Motivated by the need to introduce design improvements to the Internet network to make it robust to high traffic volume anomalies, we analyze statistical properties of the time separation between arrivals of consecutive anomalies in the Internet2 network. Using several statistical techniques, we demonstrate that for all unidirectional links in Internet2, these interarrival times have distributions whose tail probabilities decay like a power law. These heavy-tailed distributions have varying tail indexes, which in some cases imply infinite variance. We establish that the interarrival times can be modeled as independent and identically distributed random variables, and propose a model for their distribution. These findings allow us to use the tools of of renewal theory, which in turn allows us to estimate the distribution of the waiting time for the arrival of the next anomaly. We show that the waiting time is stochastically substantially longer than the time between the arrivals, and may in some cases have infinite expected value. All our findings are tabulated and displayed in the form of suitable graphs, including the relevant density estimates.
Bibliographical noteFunding Information:
This research has been partially supported by NSF grants DMS?1737795, DMS 1923142 and CNS 1932413. We thank Professor Anura P. Jayasumana of the CSU?s Department of Electrical and Computer Engineering for sharing the Internet2 anomalies data.
- Heavy-tailed distributions
- Interarrival times
- Internet anomalies
- Renewal theory