Abstract
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.
Highlights
In the information age, a large scale of databases containing information on human activities on the Web are accessible
Inset: Comparison of the inter-event times (IETs) distribution obtained from the empirical data (0) with that from the theory Ptheroy(t). (b) Enlarged representation of the IET distribution P(t), in which clear periodic peaks are observed. (c) The Fourier transform of the IET distribution
We find that any inter-event time t belongs to one of the two sets of intervals T 1 and T 2, defined as
Summary
A large scale of databases containing information on human activities on the Web are accessible. Power-law or heavy-tailed behavior in the distribution of inter-event times (IET) between two consecutive human activities is one example of such emerging patterns This example can be seen in various systems such as email [4,5,6,7,8,9] or surface mail communications [10], Web browsing [7,11], library loans [7], financial trades [7,12], on-line movie watching [13], file downloads [14,15,16], printing requests [17], and various actions on the Web [18]. This power-law behavior indicates that human activities proceed in a bursty manner during a short time interval, which is separated from other such intervals by long intermittent periods [19,20]
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