ESTIMATION OF REALIZABILITY OF SOLVING TASKS ON COMPUTER SYSTEMS IN GROUP MAINTENANCE
Abstract
The increase in the performance of computer systems (CS) is associated with both scalability and the development of the architecture of the computing elements of the system. Cluster CS, which are scalable, make up 93% of the Top500 supercomputers and are high-performance. At the same time, there is still the problem of efficient and complete use of all available computer resources of the supercomputer and CS for solving user tasks. Failures of elementary machines (nodes, computing modules) reduce the technical and economic efficiency of CS and the efficiency of solving user tasks. Therefore, when planning the process of solving problems, reducing the loss of time to restore CS from failures is an important problem. To quantify the potential capabilities of computer systems, indices of the realizability of solving tasks are used. These indices characterize the quality of the systems, taking into account reliability, time characteristics and service parameters of incoming tasks. The paper proposes a mathematical model of the functioning of a computer system with a buffer memory for group maintenance of a task flow. The mathematical model uses queuing theory methods based on probability theory and systems of differential equations. It should be noted that the method of composing systems of differential equations is simpleenough if the corresponding graph scheme is presented. However, the exact solution of systems of equations and, as a rule, in elementary functions, does not exist, or formulas are difficult to see. Here the solution is obtained in the stationary mode of operation of the queuing system. The indices allowing to estimate the fullness of the buffer memory are calculated. The obtained analytical solutions are simple, can be used for express analysis of the functioning of computer systems.
References
Acta Numerica, 2012, pp. 1-96.
2. khoroshevskiy V.G. Arkhitektura vychislitel'nykh system [Architecture of computing systems].
Moscow: MGTU im. Baumana, 2008, 520 p.
3. TOP500 Supercomputers Official Site. TOP500 Lists 2021. Available at: http://www.top500.org.
4. Gupta S., Patel T., Engelmann C. and Tiwari D. Failures in large scale systems: long-term
measurement, analysis, and implications SC '17: Proc. of the International Conference for
High Performance Computing, Networking, Storage and Analysis (Denver, Colorado), 2017,
Vol. 44.
5. Schroeder В. and Gibson Garth. A 2006 large-scale study of failures in high-performance
computing systems, Proceedings of the International Conference on Dependable Systems and
Networks (DSN2006) (Philadelphia, PA, USA), pp. 10.
6. Korobkin V., Melnik E., Klimenko A. Fault-tolerant architecture for the hazardous object information
control systems, Application of information and communication technologies -
AICT2015 (IEEE catalog number CFPI556H-PRT): conference proceedings (Rostov-on-Don,
Russia 14-16 October 2015). Rostov-on-Don: SFedU, 2015, pp. 274-276.
7. Khoroshevskiy V.G. Modeli analiza i organizatsii funktsionirovaniya bol'shemasshtabnykh
raspredelennykh vychislitel'nykh sistem [Models of analysis and organization of functioning of
large-scale distributed computing systems], Elektronnoe modelirovanie [Electronic modeling].
Kiev, 2003, Vol. 25, No. 6.
8. Xie M., Dai Y.S. and Poh K.L. Computing system reliability: models and analysis. New York:
Kluwer academic publishers, 2004.
9. Blischke W.R. and Murthy D.N.P. Reliability. New York: Wiley, 2000
10. Hoyland A., Rausand M. System reliability theory. New York: Wiley, 1994.
11. Kuo W., Zuo M.J. Optimal reliability modeling: principles and applications. New York: Wiley,
2003.
12. Mor Harchol-Balter. Performance Modeling and Design of Computer Systems: Queueing
Theory in Action. Cambridge University Press, 2013.
13. Chechel'nitskiy A.A., Kucherenko O.V. Statsionarnye kharakteristiki parallel'no
funktsioniruyushchikh sistem obsluzhivaniya s dvumernym vkhodnym potokom [Stationary
characteristics of parallel functioning service systems with a two-dimensional input stream],
Sb. nauchnykh statey [Collection of scientific articles]. Minsk, 2009. Issue 2, pp. 262-268.
14. Pavsky V.A., Pavsky K.V. Stochastic models and calculations of distributed computer systems
reserve size, Proc. of 2019 International Multi-Conference on Industrial Engineering and
Modern Technologies (FarEastCon), Vladivostok, Russia, 2019, pp. 1-5.
15. Nazarov A.A., Terpugov A.F. Teoriya massovogo obsluzhivaniya [Queuing theory]. Tomsk:
Izd-vo NTL, 2010, 228 p.
16. Saati T.L. Elementy teorii massovogo obsluzhivaniya i ee prilozheniya [Elements of the theory
of queuing and its applications]. 3 ed. Moscow: Knizhnyy dom «LIBROKOM», 2010, 520 p.
17. Kleynrok L. Teoriya massovogo obsluzhivaniya [Theory of queuing]. Moscow:
Mashinostroenie, 1979, 432 p.
18. Borovkov A.A. Veroyatnostnye protsessy v teorii massovogo obsluzhivaniya [Probabilistic
processes in the theory of queuing]. Moscow: Nauka, 1972, 368 p.
19. Venttsel' E.S. Teoriya sluchaynykh protsessov i ee inzhenernye prilozheniya [Theory of random
processes and its engineering applications]. Moscow: Nauka, 1991, 384 p.
20. Feller V. Vvedenie v teoriyu veroyatnostey i ee prilozheniya [Introduction to probability theory
and its applications]: In 2 vol. Vol. 1. Moscow: LIBROKOM, 2010, 528 p.
