ON THE APPROXIMATION OF THE FLOW OF EVENTS FOR A POISSON
https://doi.org/10.22405/2226-8383-2017-18-2-222-234
Abstract
When modeling an extensive class of technical systems, the mathematical apparatus of queuing systems (QMS) is widely used. An example of such a system is the computer network, where computer applications are generated and executed. Applications are generated usually not regularly, but by accident, forming the so-called random order of applications (requirements). Service requests, it also continues some random time. One of the central issues in the organization of mass-service systems is the elucidation of the regularities that subordinate the moments when system requirements for service are submitted.
The article explores the flow of events in technical systems of various purposes. On the basis of the fact that under the Poisson character of the flow mathematical modeling of the systems is greatly simplified, the problem of obtaining a simple criterion for determining the degree of approximation of the flow of events to a Poisson one is posed. Pearson’s criterion, regression, correlation and parametric criteria were investigated. A criterion based on the calculation of the waiting function was obtained again. On the example of the study of the system with "competitions"it is shown that the flow of events generated by the system tends to Poisson with an infinite increase in the number of "competing"subjects.
About the Authors
E. V. Larkin
Tula State University
Russian Federation
Russian Federation
Doctor of Technical Sciences, Professor, Head of the Department of Robotics and Automation of Production
D. V. Gorbachev
Tula State University
Russian Federation
Doctor of physical and mathematical sciences, Department of Applied Mathematics and Computer Science
Russian Federation
Doctor of physical and mathematical sciences, Department of Applied Mathematics and Computer Science
A. N. Privalov
Tula State Lev Tolstoy University
Russian Federation
Russian Federation
Doctor of Technical Sciences, Professor, Professor of the Department of Informatics and Information Technologies
References
1. Sundarapandian V. Queueing Theory: Probability, Statistics and Queueing Theory. - PHI Learning. New Delhi. 2009.
2. Gross D., Harris C.M. Fundamentals of Queue Theory. John Wiley & Sons N.Y/ 1974..
3. Larkin E.V., Ivutin A.N. Dispatching in Embedded Systems //2016 5th Mediterranean Conference on Embedded Computing (MECO). – 12-16 June 2016, Bar, Montenegro – IEEE, 2016. – Pp. 215 - 217.
4. Larkin, E., Ivutin, A., Esikov, D. Recursive Approach for Evaluation of Time Intervals between Transactions in Polling Procedure // 8-th International Conference on Computer and Automation Engineering (ICCAE 2016). – March 3-4, 2016 – Melbourne, Australia – MATEC Web of Conferences, 56 (2016) 01004
5. Larkin E.V., Ivutin A.N., Kotov V.V., Privalov A.N. Interactive generator of commands // 7-th International Conference ICSI-2016. Bali, Indonesia, June 25 - 30. Proceedings. Part 2. Lecture Notes in Computer Science. LNCS Sublibrary: SL1 – Theoretical Computer Science and General Issues Springer, 2016. Pp. 601 - 609.
6. Larkin E.V., Privalov A.N. Modeling of dialogue regimes of distance robot control // Proceedings of 5th International Workshop on Mathematical Models and their Applications Krasnoyarsk, Russia, November 7-9, 2016. - Pp/ 92 - 103.
7. Markov A.A. Extension of the law of large numbers to dependent quantities, Izvestiia Fiz.- Matem. Obsch. Kazan Univ., (2-nd Ser.), - 1906, - Pp. 135–156
8. Boos D.D. Stefanski L.A. Essentioal Statistical Inference. Theory and methods. - N.Y., Springer Verlag. 2013. - 568 (XVII) Pp.
9. Draper N.R., Smith H. Applied Regression Analysis 1998 by John Wiley & sons, Inc. - 736 Pp.
10. Rank M.K. Correlation Methods. - Published by Charles Griffin & Company, London, - 1955. - 196 Pp.
11. Ventsel E.S. Probability theory. - M.: Mir Publisher, 1986. - 86 Pp.
12. Ivutin A.N, Larkin E.V. Simulation of Concurrent Games // Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software. – Chelyabinsk, 2015. – Vol. 8, №2. – P. 43 - 54. DOI: 10.14529/mmp150204
13. Larkin E.V., Ivutin A.N., Kotov V.V., Privalov A.N. Simulation of Relay-races // Bulletin of the South Ural State University. Mathematical Modelling, Programming & Computer Software. - 2016. - Vol. 9. - No 4. - Pp. 117 - 128.
14. Glushkov V. M, Amosov N. M, Artemenko I. A. Encyclopedia of Cybernetics. Vol-ume 2. Kiev, 1974.
15. Grigelionis B. On the convergence of sums of random step processes to a Poisson process. Theory Probab. Appl. 1963. Pp. 177 - 182.
Review
For citations:
Larkin E.V., Gorbachev D.V., Privalov A.N. ON THE APPROXIMATION OF THE FLOW OF EVENTS FOR A POISSON. Chebyshevskii Sbornik. 2017;18(2):222-234. (In Russ.) https://doi.org/10.22405/2226-8383-2017-18-2-222-234
Views:
618
Email this article 