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POSITION
Head of Department of Applied Statistics
WORK EXPERIENCE
1978–1998
Junior Researcher
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)
1981–1983
Senior Researcher
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)
1983–1987
Head of Research Laboratory of the Probabilistic & Statistical Methods
Taras Shevchenko national University of Kyiv, Kyiv (Ukraine)
1987–2004
Associate Professor
Taras Shevchenko national University of Kyiv, Kyiv (Ukraine)
2004–Present
Head of Department of Applied Statistics
Taras Shevchenko national University of Kyiv, Kyiv (Ukraine)
EDUCATION AND TRAINING
1970 -1975
Student at Faculty of Cybernetics
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)
1975-1978
Post-graduate student
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)
1980
Ph.D.
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)
2003
Doctor of Physical and Mathematical Sciences
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)
2007
Full professor
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)
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Asymptotic analysis of stochastic systems and networks
Research Fields:
Mathematics
Previous and Current Research
Stochastic processes, that describe modern stochastic systems of network structure (mobile networks, computer networks, technological control systems), are defined by complex system of stochastic equations, have interdependent components and complicated structure of the state space. Therefore, problems of development simplified approximation models for such systems are actual.
As part of this area methods of diffusion and Gaussian approximation, asymptotic state space enlargement is worked out. Developed approaches allowed to obtain fundamental results for stochastic networks under the critical load, to research conditions of asymptotic enlargement of network’s serving nodes set. Particular attention has been given to functional limit theorems for multivariate branching processes.
According to theoretical result new algorithms for optimal resource management of modern telecommunication networks were developed. Among them are: redistribution of frequencies between neighboring cells of mobile network, access to various types of information in the information channel, reallocation of external load for network, transmission speed control for various types of information solutions, problems of income maximization and risk minimization.
In this area within international projects «Mathematical models of economics risk» (grant DFG 2002-2006) and «Asymptotic analysis of random flows and networks» (grant DFG 2007-2009) researches of stochastic networks were made in collaboration with University of Bonn (Germany). Researches of retrial queueing systems were made in framework of INTAS-project “Advances in retrial queueing theory” (reference number INTAS-96-0828), under contracts ¹ F25/545-2007 and ¹ F25/181-2008 (project 25.1/094 «Development of mathematical methods for the study of Markov systems with repeated calls and managed local characteristics»).
Methodological and Technical Expertise
- Methods of diffusion and Gaussian approximation;
- Asymptotic state space enlargement;
- Fundamental results for multivariate branching processes, multi-channel stochastic networks in heavy traffic;
- Theory of multi-channel Markov retrial queues;
- Algorithms for modeling and optimal resource management of modern telecommunication networks.
Selected Publications
Albeverio S., Korolyuk V.S., Lebedev E.A., Chechelnitsky A.A.
Functional limit theorems for multi-channel networks
Institut fur Angewandte Mathematik, Universitat Bonn. – 2005.- Preprint N 216.- 24 p.
Lebedev E.A., Semenov V.V.
A functional limit theorem for branching processes
Cybernetics and systems analysis. – 2010. – N 3. – P. 152-161.
Lebedev E.A., Ponomarev V.D.
Retrial queues with variable service rate
Cybernetics and systems analysis. – 2011. – N 3. – P. 118-126.
Lebedev E.A., Ponomarev V.D.
Finite source retrial queues with state-dependent service rate
Communications in Computer and Information Science. – Springer. – 2013. - N 356. - P. 140-146.
Lebedev E.A., Usar I.Ya.
Retrial queues with variable rate of input flow
Cybernetics and systems analysis. – 2013. - ¹ 3. – P. 151 – 159.
Lebedev E.A., Livinska H.V. and Chechelnitsky A.A.
Approximation conditions of multi-channel networks by Gaussian diffusion processes
Georgian International Journal of Science and Technology. – NOVA Publishers. – 2014. – Vol. 6. – N 3.– P. 72-84.
Lebedev E.A., Livinska H.V.
Conditions of Gaussian non-Markov approximation for multi-channel networks
Proceedings of 29-th European Conference on Modelling and Simulation.- 2015. – Albena (Varna), Bulgaria. – P. 642-649.
Lebedev E.A., Livinska H.V.
Gaussian and diffusion limits for multi-channel stochastic networks
Journal of Mathematical Sciences. - 2016. - Vol. 218. - ¹ 3. – P. 328 – 334.
Lebedev E.A., Ponomarov V.D.
Steady-state analysis of M/M/c/c-type retrial queueing systems with constant retrial rate
TOP. – 2016. – Vol.24. – N 3.– P. 693-704.
Contacts
leb@unicyb.kiev.ua
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