# A model for studying the dependencies between Internet flow characteristics

### Universidade Técnica de Lisboa

### Résumé:

The development of realistic Internet traffic models of applications and services calls for a good understanding of the nature of Internet flows, which can be affected by many factors. Especially relevant among these are the limitations imposed by link capacities and router algorithms that control bandwidth on a per-flow basis. In the paper, we perform a statistical analysis of an Internet traffic trace that specifically takes into account the upper-bounds on the duration and rate of measured flows. In particular, we propose a new model for studying the dependencies between the logarithm of the size, the logarithm of the duration, and the logarithm of the transmission rate of an Internet flow. We consider a bivariate lognormal distribution for the flow size and flow duration, and derive estimators for the mean, the variance and the correlation, based on a truncated domain that reflects the upper-bounds on the duration and rate of measured flows. Moreover, we obtain regression equations that describe the expected value of one characteristic (size, duration or rate) given other (size or duration), thus providing further insights on the dependencies between Internet flow characteristics. In particular, for flows with large sizes we are able to predict durations and rates that are coherent with the upper-bound on transmission rates imposed by the network.