Analytical and numerical methods for solving the problems of evolution, optimization and queuing theory
| Programmee: | Institutional Projects (Supreme Council for Science and Technological Development) |
| Code: | 15.817.02.01A |
| Execution period: | 2015 – 2019 |
| Institutions: | Institute of Mathematics and Computer Science |
| Project Leader: | Lozovanu Dmitrii |
| Participants: | Kolesnik Alexander, Mishkoy Gheorghe, Sheremet Victor, Naval Elvira, Secrieru Grigore, Gutuleac Elena, Mitev Lilia, Burca Fevronia, Smolina Liudmila, Ghereg Veronica, Cuznetov Elena, Ivanov Andrei, Bodac Dumitru, Nani Alexandru |
Summary
The aim of the project is to elaborate analytical and numerical methods for solving the problems of evolution, optimization and queuing theory that arise in modeling of service and control of diverse economical, technical and information systems. The elaborated methods will be applied for studying the economic growth models, queuing priority systems, optimal transportation planning and solving some problems from mechanics, connected with studying the process of intensive loading of constructions.
The main results that are proposed for implementation represent:
- Computational complexity analysis of existing numerical methods for stochastic decision problems, optimization problems, queuing theory problems and problems from mechanics;
- Extension of classical analytical and numerical methods for multi-criteria optimization and game theory problems;
- Elaboration and theoretical argumentation of numerical methods and algorithms for solving stochastic control problems and generalized Markov decision problems;
- Application of the analytical optimization methods for solving and studying of real economic problems;
- Investigation of semi-Markov queuing model and determining the distribution priority functions for such models;
- Elaboration of the numerical methods and algorithms for the termoelastic problems and the problem of dynamic loading of the objects under the action of shock or seismic waves solving;
- Studying the linear forms for stochastic Markov evolutions in the Euclidian spaces and obtaining the explicit distribution of the sum of two independent telegraph processes and a partial differential equation for its transition density.
The elaborated methods and algorithms will be tested and estimated from computational point of view and implemented in the software environment. For certain classes of the problems will be used the High Performance Computing (HPC) technologies and clusters with multiple processors. Possibilities of the obtained results implementation in research, education and national economy will be analyzed.
