Infopaket

Probabilistic aspects of operations research.

Вибіркова дисципліна для ОП

First

2021/2022

8 Semester

6

PLO21.3. Understand the fundamental areas of mathematics and computer science, to the extent necessary for learning mathematical disciplines, applied disciplines and using their methods in a chosen profession. PLO22.3. Understand the main areas of mathematical logic, theory of algorithms and computational theory, programming theory, probability theory and mathematical statistics. PLO23.3. Be able to use professional knowledge, skills and abilities in the field of fundamental sections of mathematics and computer science for research of real processes of different nature. PLO24.3. Be able to independently analyze the relevant subject area, be able to develop mathematical and structural algorithmic models.

Full-time form

To successfully learn the discipline “Probabilistic aspects of operations research. M.1. Queueing theory. M.2. Elements of mathematical reliability theory” the student should satisfy the following requirements. They know (a) fundamentals of mathematical methods for construction, verification and investigation of qualitative characteristics of deterministic and stochastic mathematical models; (b) classical methods of Calculus, Algebra and Probability Theory. They can (a) investigate qualitative characteristics of available mathematical models; (b) apply classical methods for solving applied problems in deterministic and stochastic models. They should be able to (a) apply classical methods of Calculus and Probability Theory; (b) seek information in open sources and properly analyze it.

Characteristics of queueing systems. Kendall's notation of queueing systems. Performance measures. Poisson flow. Characteristic property of exponential distribution. Birth-and-death processes. The simplest Markov models of queueing systems: M/M/1/∞, M/M/n/∞, and their stationary characteristics. Priority systems. System M/G/1. The virtual waiting time. The busy period. System G/G/1. Lindley's equation. The main characteristics of reliability. Recovery processes and their application in reliability theory. Alternating processes. Statistical estimates for reliability test plans of type [N, B, R], [N, B, T]. Method of simulation modeling in reliability theory. Reliability of systems with independent elements. Scheme of death and reproduction and its application in the theory of reliability. Backup systems without recovery. Duplicate with recovery. General redundant system with recovery.

1. V. V. Anisimov, O. K. Zakusilo, V. S. Donchenko. Elementy teorii massovogo obsluzhivaniya i asimptoticheskogo analiza sistem. 1987. -248 s. 2. János Sztrik. Basic Queueing Theory. 2016. – 193 p. 3. Moshe Haviv. Queues - –A Course in Queueing Theory. Solution Manual 2015. – 89 p. 4. Cooper, R. Introduction to Queueing Theory, 3-rd Edition. CEE Press, Washington, 1990. – 361 p. 5. http://web2.uwindsor.ca/math/hlynka/qonline.html. 2016. 6. Gross, D., Shortle, J., Thompson, J., and Harris, C. Fundamentals of queueing theory, 5th edition. John Wiley & Sons, New York, 2018. – 556 p. 7. Gnedenko B.V., Belyayev YU.K., Solov'yev A.D. Matematicheskiye metody v teorii nadezhnosti. M.: Nauka, 1965. 8. Ushakov I.A. Kurs teorii nadezhnosti sistem. M.: Drofa, 2008. 9. Antonov A.V., Nikulin M.S. Statisticheskiye modeli v teorii nadezhnosti. M.: Abris, 2012. 10. Lou A.M., Kel'ton V.D. Imitatsionnoye modelirovaniye. M.: Piter, 2004

Lectures, seminars, consultations, test works, independent work.

Intermediate assesement: The maximal number of available points is 60. Test work no. 1: 30/18 points. Test work no. 2: 30/18 points. Final assessment (in the form of exam): The maximal number of available points is 40. The form of exam: writing. The types of assignments are 4 writing assignments (2 theoretical and 2 practical).

Ukrainian