Modeling heterogeneous and correlated human dynamics of online activities with double Pareto distributions

Modeling human dynamics is crucial for optimal resource allocation and designing effective human machine systems. Existing studies show that time intervals between consecutive events of human activities follow uniform power-law distributions and human activities are temporally correlated. Recent researches also find that the dynamics of some online human activities are heterogeneous in different time scales. A thorough understanding of the heterogeneity is crucial to accurately characterize the dynamics of online human activities. However, the causes of the heterogeneity are still not sufficiently investigated. In this paper, we study the dynamics of human activities in online social media based on the data of two kinds of online activities, including microblog posting and wild revising. We find that inter-event times of both activities follow double Pareto distributions, indicating that human dynamics are heterogeneous in different time scales. Moreover, both activities also exhibit different temporal correlations in different time scales. We develop a multiple multiplicative event chains (MMEC) model which takes human activity patterns into consideration to characterize the heterogeneity and the correlations. We prove that the model yields inter-event times following double Pareto distributions, indicating that the model is capable to characterize the heterogeneity. Finally, the simulation and empirical experiments verify that the model well captures the heterogeneity and the correlations observed in the actual data.