Markov modeling of online inter-arrival times

Abstract

In this paper, we investigate the arising communication patterns on social media, and in particular the series of events happening for a single user. While the distribution of inter-event times is often assimilated to power-law density functions, a debate persists on the nature of an underlying model that explains the observed distribution. In the present, we propose an intuitive explanation to understand the observed dependence of subsequent waiting times. Our contribution is twofold. The first idea consists of separating the short waiting times -- out of scope for power-law distributions -- from the long ones. The model is further enhanced by introducing a two-state Markovian process to incorporate memory.