Markov modeling of online inter-arrival times

One of the popular research topics on networked humanity is to understand how people interact and communicate. Scholars investigated the arising communication patterns, and in particular the series of events happening for a single user. The distribution of waiting times separating two consecutive events - also denoted by the inter-event distribution - is well known have a density fitting a power-law. A debate, however, persists on the nature of an underlying model that explains the observed distribution, and whether the model should incorporate an inter-event dependence. The purpose of the present research is to integrate the dependence of consecutive waiting times into the power-law model. One can observe that social media behavior is characterized by periods of intensive activities separated by longer periods of inactivity. We propose an intuitive explanation to understand the observed dependence of subsequent waiting times. This leads us to create a model to incorporate memory. 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. Both contributions show a significant improvement for modeling commenting events on Twitter and Reddit.