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 Выпуск 90
- Zverkina G. On exponential convergence of availability factor
The availability factor is the probability that the system is working properly at a given moment of time. It’s estimation and calculation are one the most important tasks in a reliability theory. The calculating of the stationary value of the availability factor is not difficult for the most cases. However, in real applications it is necessary to know how soon the value of the availability factor becomes sufficiently close to its limiting value, i.e. it is important to know the rate of convergence of the availability factor to its stationary value. In cases where the distributions function of the operating and recovery times are exponential, the question of the rate of convergence of the availability factor is the question of the rate of convergence of the solution of the Kolmogorov -- Chapman equations with constant coefficients. This problem is solvable by means of Laplace transform. The most processes describing the behavior of reliability systems are regenerative, and for them the type of rate of convergence of the distribution to a stationary one is known -- exponential or polynomial. Thе strong upper bounds of the rate of the convergence for regenerative processes can be obtained using the Lorden's inequality, when the distribution of the length of a regeneration period is known. But for reliability systems, it is possible to take into account the specific features of the investigated regeneration period. This article shows a method for constructing a strong exponential bounds for convergence rate of the availability factor for one restorable element.
- Shchegolev A. On rate of convergence estimates for homogeneous discrete-time nonlinear markov chains
The paper studies an improved estimate for the rate of convergence for nonlinear homogeneous discrete-time Markov chains. These processes are nonlinear in terms of the distribution law. Hence, the transition kernels are dependent on the current probability distributions of the process apart from being dependent on the current state. Such processes often act as limits for large-scale systems of dependent Markov chains with interaction. The paper generalizes the convergence results by taking the estimate over two steps. Such an approach keeps the existence and uniqueness results under assumptions that are analogical to the one-step result. It is shown that such an approach may lead to a better rate of convergence. Several examples provided illustrating the fact that the suggested estimate may have a better rate of convergence than the original one. Also, it is shown that the new estimate may even be applicable in some cases when the conditions of the result on one step cannot guarantee any convergence. Finally, these examples depict that the original conditions may not be an obstacle for the convergence of nonlinear Markov chains.
- Chaplinskaya N. Research of complete homogeneous "greedy-vertices" resource networks: zone of "sufficient large" resource
"Resource network with greedy vertices" -- the modification of the graph dynamic model "resource network". At each discrete-time moment the graph vertices transfer resources to each other through the edges with limited throughput, first passing the available resource to themselves via the loop and then distributing the remaining resource (if it is available) to outgoing edges according to the "standard" resource network rules. These are two rules with threshold switching: if the vertex has resource, that exceeds the total throughput of all vertex's outgoing edges, it transfers the full throughput to each outgoing edge; otherwise, it gives away the entire available resource, distributing it in proportion to the throughputs of the outgoing edges. The particular case of a complete homogeneous resource network with "greedy" vertices is considered. For networks of such type there are two total resource thresholds, separating zones of different network behaviour: the first threshold divides the zones of "insufficient" and "sufficient" resources, the second divides the zones of "sufficient small" and "sufficient large" resources. In the article the last zone -- "sufficient large" resource -- is investigated: the functioning of the network is described, the asymptotic state is found.
- Shevyrenkov M. Correctness of control task setting
In this paper, the problem of reducing the influence of negative factors on the correctness of the problem statement was considered. Since these factors are of a complex, complex nature, this paper presented an approach based on the use of interrogative logic, which, according to the author, is able to reduce the degree of influence of these factors on the effectiveness of managerial decision-making. As part of the creation of this approach, a number of problems were solved. To solve the problems associated with the correctness of the formulation of managerial tasks with active forecasting, a mechanism for adjusting the formulation of managerial tasks for information management of socio-economic systems was developed based on the apparatus of interrogative logic. A list of necessary conditions for the correct formulation of a management problem in the information management of socio-economic systems using active forecasts was formulated and substantiated. Also, a special formal-meaningful interrogative language was formulated, which is used to reduce the loss of information when transferring the task to the performer.
- Klochkov V., Toporov N., Yegoshin S. Integrated aviation systems
Improving the efficiency of management of aircraft industry scientific and technological development at this stage is possible through the transition to the consideration of large-scale systems with a large number of "degrees of freedom". For the first time methodological approach to forecasting and strategic planning of scientific and technological development of aircraft industry, based on analysis and synthesis of integrated systems, rather than individual aircraft or aviation systems, has been proposed and developed. These systems are designed to address high-level objectives and include fleets of various aircraft, as well as infrastructure and control subsystems, including non-aviation subsystems of the target customer. The research methodology is based on the systems theory, system analysis and synthesis methods, and mathematical modeling. The proposed approach allows us to reveal the potential fields of application of prospective aviation in transport and various sectors of the national economy, as well as estimate the potential scale of aviation. The results of modeling and optimization of integrated aviation systems should form the basis for planning of priority research and development in aircraft industry, including the formation of state programs of the Russian Federation, the development strategy of scientific and industrial organizations of aircraft industry.
- Blinova O., Vaskovsky S., Rykov Y. Design rapid deployment communication networks using the network configuration analysis software application
A new approach to the design of rapid deployment wireless communication networks is proposed by the conditions when it is impossible to cover fully the territory with a network. The essence of this approach is to determine the optimal locations of specified sets of network equipment prepared in advance. When performing the search, the specified routes of subscribers and their speed are taken into account. The target function uses the time- depended total network access level for all subscribers. The main existing methods of designing wireless networks, their application possibilities and disadvantages when used in a certain class of tasks (rapid deployment, incomplete coverage) are also considered. For practical application of the considered approach, a software product has been created that implements the developed search procedure using simulation and genetic algorithms. The algorithm of the software product operation is considered and examples of simulation results are given. The advantages and disadvantages of the proposed solution are analyzed. The problem of placing network devices in the specified conditions is solved for the first time; the software product created has no analogues. The results obtained are applicable for rapid design of wireless communication networks in areas where there is no mobile network coverage, for example, to provide communication for rescue operations or tourist routes in mountainous areas.
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