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Abstract
In this paper, a method for detecting synergistic effects of the interaction of elements in multi-element stochastic systems of separate redundancy, multi-server queuing, and statistical estimates of nonlinear recurrent relations parameters has been developed. The detected effects are quite strong and manifest themselves even with rough estimates. This allows studying them with mathematical methods of relatively low complexity and thereby expand the set of possible applications. These methods are based on special techniques of the structural analysis of multi-element stochastic models in combination with majorant asymptotic estimates of their performance indicators. They allow moving to more accurate and rather economical numerical calculations, as they indicate in which direction it is most convenient to perform these calculations.
Highlights
Questions of composition and decomposition in multi-element stochastic systems are relevant for solving a number of problems
Taken from science history and devoting the detection of synergistic effects in complex systems, which have been obtained by famous researchers in their objective areas, using observation and mathematical intuition
The proposed approach to the study of synergistic effects in complex systems can be applied to the construction of queuing systems with a large load and a small queue, to backup systems with recovery, to insurance models and other stochastic systems
Summary
Questions of composition and decomposition in multi-element stochastic systems are relevant for solving a number of problems. Many works on the analysis of complex multi-element systems require at the initial stage the construction of simpler models that allow you to determine the main performance indicators and the main parameters with which you can influence these indicators For this purpose, it is very convenient to build procedures for comparing systems with different (alternative) structures to study their effectiveness with a large number of elements, with a large load, etc. This task is quite important and leading Russian specialists in modeling of transmission networks Samouylov K.E. and Gaidamaka Yu.V. even organized a seminar with the author’s participation to find alternative approaches to this problem solution with publishing of obtained results [18] The solution to this problem is based on the recently installed a synergistic effect in multi-server queuing system with failures, when the stationary probability of failure tends to zero as the number of servers and proportionally the input flow intensity tend to infinity. This approach opens up new opportunities in solving problems of structural optimization of stochastic systems: queuing, reliability, etc
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