Analysis of ports reliabilities

Asymptotical formulas for reliabilities of statical networks with unreliable arcs are obtained and their application to life time models is shown. Graphs with fixed initial and final nodes - ports are considered. Direct calculation of reliabilities for these models demands geometrically increasing volumes of arithmetical operations by numbers of arcs. Parameters of obtained asymptotical formulas are length of shortest way, minimal ability to handle of cross sections. Fast algorythms of these parameters calculations are constructed. These algorythms allow to analyze an influence of some elements parameters on reliability of complete network and to obtain conditions of invariance when this influence is absent. Narrow places of random networks are defined also. Recursively defined ports are constructed. These ports and structures are very interesting in modern surface physics, solid state physics and nanotechnology. Asymptotica formulas and algorythms of their reliability calculations with linear complexity are constructed.