Abstract
This paper deals with the issue of reliability evaluation in complex networks, in which both link and node failures are considered, and proposes an approximate method based on the minimal paths between two specified nodes. The method requires an algorithm for transforming the set of minimal paths into a sum of disjoint products (SDP). To reduce the computation burden, in the first stage, only the links of the network are considered. Then, in the second stage, each term of the set of disjoint link-products is separately processed, taking into consideration the reliability values for both links and adjacent nodes. In this way, a reliability expression with a one-to-one correspondence to the set of disjoint products is obtained. This approximate method provides a very good accuracy and greatly reduces the computation for complex networks.
Highlights
The network reliability theory is extensively applied in many real-world systems that can be modeled as stochastic networks, such as communication networks, sensor networks, social networks, etc
In the two sections, we address the problem of twoterminal network reliability evaluation, in which both link and node failures are considered
The methods of network reliability evaluation based on sum of disjoint products (SDP) algorithms fall in the NP-hard category and, are difficult to apply for very large networks, such as social networks
Summary
The network reliability theory is extensively applied in many real-world systems that can be modeled as stochastic networks, such as communication networks, sensor networks, social networks, etc. Based on this concept, starting from the given network with unreliable nodes, reduced models with perfect nodes but with links having increased failure probabilities can be obtained This method is simple, but not so accurate. Each term of the sum of disjoint products including state variables associated to the links is processed distinctly by considering both links and adjacent node reliability values This new approximate method reduces the computation time for large networks to a great extent, compared with an exact method. This reduction in computation time is explained by the fact that the node failures are taken into account only in the second stage when the computation process is simpler, belonging to the O n × m class of complexity, where n is the number of disjoint link-products and m is the number of the network components.
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