Mathematical model of optimal distribution of applied problems of safety-critical systems over the nodes of the information and telecommunication network

Article Sidebar

PDF (Українська)
DOI: https://doi.org/10.20998/2522-9052.2017.2.01
Keywords:
information and telecommunication network, applied problems, optimal distribution, cost minimization, nonlinear model, Boolean variables

Main Article Content

Viktor Kosenko
SE "Kharkіv Scientific-Research Institute of Mechanical Engineering Technology", Kharkiv
https://orcid.org/0000-0002-4905-8508

Abstract

The subject matter of the article is the processes of synthesis of the information and telecommunication network (ITN) for solving applied problems of safety-critical systems (SCS). The goal is to develop a mathematical model for the optimal distribution of applied tasks of safety-critical systems over the ITN nodes. The tasks to be solved are: to formalize the procedure of distribution of applied tasks and SCS software over the ITN nodes; to develop a mathematical model of optimal distribution in order to minimize the cost of network resources; to select an effective algorithm for solving it. The methods used are: alternative-graph approach, mathematical optimization models, methods for solving nonlinear integer programming problems with Boolean variables. The following results were obtained: the task of selecting the ITN optimal structure was formulated according to the alternative-graph model of information processing; in addition to structural characteristics, the requirements for the parameters necessary for performing applied tasks were taken into account while constructing a mathematical model; when minimizing the cost of a computing resource, constraints related to the capabilities for financing the development and operation of the network are taken into account; the costs for organizing additional connections among the network nodes are considered as well. As a result, a mathematical model of distributing SCS applied problems over the ITN environment was obtained in order to minimize the total costs of computing resource, data transmission, network setting and maintenance. This model is a non-linear integer programming problem with Boolean variables. Taking into account the specific nature of the objective function and model constraints with the use of pseudo-Boolean functions, the original task is reduced to a linear form. The obtained model represents the canonical form of the linear optimizing problem of large-dimensional Boolean programming, for which the method of the recession vector is effective. Conclusions. The scientific novelty of the results obtained is as follows: 1) the optimization model of distributing applied tasks over the nodes of the computer network was improved by defining the objective function in order to minimize the costs of both computational and data transmission and the constraints caused by the requirements for the technical and information structure of the network; 2) methods for solving the problems of optimizing the ITN structure on the basis of models of nonlinear Boolean programming by transforming the initial task into a linear form and applying the recession vector method was further developed, which makes obtaining a quasi-optimal solution of the problem in the context of large dimension possible.

Article Details

How to Cite
Kosenko, V. (2017). Mathematical model of optimal distribution of applied problems of safety-critical systems over the nodes of the information and telecommunication network. Advanced Information Systems, 1(2), 4–9. https://doi.org/10.20998/2522-9052.2017.2.01
Issue
Vol. 1 No. 2 (2017): Advanced Information Systems
Section
Information systems modeling
Author Biography

Viktor Kosenko, SE "Kharkіv Scientific-Research Institute of Mechanical Engineering Technology", Kharkiv

Candidate of Technical Sciences, Associate Professor, Head of Institute

References

Ageev, D.V., Ignatenko, A.A. and Kopylev, A.N. (2011), "Metodika opredeleniya parametrov potokov na raznykh uchastkakh mul'tiservisnoy telekommunikatsionnoy seti s uchetom effekta samopodobiya" ["Method for determining the parameters of flows in different sections of a multiservice telecommunications network, taking into account the self-similarity effect"], Problemy telekommunikatsiy, [Telecommunications problems], No. 3 (5), pp. 18-37, available at: http://pt.journal.kh.ua/2011/3/1/113_ageyev_method.pdf (last accessed May 24, 2017).

Losev, Yu. I. and Rukkas, K. M. (2007), "Sravnitel'nyy analiz matematicheskogo apparata modelirovaniya telekommunikatsionnykh setey ["Comparative analysis of mathematical apparatus of modeling of telecommunication networks"], Systemy obrobky informatsiyi [Information Processing Systems], No. 8 (66), pp. 55-60.

Gelenbe, E. and Pujolle, G. (2010), Analysis and synthesis of computer systems (2nd Edition), Advances in Computer Science and Engineering, 309 p.

RFC 1122 – Requirements for Internet Hosts - Communication Layers, available at: http://rfc2.ru/1122.rfc (last accessed May 24, 2017).

Marder, N.S. (2006), Sovremennye telekommunikatsii [Modern telecommunications], Moscow, IRIAS, 255 p.

Kuchuk, G.A., Gakhov, R.P. and Pashnev, A.A. (2006), Upravlenie resursami infokommunikatsiy [Information and telecommunication resources management], Moscow, Fizmatlit, 220 p.

Pepelnjak, I. (2000), EIGRP Network Design Solutions: The Definitive Resource for EIGRP Design, Deployment, and Operation, CiscoPress, 384 p.

Paulsen, S. and Boens, J. (2012), Summary of the Workshop on information and communication technologies supply chain risk management, National Institute of Standarts and Technology, 21 p.

Kuchuk, G.A. and Pashnev, A.A. (2007), "Klassifikatsiya zadach upravleniya mul'tiservisnymi setyami raspredelennykh informatsionno-upravlyayushchikh system kriticheskogo primeneniya" ["Classification of control tasks for multi-service networks of distributed information-control systems for critical applications"], Problemy upravlinnyay edynoyu derzhavnoyu systemoyu tsyvil'noho zakhystu: zb. mat. NPK, 4.04.2007, Kharkiv, MNSU, UTsZU, pp. 104-106.

Olifer, V.G. and Olifer, N.A. (2012), Komp'yuternye seti. Printsipy, tekhnologii, protokoly [Computer networks. Principles, technologies, protocols], SPb. : Piter, 943 p.

Kosenko, V.V. and Kuchuk, N.H. (2016), "Modelyuvannya tekhnichnoy i struktury informatsiyno-telekomunikatsiynoyi merezhi na osnovi konkretnoyi realizatsiy iinformatsiynoyi struktury" ["Modeling the structure of technical information and telecommunications network based on the specific implementation of information structure"], Systemy obrobky informatsiyi [Information Processing Systems], Kharkiv, No. 9(146), pp. 167-171.

Kosenko, V.V. and Kuchuk, N.H. (2016), "Vzayemodiya tekhnichnykh I prohramnykh zasobiv pry upravlinni rozpodilom trafika" ["The interaction of hardware and software in the management of traffic distribution"], Systemy ozbroyennya I viys'kova tekhnika [“Systems of Arms and Military Equipment”], No. 3 (47), pp. 72-75.

Sobol', I.M. (2006), Vybor optimal'nykh parametrov v zadachakh so mnogimi kriteriyami [The choice of optimal parameters in problems with many criteria], Moscow, Drofa, 175 p.

Ovezgel'dyev, A.O., Petrov, E.G. and Petrov, K.E. (2002), Sintez i identifikatsiya modeley mnogofaktornogo otsenivaniya i optimizatsii [Synthesis and identification of models of multifactorial estimation and optimization], Kyiv, Naukova dumka, 163 p.