Registration Number
0225U002398,
(0123U101997)
, R & D reports
Title
Development of stochastic models, statistical methods for analysis and optimization of systems in the medical and socio-economic spheres
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Дослідження побудованих моделей статистичними та аналітичними методами та створення відповідних алгоритмів.
Head
Rozora Iryna V., Доктор фізико-математичних наук
Registration Date
07-03-2025
Organization
Taras Shevchenko National University of Kyiv
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Construction and research of stochastic models of processes that describe the functioning of systems in the medical sphere, solving the optimal control problems for the corresponding service processes in a dynamic mode. Research of the stationary regime existence conditions and calculation of the main efficiency characteristics for multidimensional Markov chains with continuous time as models of medical institutions, support systems, etc. These results will allow solving the problem of choosing the optimal structure of equipment and personnel, synthesizing optimal strategies for managing service processes, and developing software for optimal management of real systems.
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Purpose of the work: construction and study of stochastic models of processes that describe the functioning of medical systems, solution of control problems in dynamic mode of the corresponding service processes.
The main tasks to which the research is aimed are the solution of the problem of finding optimal strategies for Markov and semi-Markov multi-product inventory management models, as well as for systems operating in stationary mode. New methods will be developed based on linear and stochastic programming methods, which will allow obtaining optimal strategies in the inventory management problem for systems operating in stationary mode.
Hypothesis: optimal strategies for the functioning of such systems and their management depend on the existence and type of stationary distribution of stochastic service processes in such models.
Idea: for different types of models, in particular stochastic network models, models with repeated calls, models with reserves, to identify the conditions for the existence of a stationary mode of operation, to derive formulas for calculating stationary probabilities, and to formulate and solve optimization problems based on the obtained formulas.
Object of research: service networks, telecommunication systems, the many-armed bandit, regression models, impulse transition function, input process models, vector problems of partial integer optimization. Purpose of work: to study the functioning of multidimensional stochastic systems with controlled parameters in a stationary mode, to build effective algorithms for solving optimization problems and calculating integral indicators of the efficiency of controlled stochastic systems, to build models of sequential resource allocation in order to maximize profit, to develop a method for detecting damage to coronary vessels and myocardium, to study the stability of solutions to vector problems of partial integer optimization.
Product Description
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Vasylyk Olha I.
Hryhorieva Nataliia M.
Zatula Dmytro V.
Knopov Pavlo S
Livinska Hanna V.
Lukovych Olha V.
Pererva Antonina H.
Ponomarev Vadym D.
Semenova Nataliia V
Usar Iryna Ya.
Frankov Oleksii О.
Chaikovskyi Illia A.
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2025-03-07
