Impact of interactions on human dynamics

Oliveira, J. G.; Vázquez, Alexei

doi:10.1016/j.physa.2008.08.022

Cited by 71 publications

(60 citation statements)

References 17 publications

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“…The pure priority selection mechanism can also be altered, e.g., to a hybrid priority-FCFS or priority-random selection mechanism. Finally, some kind of coupling between different queues is an important topic, for instance for modeling the interaction between (the tasks of) two people [24][25][26]. An analysis of a useful coupled model can be found in Ref.…”

Section: Discussionmentioning

confidence: 99%

Stochastic queueing-theory approach to human dynamics

et al. 2012

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Recently, numerous studies have shown that human dynamics cannot be described accurately by exponential laws. For instance, Barabási [Nature (London) 435, 207 (2005)] demonstrates that waiting times of tasks to be performed by a human are more suitably modeled by power laws. He presumes that these power laws are caused by a priority selection mechanism among the tasks. Priority models are well-developed in queueing theory (e.g., for telecommunication applications), and this paper demonstrates the (quasi-)immediate applicability of such a stochastic priority model to human dynamics. By calculating generating functions and by studying them in their dominant singularity, we prove that nonexponential tails result naturally. Contrary to popular belief, however, these are not necessarily triggered by the priority selection mechanism.

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Section: Discussionmentioning

confidence: 99%

Stochastic queueing-theory approach to human dynamics

et al. 2012

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“…It has been shown in (19,20) that interaction between priority queues can change the exponent of the power-law distribution of the waiting time. The priority queues and the schemes of interaction in these models, however, are highly simplifed and could be reasonable only for some special interaction processes in human society.…”

Section: Modelmentioning

confidence: 99%

“…(1) We introduce a time scale in terms of the processing time t p and tasks are removed and added to the list every t p seconds. (2) We distinguish interacting tasks (I-tasks) from the other tasks (O-tasks), similar to (19,20); and (3) the I-tasks are added to the task list randomly with a small rate λ p ¼ λt p at each processing step to incorporate the Poisson initiation of tasks observed in the data. (ii) The interaction between individuals.…”

Section: Modelmentioning

confidence: 99%

“…In particular, are there Poisson processes at all in individual activity, and how do they express themselves when interacting with the decision-making mechanism of individuals and the interaction among individuals? Unfortunately, previously examined data often do not allow us to evaluate precisely both the waiting times and the interevent times, and a detailed analysis of the relationship between individual and collective human activities is still lacking apart of some simple models of coupled priority-queues (19,20).…”

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confidence: 99%

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Evidence for a bimodal distribution in human communication

Zhou

Xiao

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

248

221

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Interacting human activities underlie the patterns of many social, technological, and economic phenomena. Here we present clear empirical evidence from Short Message correspondence that observed human actions are the result of the interplay of three basic ingredients: Poisson initiation of tasks and decision making for task execution in individual humans as well as interaction among individuals. This interplay leads to new types of interevent time distribution, neither completely Poisson nor power-law, but a bimodal combination of them. We show that the events can be separated into independent bursts which are generated by frequent mutual interactions in short times following random initiations of communications in longer times by the individuals. We introduce a minimal model of two interacting priority queues incorporating the three basic ingredients which fits well the distributions using the parameters extracted from the empirical data. The model can also embrace a range of realistic social interacting systems such as e-mail and letter communications when taking the time scale of processing into account. Our findings provide insight into various human activities both at the individual and network level. Our analysis and modeling of bimodal activity in human communication from the viewpoint of the interplay between processes of different time scales is likely to shed light on bimodal phenomena in other complex systems, such as interevent times in earthquakes, rainfall, forest fire, and economic systems, etc.human dynamics | Poisson process | power-law | priority-queue | waiting time H umans participate in various activities every day in an apparently random manner. By assuming that human actions are Poisson processes (1, 2) in which independent events occur at a constant rate λ and the interevent time τ between two consecutive actions of an individual follows an exponential distribution PðτÞ ¼ λe −λτ , one could perform a quantitative analysis of collective social activities as diverse as disease spreading, emergency response, or resource allocation, in particular phone line availability or bandwidth allocation in the case of Internet or Web use.Recent evidence from various deliberate human activity patterns, such as e-mail and letter communications and Web surfing, has shown that human activities are nonPoissonian (3-14), with bursts of frequent actions separated by long periods of inactivity, leading to power-law heavy tails in the distributions of interevent time (e.g., interval between sending two consecutive e-mails) or waiting times (e.g., the interval between receiving and replying to an e-mail), PðτÞ ∝ τ −γ . This nonPoissonian activity should significantly change the quantitative understanding of collective social dynamics, especially when taking into account complex network structures in social interactions (15-17), if those observed nonPoisson activities are solely the behavior of individual agents. Several mechanisms proposed to explain the origin of bursts and heavy tails, including priority-queui...

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“…Besides the human dynamics, however, due to the extremal nature of its dynamics the priority queue model would bear implications also to disparate problems in extremal dynamics, such as the Bak-Sneppen model for biological evolution [12] and invasion percolation [4]. * Email: kgoh@korea.ac.krBarabási model purposefully simplified many aspects of potential importance in realistic human dynamics, serving as a starting framework on which various detailed factors can be embedded [13,14,15,16,17]. One important factor that was not been accounted for is the human interaction.…”

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confidence: 99%

Waiting time dynamics of priority-queue networks

2009

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We study the dynamics of priority-queue networks, generalizations of the binary interacting priority queue model introduced by Oliveira and Vazquez [Physica A 388, 187 (2009)]. We found that the original AND-type protocol for interacting tasks is not scalable for the queue networks with loops because the dynamics becomes frozen due to the priority conflicts. We then consider a scalable interaction protocol, an OR-type one, and examine the effects of the network topology and the number of queues on the waiting time distributions of the priority-queue networks, finding that they exhibit power-law tails in all cases considered, yet with model-dependent power-law exponents. We also show that the synchronicity in task executions, giving rise to priority conflicts in the priority-queue networks, is a relevant factor in the queue dynamics that can change the power-law exponent of the waiting time distribution.PACS numbers: 89.75. Da, 02.50.Le, 89.65.Ef In the last century, queueing theory has proved useful for various problems ranging from operations research to telecommunications [1]. There is a recent resurgence of interest for the queueing theory among the statistical physics community with the application to the problems in human dynamics. Specifically, various queueing models based on the prioritization of tasks, or the priority queue models to be short, have been introduced to account for the heavy-tailed distributions observed in the waiting time and response time distributions [2,3,4,5,6,7,8]. The priority queue model is grounded on the assumption that the human dynamics is the result of an inherent decision-making process of the individual, with implicit priorities assigned for every tasks in his/her task queue, according to which he/she decides which task to execute next.To be specific, the priority queue model by Barabási [2] consists of a single fixed-length queue, filled with tasks each of which is assigned a priority value drawn randomly when it enters into the queue. Every step the task with the highest priority is executed and is replaced by a new task with random priority value. Upon execution, the waiting time τ , that is, how long the task has sat (waited) on the queue, is measured. Waiting time distribution P (τ ) of the Barabási model has been shown to exhibit a power-law tail for large τ aswith the exponent α = 1 [2, 3], conforming to the behaviors observed for the e-mail, library loan, and website visitation records [2,9,10,11]. Besides the human dynamics, however, due to the extremal nature of its dynamics the priority queue model would bear implications also to disparate problems in extremal dynamics, such as the Bak-Sneppen model for biological evolution [12] and invasion percolation [4]. * Email: kgoh@korea.ac.krBarabási model purposefully simplified many aspects of potential importance in realistic human dynamics, serving as a starting framework on which various detailed factors can be embedded [13,14,15,16,17]. One important factor that was not been accounted for is the human interaction...

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Impact of interactions on human dynamics

Cited by 71 publications

References 17 publications

Stochastic queueing-theory approach to human dynamics

Stochastic queueing-theory approach to human dynamics

Evidence for a bimodal distribution in human communication

Waiting time dynamics of priority-queue networks

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