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DOI:
Journal of Software:2007.18(12):3071-3079

一种网络自组织演化的数学模型
董攀,朱培栋,卢锡城
(国防科学技术大学,计算机学院,湖南,长沙,410073)
A Mathematical Model for Network Self-Organized Evolvement
DONG Pan,ZHU Pei-Dong,LU Xi-Cheng
()
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Received:February 22, 2006    Revised:August 29, 2006
> 中文摘要: 根据计算机网络本身所具有的自组织特点,提出了网络自组织演化的数学模型.在该模型中,网络行为表现为节点对信息价值的追求以及维护网络连接所付出代价的权衡.模型将网络的演化表述为一个收敛的随机过程.对一种简单的信息网络进行了具体建模和演化结果的数学证明,进而给出了这种网络的一种实例--PGP(pretty good privacy)证书网络.针对PGP证书网络实例,根据参数的改变对其自组织演化的其他可能结果进行讨论,最后指出这些结果和自组织临界理论是一致的.该模型可以为计算机网络的拓扑模型研究以及网络自组织理论研究提供一种新方法.
中文关键词: 网络  自组织  演化  建模  PGP(pretty good privacy)
Abstract:This paper develops a self-organized dynamic network model based upon the network's self-organization natures.In this new model,network behavior is treated with nodes' trade-off between the value of information and the cost of establishing link,and the evolvement of network is described as a convergent stochastic process.The paper gives a detailed deduction for the possible result of network evolution.It should be pointed out that PGP(pretty good privacy) certificate network is a good example of this model.Furthermore,according to the change of parameters of the model,the self-organized evolvement exhibits multiform possible results.This phenomenon is consistent with self-organized criticality theory.The work provides a new method for the topological model research and self-organization theory in computer network.
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基金项目:Supported by the National Natural Science Foundation of China under Grant Nos.60573136, 60673169 (国家自然科学基金); the National High-Tech Research and Development Plan of China under Grant No.2005AA121570 (国家高技术研究发展计划(863)); the National Basic Research Program of China under Grant No.2005CB321801 (国家重点基础研究发展计划(973)); the Fund of National Laboratory for Modern Communications of China under Grant No.51436050605KG0102 (现代通信实验室基金) Supported by the National Natural Science Foundation of China under Grant Nos.60573136, 60673169 (国家自然科学基金); the National High-Tech Research and Development Plan of China under Grant No.2005AA121570 (国家高技术研究发展计划(863)); the National Basic Research Program of China under Grant No.2005CB321801 (国家重点基础研究发展计划(973)); the Fund of National Laboratory for Modern Communications of China under Grant No.51436050605KG0102 (现代通信实验室基金)
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董攀,朱培栋,卢锡城.一种网络自组织演化的数学模型.软件学报,2007,18(12):3071-3079

DONG Pan,ZHU Pei-Dong,LU Xi-Cheng.A Mathematical Model for Network Self-Organized Evolvement.Journal of Software,2007,18(12):3071-3079