Models of describing the dynamics of blocking nodes of computer networks by viruses based on the use of percolation KINETIC AND STOCHASTIC METHODS
The paper presents a set of models describing the dynamics of blocking nodes of computer networks created on the basis of taking into account their percolation properties and blocking mechanisms (kinetic and stochastic). On the one hand, this model is based on the use of percolation theory methods, which make it possible to determine the structural and informational characteristics of networks, such as the dependence of their percolation threshold on the average number of bonds per node (network density). On the other hand, dynamic processes of blocking the nodes and reaching the percolation threshold are considered. The percolation threshold is the minimum proportion of blocked nodes at which the entire network loses the properties of information transmission (there is no free path between any randomly selected nodes). In the kinetic model, the processes of propagation in computer networks of evolving viruses in the course of obsolescence and delay of the action of antiviruses are considered. Further, on the basis of the graphical description of the possible transitions between the states of the nodes, systems of kinetic differential equations for the spread of viruses were obtained. Then using these equations and the percolation threshold value calculated by the network density, one can estimate the time of loss of its overall performance. Any network node can be in one of three states: in a protected (immunized) state, and it can itself send randomly (stochasticity) antiviruses (cures infected and immunizes free nodes) by selecting them in the address space; in the infected state (can send copies of viruses to network nodes); in a neutral state (may be infected). Analysis of the solutions obtained shows the possibility of the existence of various modes of spread of viruses. With some sets of values of the coefficients of differential equations, an oscillating pattern of the spread of viral epidemics is observed, which largely coincides with real observations. One of the advantages of the developed model is the possibility of its modification and expansion based on the creation of more complex graphical diagrams of state changes and transitions between them. In particular, it is possible to supplement the system of kinetic equations with a term that takes into account the general increase in the number of users and devices in computer networks over time. A second-order differential equation was obtained in the model of stochastic dynamics of blocking nodes, based on a consideration of probability schemes for transitions between network states, and a boundary value problem was formulated, whose solution describes the dependence of the probability and time to reach the percolation threshold on the blocking probability of an individual network node. The percolation threshold itself is determined based on the density of the network.
Keywords
блокирование узлов сети,
порог перколяции сети,
кинетическая модель блокирования узлов,
стохастическая динамика блокирования узлов,
blocking network nodes,
network percolation threshold,
kinetic model of blocking nodes,
stochastic dynamics of blocking nodesAuthors
| Lesko Sergey A. | Russian Technological University (MIREA) | sergey@testor.ru |
| Zhukov Dmitry O. | Russian Technological University (MIREA) | zhukovdm@ya.ru |
| Istratov Leonid A. | Russian Technological University (MIREA) | kuyahshtibov@gmail.com |
Всего: 3
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