Y.M. Monakhov – Ph. D. (Eng.), Associate Professor, Vladimir State University named after A.&N. Stoletovs. E-mail: email@example.com
A.M. Vlasova – Undergraduate, Technician, Vladimir State University named after A.&N. Stoletovs. E-mail: firstname.lastname@example.org
In the course of our research we examine the availability of directed network with complex random topology and duplex links between neighboring nodes, whereas every node in the network has a corresponding probabilistic level of availability that depends on different characteristics, i.e. throughput value, load level, types of implemented services, etc. By the term «complex network» we mean the network structurally different from the widespread topologies like the «ring», the «star» or combinations thereof.
Our research is theoretically and methodologically based on the principles of graph theory, integral calculus, linear algebra. We use modeling and statistics as a means of research. The scientific novelty of our research is concluded in that we offer an algorithm for calculating the availability level of the network and its components using the Kolmogorov distance in the metric space of vector functions.
We hypothesize that the set of availability criteria corresponding to the prioritized links between any pair of nodes comprises the value of availability criterion of the network as a whole. That holds because tasks carried throughout the network are executed mainly using said prioritized links, the priority of which depends on the parameters of used edges and ultimately on the routing mechanism of the network. Therefore our method of evaluating the scalar network availability criterion is based on the search for minimal and maximal links between network nodes.
Furthermore using the proposed method we find the distance between adjacency matrices using the Kolmogorov formula. We use mathematical tools for distance measurement because in spaces of arbitrary nature the addition does not exist, thus statistic calculations cannot be based on summation.
During the final stage of our method we normalize the calculated distance. That normalization allows us to assign probabilistic meaning to the availability criterion.
The proposed method can be used for evaluation and improvement of network infrastructure security during design stages.