Forming the Telecommunication Networks’ Cross-Sections to Analyze the Latter Stability with Different Connectivity Measures

The problem of stability analysis and its components of reliability and survivability is quite popular both in the field of telecommunications and in other industries involved in the development and operation of complex networks. The most suitable network model for this type of problem is a model that uses the postulates of graph theory. At the same time, the assumption of the random nature of failures of individual links of the telecommunications network allows it to be considered in the form of a generalized Erdos–Renyi model. It is well known that the probability of failure of elements can be interpreted in the form of a readiness coefficient and an operational readiness coefficient, as well as in the form of other indicators that characterize the performance of elements of a telecommunications network. Most approaches consider only the case of bipolar connectivity, when it is necessary to ensure the interaction of two end destinations. In modern telecommunications networks, services such as virtual private networks come to the fore, for which multipoint connections are organized that do not fit into the concept of bipolar connectivity. In this regard, we propose to extend this approach to the analysis of multi-pole and all-pole connections. The approach for two-pole connectivity is based on a method that uses the connectivity matrix as a basis, and, in fact, assumes a sequential search of all combinations of vertex sections, starting from the source and drain. This method leads to the inclusion of non-minimal cross-sections in the general composition, which required the introduction of an additional procedure for checking the added cross-section for non-excess. The approach for all-pole connectivity is based on a method that uses the connectivity matrix as a basis, and, in fact, assumes a sequential search of all combinations of vertex sections, not including one of the vertices considered terminal. A simpler solution was to control the added section for uniqueness. The approach for multipolar connectivity is similar to that used in the formation of the set of minimal all-pole sections and differs only in the procedure for selecting the combinations used to form the cross-section matrix, of which only those containing pole vertices are preserved. As a test communication network, the Rostelecom backbone network is used, deployed to form flows in the direction of "Europe-Asia". It is shown that multipolar sections are the most general concept with respect to two-pole and all-pole sections. despite the possibility of such a generalization, in practical applications it is advisable to consider particular cases due to their lower computational complexity.

communication network, graph, structure, connectivity probability, bipolar connectivi-ty, multipolar connectivity, all-pole connectivity