Authors V.V. Lisyak, N.K. Lisyak, D.F. Malukolov
Month, Year 06, 2016 @en
Index UDC 658.512.2.011.5
Abstract There is considered a task of system level of design, which allows studying the system, where the clients request for services at random moments, and require different service time, and can line up in queue. Considered models provide the probability distribution of queue length, moments of requests’ receiving, and times of waiting for service. These parameters are important in the systems, where losses caused by overloading can be compensated with better organization problem of stochastic net structure models analysis. Stochastic nets present sufficiently general cases of resources interaction with different classes of service. Variety of CAD resources and complexity of their interaction cause the of requests, different service procedures, etc. However those models are difficult to use for description of processes, which apply to several system resources simultaneously. Estimation of system parameters during systems development is performed by means of simulation and analytical modeling. Simulation provides quite precise system modeling, but requires significant time costs. Analytical modeling provides approximate estimates, but requires essentially less time. This work is dedicated to analytical approach, where system is considered as a queuing model. The most valuable characteristic in such an approach is estimation of system performance and performance of its modules. Therefore system is represented as a queuing model, described by means of Markov process. Instrument of such process analysis is Kolmogorov equations solution, which allows getting output parameters of system performance. Distinction of the proposed work is development of software tools, simplifying modeling process for an engineer due to automation of transition from investigated process flowgraph to Kolmogorov equations system.

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Keywords CAD analysis; Kolmogorov equations; Markov process; simulation modeling; analytical model; system performance; queuing system; requirements flux density; relative system channel capacity
References 1. Lisyak V.V., Lisyak N.K. Vvedenie v razrabotku SAPR elektronnoy apparatury [Introduction to the design CAD electronic equipment]. Taganrog: Izd-vo TTI YuFU, 2010, 78 p.
2. Lisyak V.V., Lisyak N.K. Metodiki razrabotki i osnovy modelirovaniya SAPR [Techniques for the design and CAD modeling framework]. Taganrog: Izd-vo TTI YuFU, 2011, 94 p.
3. Lisyak V.V., Lisyak N.K. Modelling of CAD productivity, Proceedings of the International Scientific Conferences «Intelligent Systems» (АТS’08) and «Intelligent CAD» (CAD – 2008). Moscow: Physmathlit, 2008, Vol. 4, pp. 16-24.
4. Lisyak V.V. Lisyak N.K. O zadache analiza proizvoditel'nosti SAPR [On the problem of the anal-ysis of CAD productivity], Izvestiya TRTU [Izvestiya TSURE], 2007, No. 1 (73), pp. 118-124.
5. Kuzovlev V.I., Shkatov P.N. Matematicheskie metody analiza proizvoditel'nosti i nadezhnosti SAPR [Mathematical methods for the analysis of the performance and reliability of the CAD]. Moscow: Vysshaya shkola, 1990, 143 p.
6. Lisyak V.V., Lisyak N.K. Analiz mnogoresursnykh modeley SAPR [Analysis of multiresource CAD models], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2009, No. 12 (101), pp. 86-92.
7. Venttsel' E.S., Ovcharov L.A. Teoriya veroyatnostey i ee inzhenernye prilozheniya [Theory of Probability and its engineering applications]. Moscow: Nauka. Gl. red. Fiz.-mat. lit., 1988, 480 p.
8. Sigorskiy V.P. Matematicheskiy apparat inzhenera [Mathematical Engineer apparatus]. Kiev: Tekhnika, 1975, 765 p.
9. Kleynrok L. Vychislitel'nye seti s ocheredyami [Computer networks with queues]. Moscow, 1979, 221 p.
10. Zhozhikashvili V.A., Vishnevskiy V.M. Seti massovogo obsluzhivaniya. Teoriya i primenenie k setyam EVM [Queueing Networks. The theory and application to computer networks. Moscow, 1988, 193 p.
11. Kureychik V.M., Kureychik V.V., Gladkov L.A. Geneticheskie algoritmy [Genetic algorithms]. Rostov-on-Don: RostIzdat, 2004, 400 p.
12. Malyukh V.N. Vvedenie v sovremennye SAPR [Introduction to modern CAD]. Moscow: DMK Press, 2010, 192 p.
13. Sovetov B.Ya., Yakovlev S.A. Modelirovanie system [Modeling systems]. Moscow: Vysshaya shkola, 2005, 343 p.
14. Kel'bert M.Ya., Sukhov Yu.M. Markovskie tsepi kak otpravnaya tochka teorii sluchaynykh protsessov i ikh prilozheniya [Markov chain as the starting point of the theory of random processes and their applications]. Moscow: MTsNMO, 2009, 295 p.
15. Takha Khemdi A. Vvedenie v issledovanie operatsiy [Introduction to Operations Research]. 7th ed.: translation from English. Moscow: Izd. dom «Vil'yams», 2005, 912 p.
16. Sheldon M. Ross. Introduction to Probability Models, Tenth Edition. Academic Press, 2009.
17. Hillier F. Introduction to Operations Research. McGraw-Hill Science. 9th edition, 2009.
18. Olive Ibe. Markov Processes for Stochastic Modeling. Academic Press 2008. Chapter 5.
19. Shelukhin O.I., Tenyakshev A.M., Osin A.V. Modelirovanie informatsionnykh sistem: Uchebnoe posobie [Modeling of information systems: tutorial]. Moscow: Radiotekhnika, 2005, 368 p.
20. Dvoretskiy S.I., Muromtsev Yu.L., Pogonin V.A. Modelirovanie sistem: uchebnik dlya vuzov [Modeling systems: A Textbook for high schools]. Moscow: Izd. tsentr «Akademiya», 2009, 320 p.
21. [Electronic resource]. Available at: Queuing system (accessed 20 April 2013).
22. [Electronic resource]. Available at: Queuing theory (accessed 25 April 2013).
23. [Electronic resource]. Available at: Markov Processes (accessed 25 April 2013).
24. [Electronic resource]. Available at: Markov Chain (accessed 22 April 2013).

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