Dynamics of calling activity to toll-free numbers in China

The quantitative understanding of human behavior is a key issue in modern science. Recently, inhomogeneous human activities have been described by bursts (consecutive activities separated by long periods of inactivity) and characterized by fat-tailed inter-event time (interval between two activities) distributions. However, the dynamics between number of activities and activity duration are still unclear. In this study, we analyzed 133 million toll-free call records from China to study the dynamics between call frequency and call duration. We confirmed that both call frequency and call duration exhibit circadian cycles and weekly cycles. By analyzing intraday patterns of these two metrics, we found the opposite volatility and clustered distributions. Results of clustering analysis showed that calling activity to toll-free numbers can be clustered into four clusters. In the "Work" cluster, the distribution of call duration was significantly different from that in the other clusters. The corresponding time of "Work" cluster was much shorter than estimates based on common sense. Intraday patterns and clustering results showed that both call frequency and call duration are primarily related to circadian cycles, the nature of human beings, and that work is a secondary factor that affects these variables. Moreover, we found a strong positive correlation between call frequency and call duration, as well as polarization of joint probability. The polarization indicates two extremes in inhomogeneous calling activity to toll-free numbers, i.e., either people are very busy or very idle. The empirical probability of the extreme was approximately four times that of random probability. Our findings may have great usage for studying the dynamics of inhomogeneous human behavior.