Microscopic Modelling Circadian and Bursty Pattern of Human Activities

Recent studies for a wide range of human activities such as email communication, Web browsing, and library visiting, have revealed the bursty nature of human activities. The distribution of inter-event times (IETs) between two consecutive human activities exhibits a heavy-tailed decay behavior and the oscillating pattern with a one-day period, reflective of the circadian pattern of human life. Even though a priority-based queueing model was successful as a basic model for understanding the heavy-tailed behavior, it ignored important ingredients, such as the diversity of individual activities and the circadian pattern of human life. Here, we collect a large scale of dataset which contains individuals’ time stamps when articles are posted on blog posts, and based on which we construct a theoretical model which can take into account of both ignored ingredients. Once we identify active and inactive time intervals of individuals and remove the inactive time interval, thereby constructing an ad hoc continuous time domain. Therein, the priority-based queueing model is applied by adjusting the arrival and the execution rates of tasks by comparing them with the activity data of individuals. Then, the obtained results are transferred back to the real-time domain, which produces the oscillating and heavy-tailed IET distribution. This microscopic model enables us to develop theoretical understanding towards more empirical results.