Stochastic model of information - computer network blocking in generation and transmission of malicious big data

Abstract

This work reviews a stochastic model of information -computer networks blocking in generation and transmission of large volumes of malicious data, developed by the authors. Rapid development of the Internet of things (IoT) leads to short time emergence of tens and hundreds of millions of new devices with their IP – addresses in the global network, capable to form a very large -scale botnets in case of infection. Therefore, development of network blocking models when generating and transmitting large amounts of malicious data is a crucial task to solve the problem of traffic filtering and balancing. When creating the model, we considered probability diagrams of transitions between possible states (share of infected devices) of computer networks, which describe the logic of the on-going processes. Based on approach used, the nonlinear second-order differential equation was deduced, allowing to formulate and solve boundary problems for determination of time-dependence of the probability density function for observation of different system states.The resulting differential equation contains the second and first time - derivatives, and the derivatives with respect to a variable, describing the change in the state of the system under consideration. Considering the second time - derivative of the probability density corresponds to the case in which the existing states generate additional new states, causing acceleration of processes and self-organization.The created model allows to assess time to achieve the state, when there is a limit value of share of potentially infected devices or, for example, achievement of its percolation threshold in a computer network. Percolation threshold is the minimum percentage of blocked nodes, at which the entire network loses the information transmission features (there is no free path between any randomly selected nodes). Using the approach adopted in the theory of percolation allowed to link structural and information characteristics of networks, such as dependence of their percolation threshold on the average number of links per node (network density) with dynamic characteristics of their blocking (time to reach the percolation threshold).