饱和非时齐泊松失效过程下网络系统连边交互机理分析  

Analysis of link interaction regarding network failure subject to a saturated nonhomogeneous poisson process

作　　者：杜永军 张攀 蔡志强[2] DU Yong-jun;ZHANG Pan;CAI Zhi-qiang(School of Economics and Management,Lanzhou University of Technology,Lanzhou 730050,China;School of Mechanical Engineering,Northwestern Polytechnical University,Xi’an 710072,China)

机构地区：[1]兰州理工大学经济管理学院,兰州730050 [2]西北工业大学机电学院,西安710072

出　　处：《控制与决策》2024年第1期180-188,共9页Control and Decision

基　　金：国家自然科学基金项目(72161025,71871181,12072139);陕西省重点研发计划项目(2021ZDLGY10-03,2021ZDLGY12-06)。

摘　　要：给定由若干连边和节点组成的网络系统,为了有效、经济地提升整个网络的可靠性,一些耦合的2条连边关于整个网络失效的交互机理需要加以分析.首先,采用饱和非时齐泊松过程刻画连边的失效过程,基于组合计数的思想,导出2条连边处于4种不同状态的概率公式,并结合2条连边的联合D-谱,发展联合失效重要度的计算公式,用于分析2条连边关于网络失效的交互机理.理论分析表明,当时间t趋于0或趋于无穷大时, 2条连边的交互效果越来越微弱.然后,由于精确的计算联合失效重要度的值是NP-难问题,设计蒙特卡洛近似算法求其值.最后,提供一个路网的算例,其数值结果表明,所提出联合失效重要度计算方法能够有效地阐释2条连边关于网络失效的交互机理.The communication,computer and transportation systems can all be modelled as a network composed of vertices and links.To economically and efficiently improve network reliability,the interactions of these coupled two links regarding network failure must be analyzed.Therefore,under the condition that link failures appear according to a saturated nonhomogeneous Poisson process,we propose a novel method to calculate the joint failure importance(JFI)for the two links given,which can characterize how the links interact in contributing to network failure.Specifically,based on the knowledge of combinatorial counting,the probabilities that arbitrary two links are in four different states are derived.Then,combining the joint D-spectrum for the two links,a formula to calculate the JFI is established.Theoretical analysis shows that when time t approaches zeros or infinity,the interaction effects between the two links are more and more weak.Since the exact computing for JFI is NP-hard problem,we provide a Monte-Carlo algorithm to evaluate JFI.Finally,we perform a numerical example of a road network to demonstrate the method for computing JFI.The numerical results show that proposed method for computing JFI can efficiently account for the interaction of links on network failure.

关 键 词：网络 可靠性 饱和非时齐泊松过程 联合失效重要度 交互机理 蒙特卡洛 

分 类 号：F224.33[经济管理—国民经济]