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 Выпуск 87
- Houankpo H.G.K., Kozyrev D., Nibasumba E., Mouale M.N.B. Reliability analysis of a homogeneous hot standby data transmission system
In this work, we consider the mathematical model of a repairable data transmission system as a model of a closed homogeneous hot standby system with one repair device with an arbitrary number of data sources with an exponential distribution function of uptime and an arbitrary distribution function of the repair time of its elements. We study the system-level reliability, defined as the steady-state probability of failure-free system operation. The proposed analytical methodology made it possible to evaluate the reliability of the entire system in case of failure of its elements. Explicit analytic and asymptotic expressions are obtained for the steady-state probabilities of system states and the steady-state probability of failure-free system operation, which allow us to analyze other operational characteristics of the system relative to the performance of the backup elements using the constant variation method. We developed a simulation model of the system for the cases when it is not possible to obtain expressions for the steady-state probabilities of system in an explicit analytical form and for constructing an empirical lifetime distribution function and the system reliability function. Exponential, Weibull – Gnedenko-, Pareto-, Gamma- and Lognormal distributions were selected for the numerical analysis and comparison of results.
- Chirkova J. Base stations selection and placement in wireless network
The paper considers a game-theoretic model of selfish base station selection in a wireless network, where each player tries to increase his signal-to-interference-plus-noise ratio. A system of integral equations is constructed for a model of n players distributed over a segment with a certain density. The solution of the system gives equilibrium strategies for choosing base stations. We also investigate the problem of optimal placement of base stations on a segment where the owners of base stations maximize the number of their subscribers, who act according to the strategies in the previous model. Systems of integral equations are constructed, the solution of which gives strategies for the placement of base stations for two scenarios: socially optimal and selfish behavior of station owners. Software has been developed for numerical finding and visualization of solutions for these models.
- Kazakov A., Lempert A., Ta T.T. On unequal balls packing problem in three-dimensional space
The article is devoted to the construction of optimal packings of unequal balls in a three-dimensional closed set. It is required to find such an arrangement of a fixed number of balls that their radii are maximal. This problem is NP-hard. To solve it, we propose a computational algorithm based on the optical-geometric approach and billiard modeling. Using this approach allows us to solve packing problems not only in Euclidean, but also in other metric spaces. We consider a problem in which, instead of the distance between the centers of the balls, the optimization parameter is the minimum traveling time between them. Such statements often arise if we consider problems of protecting the perimeter, in which the time of movement of the "intruder" to the protected object plays a much more significant role than the distance traveled, as well as in logistics, where the delivery time is paramount important. The algorithm was implemented, and computational experiments were performed. Both convex and non-convex sets were selected as container sets. The results of calculations allow us to positively assess the efficiency and effectiveness of the proposed algorithm. We performed a 3-D visualization of the results.
- Burkov V., Sergeev V., Korgin N. One-hot approach to identification of integrated rating mechanisms
The problem of identifying the integrated rating mechanisms for a given set of training examples is considered. An approach to the solution based on one-hot encoding is proposed. Basic concepts and definitions are formalized, such as: an integrated rating mechanism with a binary tree and convolution matrices, an integrated rating mechanism with a binary tree for discrete scales, a training example, a training set (consistent, complete, uniform scaled), a monotone training set. Identification tasks are formulated in the form of tasks for the implementation of the training set by the integrated rating mechanism and approximation. The proposed one-hot representation of the complex estimation mechanism using the quadratic form is illustrated with several examples. The rules for coding the integrated rating mechanisms are presented. It is shown that the problem of approximation and the problem of implementation as its particular case can be reduced to the problem of maximizing a certain polynomial obtained for a given binary tree and a set of examples using one-hot encoding. Assertions about the properties of these polynomials for an arbitrary integrated rating mechanism are formulated and proved. Examples of solving the problem of identification of an integrated rating mechanism are given, which implements an example through solving a system of equations based on one-hot encoding. In conclusion, the results of a numerical experiment on the approximation of all Boolean functions of three variables by the integrated rating mechanism are presented.
- Malsagov M., Ougolnitsky G., Usov A. Dynamic model of evaluation with corruption
A model of interaction between a professor and a student with possible corruption is studied in the game-theoretic setting. The model is formalized as a two-person game in extended form with perfect information. It is assumed that students have high or low qualification only. At the same time, corruption will manifest itself in the form of capture in the case of a low qualified student and in the form of extortion for students with high qualification. The decision is made by the method of backward induction using the Kuhn algorithm for analyzing the game in an extended form. This algorithm is based on analysis of the values of payoffs of the control subjects by the method of backward induction. An algorithm for constructing the solution is given. Simulation modeling is carried out based on the values of the payoffs of the control subjects. The results of numerical experiments are presented and analyzed. The meaningful conclusions are made on the base of the analysis of the results of simulation experiments in the case of a student of high and low qualification. The main conclusion is as follows. In the case of highly qualified students, one reduction in their moral costs when filing complaints about corrupt behavior of a professor is enough to eliminate corruption in a professor – student system. In the case of a low qualified student, it is more difficult to eradicate corruption. This requires a comprehensive approach that involves a significant increase in the amount of the professor's punishment for a bribe, as well as his payoffs in a non-corrupt case, and increasing the probability of detecting the fact of a bribe by strengthening administrative control over a professor.
- Kalmykov N., Sidelnikov Y. Experimental studies on the test questions based on the histogram ratio
The article proposes a histogram ratio as a tool of an integral assessment of the degree of confidence of experts in their estimates. Herewith, the experts evaluate test questions presented in the form of a problem. Experimental studies of test questions based on this ratio are proposed as a tool for studying the phenomenon of over-confidence among experts. A hypothesis about the correlation between the degree of confidence of an expert in his assessment and a posteriori assessment of his accuracy is proposed and substantiated. Explanations of the factors that determine the correctness of the conclusions obtained in these studies are provided. Requirements for the form and type of test questions have been introduced. Also, hypotheses that characterize the dynamics of changes in the values of the histogram ratio from the sample size are proposed and experimentally substantiated, and their consistency is confirmed. The dynamics of the integral assessment of experts ' confidence in their assessments were studied. The factors on which the conclusions of experimental studies depend are revealed. It is shown that the histogram ratio is not only an integral assessment of the degree of confidence of experts in their estimates, but also an analogue of any discrete indicator of the error of a particular expert when evaluating a particular question.
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