Download Network Reliability and Resilience by Ilya Gertsbakh, Yoseph Shpungin PDF

By Ilya Gertsbakh, Yoseph Shpungin

This ebook is dedicated to the probabilistic description of a community within the technique of its destruction, i.e. removing of its parts (links, nodes) showing due to technical mess ups, usual mess ups or intentional assaults . it's taken with a pragmatic method of community reliability, in accordance with software of Monte Carlo method to numerical evaluate of community most crucial structural parameters. this enables to acquire a probabilistic description of the community within the strategy of its destruction, to spot most crucial community elements and to boost effective heuristic algorithms for community optimum layout. The method works with passable accuracy and potency for small –to-medium measurement networks.

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Example text

We will define three states of 32-node network which will be subject to a random “attack” on its nodes: x max > 10, 3 < x max ≤ 10, and xmax ≤ 3. 6 Renewal Process of Component Failures There might be several approaches to modeling the process of network component failures. The simplest one is to assume that the components fail according to independent random “lotteries” in which component i is declared to be up or down with probability pi ≡ p and 1 − pi ≡ q, respectively. d. 24 1 Theory component lifetimes X 1 , X 2 , .

In the multistate situation we define K BIM-spectra, for each J = K , K −1, . . , 1, in the following way. Fix some J0 , 1 ≤ J0 ≤ K . Define all states J ≥ J0 as the UP state and all other states J < J0 as the DOWN state. Now for each J0 we have a dichotomy of all network states into UP and DOWN, and the definition of BIM and of the BIM-spectra given in the previous section may be applied to this binary situation. Let us reformulate the BIM definition. 3 For each J0 , 1 ≤ J0 ≤ K , element’s j BIM is defined as BIM j = ∂ R( p1 , .

We will not go into this rather technical issue. Remark The number of isolated clusters in the network is not the only way to define the number of states in the multistate case. Another approach of practical importance to defining the state of the network is the follow-up of the size of the maximal isolated component in the network determined as the number of nodes in this component. Consider, for example, the bridge network, Fig. 3a. It has four nodes and five links. Suppose the links fail in our destruction process in the following order: 1, 5, 2, 3, 4.

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