ANALIYSIS OF DISCRETE CONTROL QUEUEING SYSTEMS AND SYSTEMS FOR CALCULATING BOOLEAN FUNCTIONS

ANALIYSIS OF DISCRETE CONTROL QUEUEING SYSTEMS AND SYSTEMS FOR CALCULATING BOOLEAN FUNCTIONS:

– Development of the theory of controlled random servicing processes, and of the theory for choosing and making statistical decisions;
– Analysis and optimization of probabilistic models of evolutionary experiments with control for which not all the conditions are known;
– Development of the mathematical control theory.

Main results:

- The method for representation of time-sharing queueing systems in the form of a discrete control system has been proposed. The scheme of the method has been constructed, coordinates, information and functions have been determined for servicing processes with time sharing;
- Forms of the necessary and sufficient conditions for the existence of a stationary mode of a servicing process in conflict flows control systems, which are required for optimization of such systems, have been obtained;
- The problem of optimization of control of the flows has been solved for the condition of the minimum of the cost criterion;
- Connection between the time-sharing queueing systems and cybernetic control systems in the sense of Lyapunov – Yablonsky has been revealed;
- Circuits made up of the functional elements that represent mathematical models of discrete converters of combinational type have been investigated. For such circuits implementing Boolean functions, and for a large family of possible malfunction type in these circuits (such as "AND" and "OR" short circuits, constant malfunctions, malfunctions of denying or crossing types and their combinations), time estimates have been obtained with regard to complexity of decision trees (conditional tests) both for controlling (detection) and for the diagnostics (search) of these malfunctions;
- Algorithms for construction of executable paths in the tree of decisions for controlling and diagnostics of similar types of constant malfunctions at circuit inputs have been proposed.

The obtained results have no analogues, they are universally recognized among experts in the fields of probability theory and mathematical statistics, theory of random processes, modelling of queueing systems, and discrete mathematics.

The results can be used:
– When solving current problems of analysis, synthesis and optimization of nonconventional systems for servicing conflict flows, systems for adaptive control and for making statistical decisions with incomplete data;
– When designing and producing reliable discrete converters on the basis of very large scale integration circuits (for example, programmable logic matrices) possessing effective tests for control and diagnostics.

Leading experts:

- Mikhail Andreevich Fedotkin, D.Sc. (Physics and Mathematics), Professor;
- Vladimir Ivanovich Shevchenko, Cand.Sc. (Physics and Mathematics).

Main partners:

- Institute of Applied Mathematics of the Russian Academy of Sciences,
- Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences,
- State Universities of Moscow, Kazan, Penza, Saratov.

Key projects (sources of financing):

- Projects of the Russian Foundation for Basic Research 02-01-00543 а , 06-01-03010 а.
- Projects of the Program «Universities of Russia », UR.04.01.021, UR.04.01.060, UR.04.01.181.
- The analytical departmental target program of the Federal Agency for Education «Development of the scientific potential of higher education institutions», Project 1.51.05.

Main publications:

- Fedotkin M.A., Proydakova E.V. Controlling output flows in a system with cyclic servicing and adjustments. // Automation and telecontrol. RAS, No. 6, 2008. Pp.96-106.
- Shevchenko V.I. On controlling and diagnostics of constant malfunctions and malfunctions of crossing type in circuits // Discrete analysis and operations research. 2007. V.14, No.4. Pp. 57-78.
- Proidakova E.V., Fedotkin M.A. Output flows in a priority queueing system // Collection of papers "Mass servicing: flows, systems, networks ". Minsk . BSU. 2007. Pp. 210-215.
- Fedotkin M.A., Fedotkin A.A. Output processes in cyclic control of unconventional flows // Probability theory, random processes, mathematical statistics and applications: Collection of papers of the International scientific conference. Minsk , 2008. BSU. Pp. 362-369.
- Proidakova E.V. Necessary conditions for the existence of stationary distribution of output flows in a priority direction system // Vesntik of the Nizhni Novgorod University . 2007. 1. Pp. 167-172.

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