Markov Random Process Research Articles

КОМПЛЕКСНАЯ МЕТОДИКА ОЦЕНКИ РИСКОВ ИНФОРМАЦИОННОЙ БЕЗОПАСНОСТИ В КОММЕРЧЕСКОМ БАНКЕ

This paper discusses the methods of improving the security of the information system of a commercial bank. The subject of the study is a comprehensive methodology for assessing information security used to determine the level of security and risk of information security of an automated system based on predictive estimates and specialized software tools. The purpose of the study and the carried out analysis are to improve the effectiveness of decisions made when performing work on risk assessment and management in a commercial bank. The results presented in the framework of the developed methodology can be used to solve the problems of increasing the reliability of an automated information system in various fields and sectors of activity, including organizations of the industrial sector, as well as commercial organizations. The main approaches used in the development of a comprehensive risk assessment methodology relate to the methods of expert assessment, the theory of random Markov processes, methods and models of mathematical statistics and probability theory, methods of applied system analysis and forecasting.

Reliability analysis of heat exchanging system of deep-sea manned submersibles using Markov model

This study introduces reliability assessment models for heat exchanging systems in deep-sea manned submersibles based on the Markov analysis method. Three distinct design systems—a series solution and two series–parallel solutions, considering cold and hot standby components—were presented. In addition, the state transition models of the Markov random process were established with relation to common-cause failures. Moreover, the calculation methods were derived for the two reliability indices of the heat exchange system: steady state availability and mean time to failure. Thus, the reliability of various design solution cases was investigated by comparing the reliability indices with variations in the failure and repair rates. The influence of common-cause factors on the system reliability was discussed as well. Furthermore, design solutions were suggested based on the results of the quantitative calculations and analysis.

Can Boosted Randomness Mimic Learning Algorithms of Geometric Nature? Example of a Simple Algorithm That Converges in Probability to Hard-Margin SVM.

In the light of the general question posed in the title, we write down a very simple randomized learning algorithm, based on boosting, that can be seen as a nonstationary Markov random process. Surprisingly, the decision hyperplanes resulting from this algorithm converge in probability to the exact hard-margin solutions of support vector machines (SVMs). This fact is curious because the hard-margin hyperplane is not a statistical solution, but a purely geometric one-driven by margin maximization and strictly dependent on particular locations of some data points that are placed in the contact region of two classes, namely the support vectors. The proposed algorithm detects support vectors probabilistically, without being aware of their geometric definition. We give proofs of the main convergence theorem and several auxiliary lemmas. The analysis sheds new light on the relation between boosting and SVMs and also on the nature of SVM solutions since they can now be regarded equivalently as limits of certain random trajectories. In the experimental part, correctness of the proposed algorithm is verified against known SVM solvers: libsvm, liblinear, and also against optimization packages: cvxopt (Python) and Wolfram Mathematica.

Пространственно-временная обработка широкополосных сигналов на основе модели линейного предсказания

The main developments in the field of radar surveillance systems are aimed at studying their functioning, taking into account the influence of various factors, such as the effect of interference. The most important thing seems to be the detection of a broadband signal, which makes it possible to increase the range and speed resolution. This raises the problem of suppressing broadband interference with existing methods. The paper develops methods for processing broadband signals in the presence of active interference as applied to the use in systems with various variants of spatio-temporal antenna elements, in particular on the example of linear antenna arrays. The approach is based on the representation of signals and interference recorded by a digital antenna array in the form of multidimensional spatiotemporal processes, i.e. functions of spatial and temporal coordinates. This is due to both the spatial distribution of the antenna array elements and the spatial distribution of interference. Bayesian signal detector is the optimal algorithm and has the best characteristics, but at the same time its practical implementation is extremely difficult, carried out in the field of spatiotemporal coordinates. The investigated processing algorithms are based on the linear prediction model, i.e. by using the model of a Markov random process to describe interference on spatially distributed antenna elements. Particular attention is paid to the development of algorithms that can be implemented with limited computing resources and work in real time, which is a problem of statistical methods of signal processing.

Моделирование APT-атак, эксплуатирующих уязвимость Zerologon

Purpose: the need to assess the effectiveness of the security systems for significant objects of critical information infrastructure determines the need to develop simple and adequate mathematical models of computer attacks. The use of mathematical modeling methods in the design of security system of significant object allows without significant cost and impact on the functioning of the object to justify the requirements to the system as a whole or its individual parts. The purpose of the present paper is to develop a model of the process of multistage targeted computer attack that exploits the Zerologon vulnerability, based on the representation of the attack by a Markov random process with discrete states and continuous time. Methods: methods of Markov process theory, probability theory, computational mathematics and graph theory are used in the model to formalize the attack. Novelty: application of methods of computational mathematics for functional analysis of the results of Kolmogorov’s system of equations allows to solve the problem of maximizing the time of stable operation of critical information infrastructure during computer attacks against it, using the known methods of analysis of continuous functions. Result: formulated a general statement of the problem of modeling the process of a multistage targeted computer attack using a system of Kolmogorov equations, describing the probabilities of being in conflict states of the security system with the intruder. By the Adams method implemented in Mathcad environment, numerical solutions depending on time were obtained. We introduce a security system performance index as a ratio of probability of triggering the security system and blocking intruder’s actions during the attack to the probability of successful completion of the attack. We give an example of research of computer attack realization in a typical information infrastructure, including a corporate network with domain architecture and an automated control system of some technological process. 1 For the considered example defined the optimal values of time parameters of security system. When implementing protective measures with reasonable probabilistic-time characteristics proved an increase in time of stable operation of critical information infrastructure from 11 to 189 hours.

МАТЕМАТИЧЕСКАЯ МОДЕЛЬ ОЦЕНКИ ФУНКЦИОНАЛЬНЫХ ВОЗМОЖНОСТЕЙ РОБОТОТЕХНИЧЕСКИХ КОМПЛЕКСОВ ПО ПРОТИВОДЕЙСТВИЮ ПРОТИВНИКУ НА ОСНОВЕ УРАВНЕНИЙ ДИНАМИКИ ВЫСОКООРГАНИЗОВАННОГО БОЯ

The paper presents an analytical model for solving the problem of predicting an average number of hit and unaffected enemy forces and robotic systems group based on a mathematical model of highly or-ganized combat. The dynamics of the battle is described as a random Markov process that allows us to determine the average number of the parties for any given time.

Green Measures for Time Changed Markov Processes

In this paper we study Green measures for certain classes of random time change Markov processes where the random time change are inverse subordinators. We show the existence of the Green measure for these processes under the condition of the existence of the Green measure of the original Markov processes and they coincide. Applications to fractional dynamics in given.

Оптимизация надежности теплоснабжения с учетом функций активного потребителя

The article considers the problem of analyzing and optimizing the reliability of heat supply to an active consumer (AP) of thermal energy in heat supply systems (HSS), taking into account their additional thermal power provided by their own sources of thermal energy (IT). The stated scientific and methodological problem consists in determining the optimal ratio of the values of the reliability parameters of the HSS elements (failure rates and / or restorations) and the power of the own IT AP, which ensures the required level of reliability of heat supply with minimal total costs to ensure the elemental reliability of the system and the operation of its own IT AP. The authors propose solutions based on the use of the theory of reliability, models of Markov random processes, some regularities of the theory of probability, nodal PN, models of the theory of hydraulic circuits and enlarged regularities of thermophysical processes occurring during heat supply to consumers. A computational experiment was carried out using the developed methods based on the TSS test circuit with characte­ristics close to real systems, providing the basis for conclusions and directions for further research.

Модель функционирования защищенной технологии файлового обмена

The purpose of this work: to develop a model that allows to assess the security of the information system of file exchange, to ensure the efficiency of servicing the maximum number of requests of authorized customers with a simultaneous decrease in the quality of service of requests from the attacker’s means. Methods used: formalization of service processes in the form of Markov random processes, as well as numerical methods. The result of the study: a criterion evaluation base for the effectiveness of the functioning of the information system of file exchange has been developed. The problem of dynamic management of the resource capabilities of the information system of file exchange by managing the parameters of data transmission has been solved. An assessment of the asymptotic stability and robustness of the model relative to the perturbations of the values of the initial parameters is solved in order to increase the adequacy of the model when choosing control modes for the data transmission process. Probabilistic and temporal characteristics and the process of functioning of the information system of file exchange in the conditions of unauthorized influences in various situations of interaction of the parties to the conflict, as well as in the managementand computational and time resource of the means of network intelligence of the attacker are obtained. The optimal modes of functioning of information systemsand file exchange, ensuring its compliance withthe established security requirements of critical information infrastructure objects, aresubstantiated.

Method for Predicting the Stability Limit to Acoustic Oscillations in Liquid-Propellant Rocket Engine Combustion Chambers Based on Combustion Noise

An experimental method for determining the critical pressure perturbations leading to acoustic instability in combustion chambers of liquid-propellant rocket engines has been developed and used to estimate the stability of the working process. The method involves statistical processing of recorded noise pressure pulsations near the natural resonant frequency range for all normal modes of acoustic oscillations in cylindrical combustion chambers and gas generators. The oscillation damping coefficient (decrement), characterizing the difference between the generated and dissipated energy, is used as a diagnostic criterion for predicting the stable or unstable states of a dynamic system. The method is based on the theory of self-oscillating dynamic systems and one-dimensional Markov random processes using the Fokker–Planck–Kolmogorov equation. Analysis of a nonlinear differential equation with a symmetrized stochastic right-hand side describing white noise for experimentally determined amplitudes of pressure pulsations and their statistical processing using Mera software allows the state of self-oscillating systems to be identified as stable or unstable. The method is “passive;" it is applicable without using standard external impulse disturbing devices.

Optimal and Quasi-Optimal Algorithms for Receiving and Processing BOC Signals in Promising Global Navigation Satellite Systems

The problem of synthesis of optimal and quasi-optimal algorithms for receiving and processing BOC signals intended for use in global navigation satellite systems (GNSSs), such as GPS (USA), Galileo (European Union), GLONASS (Russia), and BeiDou (China), is solved on the basis of the Markov theory of random process estimation by the method of step-by-step solution of the Stratonovich equation. The problem of optimal nonlinear filtering is solved in relation to a vector discrete-continuous Markov random process for the case when its continuous part is a vector diffusion Markov process, and the discrete part is characterized by a simple Markov chain of several positions. It is assumed that useful BOC signals are observed against a background of additive white Gaussian noise. The main analytical relations of optimal and quasi-optimal algorithms for receiving and processing BOC signals are presented, as well as the corresponding block diagram of a quasi-optimal system for receiving and processing GNSS BOC signals. The results of the study are also applicable in cases of noise-like signals of modern GNSSs, for which BOC signals are not used yet.

Обеспечение целостности данных, передаваемых по каналам связи виртуальных частных сетей

Annotation A method of ensuring the integrity of data transmitted over communication channels of VPNs of large-scale information systems functioning in the conditions of the destructive influence of the attacker is considered. The proposed method allows to recover data packets subjected to erasure and imitation. The purpose of the research is to increase the stability of data transmission over VPN communication channels by implementing the procedure for recovering erased IP-packets and increasing the level of imitation security of the transmitted data. Research methods: aggregation of methods of cryptographic control of data integrity and methods of redundant coding of data, application of methods of the theory of Markov random processes to determine the probability of providing satisfactory support for applications in conditions of destructive influence of an attacker with various parameters. Research results: analysis of the object of research – VPN of large-scale information systems was carried out. It leads to the conclusion about the need to protect data transmitted through such communication channels for the implementation of national strategies for economic development. A mathematical model of the functioning of a data transmission system over a VPN communication channel under the conditions of a destructive influence of an attacker is presented. A method is proposed to ensure the integrity of transmitted data based on an original scheme for sharing known solutions, generating a synergistic effect. The method allows recovering dmin −1 erased data packets. The proposed solution makes it possible to increase the stability and speed of data transmission over the communication channels of the network in the conditions of the destructive influence of the attacker and the imitation of data by the attacker.

МОДЕЛИРОВАНИЕ ПРОЦЕССА СМЕШИВАНИЯ В ДИСКОВОМ ГОМОГЕНИЗАТОРЕ-ДИСПЕРГАТОРЕ

The movement of viscous fluid in a small gap between stationary and rotating disks is investigated and a mathematical description is given for flat and stepped disks. Using the mathematical apparatus of random Markov processes discrete in space and time, a model of the process of mixing grease with graphene plates in a rotary homogenizer disperser has been created. Decomposition of the process and consideration of separate mixing processes in the radial and circumferential directions made it possible to assess the intensity of these processes and develop recommendations for the transition from laboratory installations to industrial devices.

Determination of risk magnitude at refusal of band conveyers frame working in the conditions of mining enterprises

Abstract. At present, due to the complexity of technical systems, industrial production is becoming a source of accidents, disasters, leading to large human and material losses, as well as to environmental pollution. In particular, this applies to conveyor systems for mining enterprises. The main causes of accidents and disasters in the conveyor transport of mining enterprises are the influence of the external environment, the reliability of equipment, as well as the level of operation. The experience of conveyor transport operating at mining enterprises has shown that a large number of accidents on conveyor belts is associated with failures of the frame. This is due to the fact that when the belt with a load moves along the conveyor frame, dynamic loads arise on the roller bearings leading to the failure of the pillow-blocks. At the same time, as the analysis of the data on operation of the belt conveyors shows, accidents that occur because of the rollers failure often lead to large material losses. These material losses are associated with the destruction of the rollers of the roller supports, as well as with the rupture of the conveyor belt. In addition, the elimination of accidents at the line of belt conveyors often lead to long downtime of the entire conveyor transport and, as a result, to a loss of its productivity. In this paper, on the basis of the theory of random Markov processes of death and reproduction, the risk rate in case of failure of the belt conveyor frame is determined by the factor of the rollers failure of the roller supports. The risk rate was determined as a mathematical expectation of the product of the probability of failures of rollers by the value of material losses caused by downtime of the conveyor and repair of roller supports. As a result, the dependence of the risk rate of failure of the belt conveyor frame on the conveyor productivity, the intensity of failures and recovery of the rollers of the roller supports, as well as on the average resource of the rollers, was obtained. It is established that with an increase in the conveyor productivity, the risk of failure of the belt conveyor becomes linear, and with a decrease in the recovery rate of the roller support, the risk increases according to the hyperbolic law. At the same time, with an increase in the failure rate of rollers, the rate of risk increases. In addition, with an increase in the resource of the rollers of the belt conveyor rollers bearings, the rate of the risk of failures of the frame decreases. It is established that the maximum rate of risk has the frame of a belt conveyor with rigid roller supports, and the minimum – the frame of a belt conveyor with shock-absorbed roller supports. Keywords: belt conveyors, frame, roller supports, risk rate.

Stochastic model of oxygen adsorption

The authors propose a microscopic stochastic model of the process of oxygen adsorption on the surface of a solid object. As a first approximation, the constructed model describes the dynamics of the system in terms of a planar surface coating with oxygen adatoms. A simplified diagram of the adsorbent surface oxidation mechanism is presented in five stages. The reaction conditions are determined by the temperature of the crystal surface and the partial pressure of the reagent in the gas phase. The reaction is considered as a random Markov process with a discrete set of states for a stream of elementary events occurring on a fragment of an ideal square lattice of ferrous sulfide with periodic boundary conditions. For the constructed model, numerical calculations are done using a software solution and the results of computational experiments are presented. The research results analysis suggests that the presented mathematical process model of oxygen adsorption on the ferrous sulfide surface along with the software solution for simulation studies can be used to determine control parameters for various technological processes.

Application of the Methods for Comprehensive Reliability Analysis of District Heating Systems

Abstract The general idea of the methodology for the comprehensive reliability analysis of district heating systems (DHS), developed earlier by the author of this paper, is a joint considering and modelling of each technological processes, including fuel supply to heat sources (HS), generation of heat energy by these HS and its distribution on district heating network (HN). For solving this problem different methods and models are applied: statistical testing method, Markov random processes, methods of the theory of hydraulic circuits, basic laws of district heating and heat transfer processes, etc. In this paper the main attention is paid to the results of the practical application of methods and models of a comprehensive reliability analysis of DHS using the example of calculations performed for the actual DHS scheme of the Shelekhov city (Irkutsk region, Russia). Different stages of the case study are considered, including preparation of initial data, simulation modelling of fuel supply to HS, modelling of the Markov random process describing operate of DHS, calculation of post-failure modes in HN, evaluation of nodal reliability indices (RI), decomposition analysis of reliability. Based on the analysis of calculation results some preliminary directions are formulated to the increase of reliability for studied DHS. These data are the basis for a comprehensive reliability synthesis (optimization) of DHS, the solution of which is the subject of special perspective stage in development of the research.

Mathematical Single-Player Computer Game Model to Reproduce Duel Fight of Tanks

In improving computer games, which reproduce a battle of tanks, two tasks can be distinguished: increasing a collection of game tools to represent virtual prototypes of real tank models and ensuring a realistic game. To solve these problems, a tool is necessary that allows us to compare gaming capabilities of virtual tank brands with combat capabilities of their real prototypes. A mathematical model of a computer game that reproduces a duel battle of tanks can be used as the tool. The specified model satisfies the following requirements: the sequence of operations reproduced in the model is in line with the sequence of operations implemented by the player in the course of the game; the maximum amount of ammunition that a tank can use in a model must correspond to the amount of tank ammunition. The duel lasts until one of the tanks is hit, or until all the gunshots available to hit the enemy are expended. It is necessary to find the probabilities of possible outcomes of a duel battle, the mathematical expectation of its duration, the mathematical expectation of the ammunition consumption of each side.The solution to the problem is obtained by constructing a mathematical model according to the scheme of Markov random process with discrete states and continuous time. It is implemented as a program for a model of a duel battle of tanks and can be used when developing a computer game of the genre of tank simulators to assess the gaming capabilities of the virtual tanks in a duel battle from the data on the amount of their ammunition and on the intensity of the game process transition from one state to another; for selecting the intensity values of the game process transition from one state to another, based on the data on the estimated game capabilities of virtual tanks in a duel battle. Thus, game participants can use this model to conduct their own research. Developers of computer games can use it for setting up the game and setting such intensity values of the game process transition from one state to another, at which the gaming capabilities of virtual tanks will correspond to the combat capabilities of their real prototypes on the battlefield.

Peculiarities of container terminal functioning in delivery chains

The purpose of this article is to study the container terminal as a complex technical system. The object of study is a container terminal. The subject of the study is a functional study of the container terminal at the junction of road and rail transport. The research methodology is based on the Markov random processes scheme. An example of a method for determining the number of reach players is given.

Calculation of the reliability of frame systems under seismic impact and survivability assessment during the formation of plastic hinges in the nodes

Aim . The research aims to develop mathematical models for evaluating the reliability of two-story frame systems under the seismic impact, covering all possible ways of transition to the mechanism state due to the formation of plastic hinges in the frame nodes. Methods . The study is based on the application of the theory of Markov random processes in continuous time and their discrete states to describe the transition of a system into a different state. Such states include faults resulting from the formation of plastic hinges in the frame nodes. Results . Possible schemes of forming plastic hinges in two types of statically indeterminate frames under horizontal seismic impact are described: in the frame of a 2-story industrial building with a large-span upper floor and with the support of the roof truss on the heads of columns and a two-story two-span frame of a simple regular structure with rigid nodes. Possible states are noted and transition graphs are compiled, which are typical for the frames under consideration in the case of rigid disks of floor slabs during seismic impact, represented as a stationary random process. By representing the transition of systems to the states under consideration caused by the formation of plastic hinges in one or another sequence under seismic action in the form of a Markov random process in continuous time and discrete states, systems of first-order differential equations describing these transitions are obtained. Having solved them by applying the Laplace transform, analytical expressions for estimating the probabilities of finding frame systems in the states under consideration and expressions for estimating the probabilities of failure-free operation of these systems are obtained. Conclusion . By constructing transition graphs covering all possible states of frame systems during the formation of plastic hinges in nodes under seismic action and describing the process of frame transitions from one state to another by a Markov random process in continuous time and discrete states, analytical expressions for evaluating the probabilities of these system states, as well as their reliability and survivability under seismic action, can be obtained.

Динамическая модель разработки и реализации проекта под влиянием внешних факторов

When planning projects, events, work packages, it is always necessary to take into account the influence of internal conditions and the external environment. In most cases, the influence of external factors on the project is stochastic and is a random process. Scientific developments allowing to take into account the influence of the external environment on the development and implementation of projects are always relevant, since they will allow to predict the temporal characteristics of projects in real conditions. Aim. In scientific research, the task is to develop a mathematical model that allows dynamics to predict the temporal performance of projects, taking into account the influence of random external factors on them. Materials and methods. It is possible to solve the problem by describing the process of the influence of external factors on the project by mathematical methods of the theory of Markov random processes. At the same time, factors affecting the project are conditionally divided into those that lead to the need for additional activities in the development of projects, and to factors that require a fundamental change in the project. In a scientific study, mathematical methods of probability theory, the theory of differential equations, and numerical methods are used. Results. Based on the theory of Markov random processes, a dynamic model for the development and implementation of the project was developed taking into account the influence of external random factors on these processes. A methodology for the formation and solution of a mathematical model is described, which allows one to find the time dependences of the probabilities of completion of individual stages of project development and the probability of successful implementation of the project as a whole. The analysis of the solutions obtained is carried out, general trends in the development and implementation of projects are described taking into account the influence of external factors on them. Conclusion. The presented model makes it possible to evaluate the probabilities of the project in general and of its individual stages for different time intervals, which will allow you to plan timelines for project management. The model can complement the network planning and management procedures and provide additional probabilistic estimates of the project time.