The origin of bursts and heavy tails in human dynamics
Citation
Albert-László Barabási. The origin of bursts and heavy tails in human dynamics. Nature 435, 207-211 (12 May 2005)
Online Version
Summary
This paper argues that in contrast to a Poisson distribution, the waiting time of tasks will follow Pareto distribution if it is the case that people execute tasks based on some perceived priority.
This paper discussed three different models and their corresponding task waiting time distribution:
1. The first-in-first-out model. This model assumes that the tasks are first come first served. The tasks waiting time is based on all the tasks ahead of it, thus most of the tasks have approximately the same waiting time and have an exponential tail.
2. The random order model. The tasks are pickup randomly to be executed. Such model also make the task waiting time distribution exponential.
3. The priority model. People will execute the task with the highest priority in the task bucket first. By maths deduction and computer simulation, the author has the conclusion that such model will lead to a heavy-tail process: most of the tasks will be rapidly executed and a few will have long waiting times.
The author believes that, according to the third model, the bursty nature of human dynamics is the consequence of the decision-make process by the human-being.
The dataset and experiment
The author studied based on several thousands of emails with the information of senders, receivers, time and the size of each email.
The following graph shows the distribution of time intervals between consecutive e-mails sent by a single user over three-month time interval. We can clearly se e the heavy-tailed activity pattern in the graph. The x-axis extends exponentially instead of linearly. The slope rate of the solid line is roughly -1.
Similarly, the time taken by the user to reply a received message also follows the same pattern:
Study plan
Basically it is a straight forward article just requiring some basic statistics knowledge.
