results from the increasing operational need to provide for a longer term estimation of the Internet routing-forwarding system performance and operating conditions using well-proven statistical analysis accounting for recurrence of events and correlation between instability events.