Analysis and synthesis of communication network structures by state enumeration method

K. A. Batenkov

Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 18 (2022) no. 3, pp. 300-315

Résumé

One of the methods of analysis and synthesis of communication network structures is considered, based on the simplest approach to calculating the probability of connectivity — the method of iterating over the states of the network edges. Despite its significant drawback, which consists in the considerable complexity of the calculations carried out, it turns out to be quite in demand both at the stage of debugging new analysis methods and when performing the procedure of sequential synthesis of network structures. The proposed method of sequential synthesis can be presented in the form of stages, at each of which one or more edges (network elements) are added. An increase in the number of edges used leads to an increase in the number of variations of the connectivity functions of a graph with an added edge, and hence to an increase in the complexity of operations for calculating conditional probabilities. At the same time, such a complication makes it possible to more accurately solve the synthesis problem, since not in all situations the sequential addition of edges is equivalent to sorting through all possible alternatives. Both the described method of analyzing the structures of communication networks based on the enumeration of states and the synthesis method differ in the essential simplicity of the implementation of the processes of the calculations carried out. It is this circumstance that allows us to use these methods as reference. The accuracy of the calculations depends solely on the capabilities of hardware and software systems and is in no way limited directly by the method of sorting states. As a result, the calculation of the probability of connectivity with precision accuracy, which is typical for situations of comparative analysis of communication networks with the availability and survivability coefficients of individual network elements close to the threshold values, also turns out to be feasible on the basis of the methods considered.

Détail

Keywords: network, graph structure, connectivity probability, coefficient of readiness, coefficient of operational readiness, complete state enumeration method.