Human Dynamics Model And Its Impact To Propagation Process In Networks

Behind all kinds of dynamics phenomena in the society, technology and economics, thereis driving force of human behaviors. However, the regularity of human behaviors is impactednot only by physiological cycles, but also limitations of environment resources, so that hard tobe studied. The requirement to analyze human behaviors from time aspect is getting stronger.It is a hot scientific topic to uncover the regularity of human behaviors quantitatively. The firsthuman dynamics models for venture evaluation always assumed that human behaviorsdistribute randomly in time, so it could be modeled with Poisson process. While more andmore evidences are showing recently that, human behaviors have the attributes of non-Poisson,which leads to that the waiting time or inter-event time could be described by power-lawdistribution with heavy tails. This kind of phenomena has already been found in data setsfrom the real world, including E-mail communications, short-messages communications, webbrowsing and library visiting, etc. To model the phenomena and investigate its mechanismand reason, this paper purposed a human dynamics model based on habit, which combinedqueuing-theory and the attribute of habit of humans. The model adjusts the distributionfunction according to frequency and average interval time of events happened, uses normaldistribution to simulate inter-event time between consecutive events, sets random variables asinterruption caused in reality by lack of resources or nonscheduled vacations, and forcesqueues waiting at the service table for some time, which reflects the situation that humansalways pay attention to an event for several hours or days.Currently there are many hot topics concerned in the area of network propagationdynamics. One of them is how to control virus propagation. Through the models of networkpropagation process, researchers could find out disadvantages and weakness of networks tobetter understand the mechanism of attacks and propagation of viruses, and as a result toimprove the denfense ability of networks. Besides, efficient virus propagation models couldalso be used for testing and improving networks' exsiting defense mechanism and ability, andto control spreading of viruses. Another important research topic in network propagationdynamics is congestion propagation dynamics. In scale-free networks, degrees of nodes are heterogeneous, and follow power-law distribution. That is to say, some of the nodes in thenetwork have much more links than the others. These nodes would become overloaded statewhen being attacked, and their efficiency could be decrease so much that they could not workany more. Afterwards the data packs which were supposed to transmitted by the overloardednodes have to look for a new routing way to avoid the conjested nodes. Normally this policycould be fine. But this could also cause the other nodes at the down strea of the routerbecoming overloaded and congested, and furthermore there would be more data packs to bere-routed, which could cause more nodes congested. In this way, congestion spreads in thenetwork, and produces large-scale failures. The worse is, the large-scale failures always bringshuge impact and disasters. Therefore, it is necessary to analyze and study the mechanism andmodels of congestions. In most studies, Poisson assumption is used for network dynamicsresearch, i.e. assuming the contact mode of nodes in networks follows the Poisson distribution,therefore the topologies of networks and its impact to network propagation dynamics areusually more focused on.While it is worthy to notice that, in complex network where humans are as the nodes,such as social networks, or in networks where some devices manipulated by humans are asthe nodes, such as e-mail communication networks or mobile networks, the contact modes ofnodes mainly depend on contact modes of humans, although in e-mail networks the contactmode could depend mostly on transferring mode and protocol design in small scale of timesuch as seconds, but in large time scale such as hours or days or even weeks, they are stilldecided by human behaviors. Therefore it is necessary to study how the non-Poisson characterof human dynamics would impact propagation dynamics. To model this dynamics process,and discuss its impact, this paper proposed a virus spreading model based on human dynamics,by considering habit of human behaviors, and combining with SI models. Compared withcommunication patterns of nodes assumed by Poisson process, the model based on humandynamics takes more psychological factors into account, so is more like humans' realbehaviors; as a result the virus propagation model could build and simulate the propagationdynamics phenomena as the real world.This paper also analyzed the characters of Internet cascading dynamics, and figured outthe two reasons causing cascading failures. Different from betweenness centrality, this paperdesigned a congestion function to represent the congested extent of nodes; by introducing theconceptual "delay time", this paper built the correlation between permanent removal andnon-removal. This paper also gave a new assessing function of network efficiency based oncongestion effects in order to measure the destructive degreeof cascading failures. Moreover, the paper modeled congestion propagation process based on the proposed human dynamicsmodel.Humans are born to have social attribute. In fact every human is in different socialnetworks all the time. All activities of humans are essentially about information, whileinformation is transferred through the networks composed by humans. The non-Poissoncharacter of single person's behaviors has an impact on human group dynamics withoutdoubts. Besides, the group dynamics is also impacted by structures of human societynetworks and relationships between humans. To analyze the human group dynamics, thispaper proposed a human group dynamics model considering friendly degree of relationshipsbetween persons, based on a model of community evolution. The proposed model describedrelationships between persons with edges between nodes, friendly or hostile relationships withpositive and negative weight values respectively, and then the communication rate isaccelerated or decelerated according as the weight. Consequently, this paper built a humangroup dynamics model according with reality in the three aspects: network topology,relationships between nodes, and communication mode of nodes.