Asymptotic formulas of network operation time distribution

For a network in the form of a connected graph with independent times of failure-free operation of individual edges and singled out initial and terminal vertices, an asymptotic study of the distribution tail area of the time of failure-free network operation was carried out. Formulas expressing this asymptotics in terms of the asymptotics of the distribution of the failure-free operation time of individual edges were obtained. These formulas simplify substantially the calculations and can be used in the studies of the lengths of life cycles of complex systems.