Distribution of a maximal flow in an unreliable two-terminal network with a recurrent radial-and-ring-shaped structure

A two-terminal network with a radial-and-ring-shaped structure is considered. Failures of elements are assumed to be mutually independent while the failure probabilities are arbitrary and given. Recurrent relations are obtained for accurate finding of the distribution (or its moments) of the maximal flow between network poles. For an isotropic network an answer is obtained in a finite form. Asymptotic properties of the mean distribution are studied with the number of network objects going to infinity.