Related papers: Numerical study on the deadline-concerning priorit…
Human activity patterns display a bursty dynamics, with interevent times following a heavy tailed distribution. This behavior has been recently shown to be rooted in the fact that humans assign their active tasks different priorities, a…
Recently, increasing empirical evidence indicates the extensive existence of heavy tails in the interevent time distributions of various human behaviors. Based on the queuing theory, the Barab\'asi model and its variations suggest the…
Previous works on the queuing model introduced by Barab\'asi to account for the heavy tailed distributions of the temporal patterns found in many human activities mainly concentrate on the extremal dynamics case and on lists of only two…
Queuing models provide insight into the temporal inhomogeneity of human dynamics, characterized by the broad distribution of waiting times of individuals performing tasks. We study the queuing model of an agent trying to execute a task of…
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…
We study the effect of team and hierarchy on the waiting-time dynamics of priority-queue networks. To this end, we introduce generalized priority-queue network models incorporating interaction rules based on team-execution and hierarchy in…
Recently increased accessibility of large-scale digital records enables one to monitor human activities such as the interevent time distributions between two consecutive visits to a web portal by a single user, two consecutive emails sent…
In a recent letter, Barabasi claims that the dynamics of a number of human activities are scale-free [1]. He specifically reports that the probability distribution of time intervals tau between consecutive e-mails sent by a single user and…
Queueing theory has been recently proposed as a framework to model the heavy tailed statistics of human activity patterns. The main predictions are the existence of a power-law distribution for the interevent time of human actions and two…
In this paper we consider a real time queuing system with rewards and deadlines. We assume that packet processing time is known upon arrival, as is the case in communication networks. This assumption allows us to demonstrate that the well…
Following up on Barabasi's recent letter to Nature [435, 207--211 (2005)], we systematically investigate the time series of e-mail usage for 3,188 users at a university. We focus on two quantities for each user: the time interval between…
In this paper we study the properties of the Barab\'asi model of queueing under the hypothesis that the number of tasks is steadily growing in time. We map this model exactly onto an Invasion Percolation dynamics on a Cayley tree. This…
Empirical analysis show that, after the update of a browser, the publication of the vulnerability of a software, or the discovery of a cyber worm, the fraction of computers still using the older version, or being not yet patched, or…
Many human-related activities show power-law decaying interevent time distribution with exponents usually varying between 1 and 2. We study a simple task-queuing model, which produces bursty time series due to the nontrivial dynamics of the…
We study the dynamics of priority-queue networks, generalizations of the binary interacting priority queue model introduced by Oliveira and Vazquez [Physica A {\bf 388}, 187 (2009)]. We found that the original AND-type protocol for…
Albert-Laszlo Barabasi introduced a model which exhibits the bursty nature of the arrival times of events in systems determined by decisions of some humans. In Barabasi's model tasks are selected to execution according to some rules which…
We empirically study the activity patterns of individual blog-posting and find significant memory effects. The memory coefficient first decays in a power law and then turns to an exponential form. Moreover, the inter-event time distribution…
The dynamics of technological, economic and social phenomena is controlled by how humans organize their daily tasks in response to both endogenous and exogenous stimulations. Queueing theory is believed to provide a generic answer to…
This paper considers a GI/GI/1 processor sharing queue in which jobs have soft deadlines. At each point in time, the collection of residual service times and deadlines is modeled using a random counting measure on the right half-plane. The…
We study an admissions control problem, where a queue with service rate $1-p$ receives incoming jobs at rate $\lambda\in(1-p,1)$, and the decision maker is allowed to redirect away jobs up to a rate of $p$, with the objective of minimizing…