A new fractal reliability model for networks with node fractal growth and no-loop

Evaluating the reliability of networked systems with existing exact or approximate methods often needs to characterize the detailed topology with node scale, which brings complexity and high computation effort. In this paper, a new reliability model based on the fractal unit with a bigger scale than nodes and a much smaller scale than whole network is proposed for networks with fractal growth and no-loop (NF-NL). The introduced model simplifies the K-terminal reliability (KTR) of a NF-NL network to a multiplication of different KTR of fractal units in the network. The corresponding algorithm is also given, which has a linear-time complexity O(V) when the fractal unit scale is very small. Compared with the existing models, the proposed model provides a novel way to construct the reliability model only dependent on two factors: (1) the fractal unit characteristics and (2) its iterative process. Finally, the widely investigated Koch network case is studied with the proposed model.