Accurate and Boundary Estimate of Communication Network Connectivity Probability Based on Model State Complete Enumeration Method

Abstract

We consider one of communication network structure analysis and synthesis methods, based on the simplest approach to connectivity probability calculation – a method of full network typical state search. In this case, the typical states of the network are understood as the events of network graph connectivity and disconnection, which are simple graph chains and sections. Despite significant drawback of typical state enumeration method, which involves significant calculation complexity, it is quite popular at stage of debugging new analysis methods. In addition, on its basis it is possible to obtain boundary estimates of network connectivity probability. Thus, when calculating Asari–Proshana boundaries use full set of incoherent (top) and cohesive (bottom) communication network states. These boundaries are based on statement that network connectivity probability under same conditions is higher (lower) than that of network composed of independent disjoint (connected) subgraph complete set serial (parallel) connection. When calculating Litvak–Ushakov boundaries, only edge-disjoint sections (for upper) and connected subgraphs (for lower) are used, i.e. subsets of elements such that any element does not meet two-rods. This boundary takes into account the well-known natural monotonicity property, which is to reduce (increase) network reliability with decrease (increase) any element reliability. From a computational view point Asari–Proshana boundaries have huge drawback: they require references of all connected subgraphs to compute upper bounds and all minimal cuts for bottom, which in itself is non-trivial. Litvak–Ushakov boundaries are devoid of these drawback: by calculating them, we can stop at any searching step for variants of sets of independent connected and disconnected graph states.