Analyzing and modeling heterogeneous behavior

Recently, it was pointed out that the non-Poisson statistics with heavy tail existed in many scenarios of human behaviors. But most of these studies claimed that power-law characterized diverse aspects of human mobility patterns. In this paper, we suggest that human behavior may not be driven by identical mechanisms and can be modeled as a Semi-Markov Modulated Process. To verify our suggestion and model, we analyzed a total of 1,619,934 records of library visitations (including undergraduate and graduate students). It is found that the distribution of visitation intervals is well fitted with three sections of lines instead of the traditional power law distribution in log-log scale. The results confirm that some human behaviors cannot be simply expressed as power law or any other simple functions. At the same time, we divided the data into groups and extracted period bursty events. Through careful analysis in different groups, we drew a conclusion that aggregate behavior might be composed of heterogeneous behaviors, and even the behaviors of the same type tended to be different in different period. The aggregate behavior is supposed to be formed by “heterogeneous groups”. We performed a series of experiments. Simulation results showed that we just needed to set up two states Semi-Markov Modulated Process to construct proper representation of heterogeneous behavior.