Human activity modeling and Barabasi's queueing systems

It has been shown by A.-L. Barabasi that the priority based scheduling rules in single stage queuing systems (QS) generates fat tail behavior for the tasks waiting time distributions (WTD). Such fat tails are due to the waiting times of very low priority tasks which stay unserved almost forever as the task priority indices (PI) are "frozen in time" (i.e. a task priority is assigned once for all to each incoming task). Relaxing the "frozen in time" assumption, this paper studies the new dynamic behavior expected when the priority of each incoming tasks is time-dependent (i.e. "aging mechanisms" are allowed). For two class of models, namely 1) a population type model with an age structure and 2) a QS with deadlines assigned to the incoming tasks which is operated under the "earliest-deadline-first" policy, we are able to analytically extract some relevant characteristics of the the tasks waiting time distribution. As the aging mechanism ultimately assign high priority to any long waiting tasks, fat tails in the WTD cannot find their origin in the scheduling rule alone thus showing a fundamental difference between the present and the A.-L. Barabasi's class of models.Comment: 16 pages, 2 figure

Hidden scaling patterns and universality in written communication

The temporal statistics exhibited by written correspondence appear to be media dependent, with features which have so far proven difficult to characterize. We explain the origin of these difficulties by disentangling the role of spontaneous activity from decision-based prioritizing processes in human dynamics, clocking all waiting times through each agent's `proper time' measured by activity. This unveils the same fundamental patterns in written communication across all media (letters, email, sms), with response times displaying truncated power-law behavior and average exponents near -3/2. When standard time is used, the response time probabilities are theoretically predicted to exhibit a bi-modal character, which is empirically borne out by our new years-long data on email. These novel perspectives on the temporal dynamics of human correspondence should aid in the analysis of interaction phenomena in general, including resource management, optimal pricing and routing, information sharing, emergency handling.Comment: 27 pages, 10 figure

Understanding the Heavy Tailed Dynamics in Human Behavior

The recent availability of electronic datasets containing large volumes of communication data has made it possible to study human behavior on a larger scale than ever before. From this, it has been discovered that across a diverse range of data sets, the inter-event times between consecutive communication events obey heavy tailed power law dynamics. Explaining this has proved controversial, and two distinct hypotheses have emerged. The first holds that these power laws are fundamental, and arise from the mechanisms such as priority queuing that humans use to schedule tasks. The second holds that they are a statistical artifact which only occur in aggregated data when features such as circadian rhythms and burstiness are ignored. We use a large social media data set to test these hypotheses, and find that although models that incorporate circadian rhythms and burstiness do explain part of the observed heavy tails, there is residual unexplained heavy tail behavior which suggests a more fundamental cause. Based on this, we develop a new quantitative model of human behavior which improves on existing approaches, and gives insight into the mechanisms underlying human interactions.Comment: 9 pages in Physical Review E, 201

Word statistics in Blogs and RSS feeds: Towards empirical universal evidence

We focus on the statistics of word occurrences and of the waiting times between such occurrences in Blogs. Due to the heterogeneity of words' frequencies, the empirical analysis is performed by studying classes of "frequently-equivalent" words, i.e. by grouping words depending on their frequencies. Two limiting cases are considered: the dilute limit, i.e. for those words that are used less than once a day, and the dense limit for frequent words. In both cases, extreme events occur more frequently than expected from the Poisson hypothesis. These deviations from Poisson statistics reveal non-trivial time correlations between events that are associated with bursts of activities. The distribution of waiting times is shown to behave like a stretched exponential and to have the same shape for different sets of words sharing a common frequency, thereby revealing universal features.Comment: 16 pages, 6 figure