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1 20, 05, 207 Vol. 20, No. 05, 207 vl Avaton Hgh Technologes, DO: / ,.. 2,.. 3,.. 4,.,, 2,.,, ,.,, 4,., - -,,, -.,. -,, -.., -, : ; -,. -., -., - ( ).. :,, -,. () -,,,.,, -,., ().,, []. [2, 3]:, - 6

2 20, 05, 207 vl Avaton Hgh Technologes Vol. 20, No. 05, 207, ; - ;, ; -, -., -, - [4, 5]: K y = K, = - - ( =, 2,, ) K K K =, K ; -o -. -, (),. (, ) - [6, 7]. [3]: (RAD-); ;.,,, - [8 ]: () ; -,, -., -, -, [4].,, G [0], X = {x, x 2,, x n } (- ), A = {a, a 2,, a m } ()., ( ). (), (,..).,,. 62

3 20, 05, 207 Vol. 20, No. 05, 207 vl Avaton Hgh Technologes, -. - [0]. x v (- ), - [9]: ( x ) = v d( x x ) σ,, 0 σ x X ( x ) = v d( x x ),, t x X, x X, () d(x,x ) x x, σ ( x ) ( x ) x X 0 σ x. x 0, σ0( x0) = mn σ0( x ), G, t x, σ ( x ) σ ( x ) = mn,. t t x t X X X G, : t ( ) ( ) = d X, x mn d x, x, x X ( ) ( ) = d x, X mn d x, x, x X (2) (3) * x X, (2) (3),, x ( X ) σ ( ) 0 t X * x. () σ σ 0 t ( X ) = v d( X, x ), x X ( ) ( ) X = v d x, X, x X σ. 0 0 X, σ 0 ( X ) mn σ 0 ( X ) X X [ ], = - G; -.,. y, n n z = mn d y (4) = = 63

4 20, 05, 207 vl Avaton Hgh Technologes Vol. 20, No. 05, 207 n y =, =, 2,..., n, (5) = n y =, (6) = y y, =, 2,..., n, (7) { } y = 0,, =, 2,..., n, =, 2,..., n, (8) y =, x x, y = 0, y =, x, y = 0. * y (4) (8), - { * } X = x y =. (4) (8). [7, 9, 0].,. - Z, Z., [9, ]. z ( =, 2, ), : : = : : K 64 ( z ) max, C( z) C, (9) = B T ( z) T, (0) = V( z) V, () =

5 20, 05, 207 Vol. 20, No. 05, 207 vl Avaton Hgh Technologes z = 0,, 2,..., Z. (2) C ; ; V,. (9) (2), [7, 0]. (9) (2) - : : : x ln K max. (3) = : Cx C, (4) = B T x T, (5) = : : { } Vx V, (6) = x = 0,, x, =, 2,..., Z, L k= 65 (7) x, x = - 0 ;, L -. (3) (7) -, [7, 2 4]. -, ( ) [8 0,5],. k

6 20, 05, 207 vl Avaton Hgh Technologes Vol. 20, No. 05, 207 q [ 0,],. Z Φ (, ) q. q = 0, - Z Φ, ( 0) q =.. Z = Z ( q), q [0,] -., q Z Φ - Z ( q ) αq = Ce, (8) α ln C α =, ε, ε,.. Z. (8) c Z = Z ( q), q [0,]. c c 2 b( q) Z ( q) = C e, (9) c 2, - q =, ln C 2 b = ε. q [ 0,] Z Z. Φ Z ( q) mn, Z ( q) mn. c 0< q< 0< q<, q Z Φ, Z C, (8) (9), - ( Z, Z ). C mn (20) 0< q< C 66

7 20, 05, 207 Vol. 20, No. 05, 207 vl Avaton Hgh Technologes - (20) (8) (9): Lq (, λ) = λz ( q) + ( λ) Z( q) mn, (2) c 0< q< λ (0,). L L( q, λ ) = 0. (2), (8) (9) q,, αq b( q) λ C2be λα e + ( ) = 0. Cb 2 ( λ) ln + b λcα q( λ) =, λ (0,). α + b q *, q * q( λ)., λ mn λ max. λ mn b( q ) Cbe 2 b( q ) q 2 + α = Cbe C e α λ * * * b =. Cb C e α 2 max 2 + α., - λ [λ mn,λ max ], , :..:, c :, Wndows..:, : /..,....:,. -,

8 20, 05, 207 vl Avaton Hgh Technologes Vol. 20, No. 05, A.A.,.. :..: -, // - «,», -. :. -, ,..,.. - /.....: XX, c. 8. Yeskov D.O. ncrease of level of stablty of functonng of systems of storage and data rocessng at the exense of realzaton of actons for ensurng safety of nformaton. Thrd nternatonal Conference "Hgh Performance Comutng" HPC-UA 203, Ukrane, Kyv, October 7, , - /..,..,..,..,.. // // (2).. vutn A., Yeskov D. Comlex of Mathematcal Models to Ensurng Sustanablty of the Dstrbuted nformaton Systems. 4rd Medterranean Conference on Embedded Comutng (MECO) June Budva, Montenegro, 205, DO: 0.09/MECO (Scous Web of Scence) 2. Yeskov D.O., vutn A.N., Larkn E.V., Kotov V.V. (207). Mult-agent Aroach for Dstrbuted nformaton Systems Relablty Predcton. Proceda Comuter Scence, 207, Vol Yeskov D.O., vutn A.N. Ratonal values of arameters of sland genetc algorthms for the effectve soluton of roblems of ensurng stablty of functonng of the dstrbuted nformaton systems. 2 6 June 206, 206 5th Medterranean Conference on Embedded Comutng (MECO) 206, DO: 0.09/MECO (SCOPUS, Web of Scence) 4...., - : /....: -..., ,.. -. :, ,, mcgeen4@gmal.com.,,, -, raknshn@yandex.ru.,,, - «"... -», a-03@yandex.ru.,,, loutn@yandex.ru. 68

9 20, 05, 207 Vol. 20, No. 05, 207 vl Avaton Hgh Technologes MATHEMATCAL MODELS OF CREATON OF A SUBSYSTEM OF ENSURNG SAFETY OF NFORMATON N THE DSTRBUTED NFORMATON SYSTEMS Dmtry O. Eskov, Ruslan N. Aknshn 2, Pavel. Abramov 3, Lly E. Loutna 4 Tula State Unversty, Tula, Russa 2 SPP RN, Moscow, Russa 3 Jont Stock Comany "Scentfc research nsttute "Polyus them M.F. Stelmakh", Moscow, Russa 4 Moscow State Unversty of Cvl Avaton, Moscow, Russa ABSTRACT Practcal mlementaton of the concet of a dstrbuted nformaton system requres the mlementaton of a comlex scentfc-techncal roblems related to the choce of comoston and use of storage and rocessng of nformaton, creaton and use of common data arrays, nformaton securty, etc. Fundamentally, a modern dstrbuted nformaton system s a system of communcaton and nformaton transmsson as well as a storage and data rocessng system. Storage and data rocessng system s desgned for organzaton of relable and fault-tolerant data storage, hgh-erformance servers to access storage devces and nformaton rocessng. The measure of qualty, and n some cases ndcator of functonng of data storage and rocessng system s roosed. The tasks that need to be tackled when constructng and oeratng the storage and rocessng requrements of hghly relable data storage, as well as ther followng confguratons: determnaton of the number and locaton of centers of data storage and rocessng n dstrbuted nformaton systems; choce of the comoston of the comlex used for storage n the storage centers and data rocessng, wth the organzaton of a backu subsystem, the backu and restore data. The task of storage structure otmzaton accordng to the crteron of maxmum values of the readness factor of the storage system s formed. Ths roblem s reduced to the knd of roblems of nteger lnear rogrammng wth Boolean varables, ths fact allows to aly the exstng methods for ts solvaton. A method for determnng the ratonal level of exendture on the formaton of the comlex used for storage n the storage and data rocessng system based on the use of elements of robablty theory and the theory of well-beng (the rncle of Pareto otmalty) s develoed. The otmal soluton of the roblem by otmzng a lnear convoluton s obtaned. Key words: mathematcal models, dstrbuted nformaton systems, nformaton securty, data storage and rocessng system. REFERENCES. Broydo V.L. Vychsltel'nye sstemy, set telekommunkats [Comutng systems, networks and telecommuncatons]. Textbook for unverstes. SPb., Peter, 2006, 703. (n Russan) 2. Kreev V.V. Vychsltel'nye sstemy [Comutng systems]. M., Gelos ARV, 2004, 52. (n Russan) 3. Nke D. Sstemy khranenya dannykh v Wndows [Storage n Wndows]. M., Wllams, 2005, 49. (n Russan) 4. Nkolaev V.., Brooke V.M. Sstemotekhnka: metody rlozhenya [Systems Engneerng: methods and alcatons]. L., Engneerng, 985, 99. (n Russan) 5. Voronn A.A., Morozov.B. Nadezhnost' nformatsonnykh sstem [Relablty of nformaton systems]. Textbook. SPb., SPbSTU, 200. (n Russan) 6. Eskov D.O. Obesechene ustoychvogo funktsonrovanya vychsltel'nykh sstem za schet obesechenya vysokonadezhogo khranenya dannykh [Towards sustanable comutng systems by rovdng vscondessa storage]. Paers of the ffteenth nternatonal scentfc-ractcal conference "Fundamental and aled research, develoment and alcaton of hgh technologes n ndustry", Sant-Petersburg. Sb., Publshng house Polytechnc. the unt, 203. (n Russan) 7. Kselev D.V., Eskov O.V., Ksltsyn A.S. Teoretcheske osnovy otmzats nformatsonno-vychsltel'nogo rotsessa sostava komleksov sredstv zashchty nformats v vychsltel'nykh setyakh [Theoretcal bases of otmzaton of comutng rocess and structure of comlexes of rotec- 69

10 20, 05, 207 vl Avaton Hgh Technologes Vol. 20, No. 05, 207 ton of nformaton n comuter networks]. Ed. by E. Sukhareva. M., Polgrafservs twenty-frst century, 2003, 98. (n Russan) 8. Yeskov D.O. ncrease of level of stablty of functonng of systems of storage and data rocessng at the exense of realzaton of actons for ensurng safety of nformaton. Thrd nternatonal Conference "Hgh Performance Comutng" HPC-UA 203 (Ukrane, Kyv, October 7, 203).Kyv. 203, Eskov O.V., Savateev S.S., Eskov D.O., Strukov A.V., Sukharev E.M. Matematcheske model, metodk algortmy obesechenya ustoychvost funktsonrovanya sovremennykh sstem khranenya obrabotk dannykh [Mathematcal models, methods and algorthms of mantenance of stable functonng of modern systems of storng and rocessng data]. Nonlnear world, 203, No. 9, (n Russan) 0. Eskov D.O. Zadach obesechenya ustoychvost funktsonrovanya rasredelennykh nformatsonnykh sstem [The roblem of ensurng stablty of functonng of dstrbuted nformaton systems]. Journal Software and systems, 205, No. 4 (2). (n Russan). vutn A., Yeskov D. Comlex of Mathematcal Models to Ensurng Sustanablty of the Dstrbuted nformaton Systems. 4rd Medterranean Conference on Embedded Comutng (MECO) 205 June , Budva. Montenegro, 205, DO: 0.09/MECO (Scous Web of Scence) 2. Yeskov D.O., vutn A.N., Larkn E.V., Kotov V.V. Mult-agent Aroach for Dstrbuted nformaton Systems Relablty Predcton. Proceda Comuter Scence, 207, Vol Yeskov D.O., vutn A.N. Ratonal values of arameters of sland genetc algorthms for the effectve soluton of roblems of ensurng stablty of functonng of the dstrbuted nformaton systems. 2 6 June 206, 5th Medterranean Conference on Embedded Comutng (MECO). 206, DO: 0.09/MECO (SCOPUS, Web of Scence) 4. Karenko A.P. Sovremennye algortmy oskovoy otmzats. Algortmy, vdokhnovlennye rrodoy [Modern algorthms of search engne otmzaton. Algorthms nsred by nature]. Textbook. M., Publshng house of MGTU m. N.E. Bauman, 204, 446. (n Russan) 5. Tutubaln P.., Moseev V.S. Veroyatnostnye model obesechenya nformatsonnoy bezoasnost avtomatzrovannykh sstem obrabotk nformats uravlenya [Probablstc models of nformaton securty n automated systems nformaton rocessng and management]. Kazan, School, 2008, 38. (n Russan) NFORMATON ABOUT THE AUTHORS Dmtry O. Eskov, Postgraduate student of the Tula State Unversty, mcgeen4@gmal.com. Ruslan N. Aknshn, Doctor of Techncal Scences, Assocate Professor, Leadng Researcher of Secton of Aled Problems under the Presdum of the Russan Academy of Scences, raknshn@yandex.ru. Pavel. Abramov, canddate of techncal Scences, assocate Professor, Deuty Drector General for nnovaton and cvl roducts of JSC "research nsttute "Polyus them.m.f.stelmakh", a-03@yandex.ru. Lly E. Loutna, Canddate of Techncal Scences, Assstant Professor of Organzaton of busness rocesses n avaton ndustry Char, Moscow State Techncal Unversty of Cvl Avaton loutn@yandex.ru Receved Acceted for ublcaton

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