THE ANALYSIS AND OPTIMIZATION OF SURVIVABILITY OF MPLS NETWORKS. Mohammadreza Mossavari, Yurii Zaychenko

Transcription

1 Internatonal Journal "Informaton Theore & Applcaton" Vol5 / TE ANALYSIS AND OTIMIATION OF SURVIVABILITY OF MLS NETWORS Mohammadreza Moavar, Yur aychenko Abtract: The problem of MLS network urvvablty analy condered n th paper The urvvablty ndexe are defned whch take nto account the pecfcty of MLS network and the algorthm of t etmaton elaborated The problem of MLS network tructure optmzaton under the contrant on the urvvablty ndexe condered and the algorthm of t oluton uggeted The expermental nvetgaton were carred out and ther reult are preented Introducton Lat year due to fat ncreae n volume of the tranferred nformaton n computer network, the necety to tranfer vdeo, audo nformaton and multmeda nformaton, the need to develop new communcaton technology ha appeared that able to upport the tranmon of varou nformaton type (uch a audo, vdeo and data wth requred qualty of ervce at hgh peed Technology АТМ (Aynchronou Tranfer Mode became the frt technology provdng ntegrated tranfer of audo, vdeo nformaton and data owever, rgd retrcton on the ze of tranferred cell - of 53 byte, and alo hgh cot of equpment, n partcular ATM wtch, preclude t wde uage Therefore, n the late 99 ntead of t the MLS technology (Multprotocol Label Swtchng appeared Th technology gve the common tranport mechanm for network whch ue protocol TC/I, Frame Relay, X25, ATM It baed on ntroducton of tream of varou clae of ervce (CoS, an etablhment of prorte n ervce of varou clae and mantenance of demanded qualty of ervce (Qualty of Servce QoS for correpondng clae [] The mportant problem arng at degnng of MLS network the problem of the analy and optmzaton of urvvablty ndexe In E achenko' work the ndcator of urvvablty for АТМ network have been defned and the method of the analy of thee ndcator ha been developed At the ame tme pecfcty of MLS technology and, n partcular, preence of varou clae of ervce (Cla of ervce and ntroducton of ther prorty ervce do not allow to ue drectly method and analy algorthm of urvvablty ndcator developed for data tranmon network and АТМ network for the analy of urvvablty of MLS network Therefore, the purpoe of the preent work development and reearch of the method, analy and optmzaton algorthm for urvvablty of MLS network Statement and model of the analy of urvvablty problem Followng work [] under urvvablty of a ytem we wll undertand t ablty to keep the functonng and to provde performance of the bac functon (n the reduced volume at the pecfed qualty of ervce ndcator A the bac purpoe of a MLS network tranfer of the pecfed ze of nput flow of varou clae, urvvablty of MLS network we etmate by ze of the maxmum flow whch poble to tranfer n a network at falure of t element - channel and node under preervaton of the pecfed level of qualty of ervce There MLS network whch decrbed by orented graph G { X, E} X = x a et of node,- {(, r } = where { } E = -a et of communcaton channel (КС μ r - capacty of channel (r, Let u admt, that n a network clae of flow are tranferred ( =, 6 (CoS accordng to the matrx of requrement, k ( = h( k =, N, =, N (Mbt/ For each cla k the qualty of ervce ndcator

2 254 Internatonal Journal "Informaton Theore & Applcaton" Vol5 / 28 (QoS n the form of the pecfed value of an average delay T ср, k ntroduced whch etmated by followng expreon [2]: k ( k ( fr fr = Tср, k =, ( ( k r E k k (, ( ( μr fr μr fr = = where ( k = n n = = h ( k, μ r - capacty of a communcaton channel (r,, (k f r - a flow value of the-k-th cla n the channel (r, It requred to defne urvvablty ndcator for the gven network In work [2] for the analy of ndcator of MLS network urvvablty the followng complex ndcator ha been uggeted: { ( ( }, { (2 (2} { ( k ( k }, (2 where ( k - flow value of k -th cla n falure-free network tate (k an actual flow value of cla k n cae of falure, r = (5 % k =, Thu for an etmaton of MLS network urvvablty the vector ndcator of knd ( ued A at falure of ome channel or the node t not known n advance, what would be the value of the maxmum flow of each cla at falure, the hypothe that the general flow tructure at falure reman defned, e the approxmate party on ze of tream of varou clae at falure hould reman, namely: ( : ( : ( = ( : ( : ( (3 Algorthm of an etmaton of urvvablty ndcator of MLS network Let' conder the MLS network G = (X, E, contng of element (channel and node, ubected to envronment nfluence n reult of whch they fal It uppoed, that are et relablty charactertc of a network element- factor of readne of channel k Гr, and node - k Гr, k Г, E =, n Let u conder followng falure tate of network: falure tate channel = { } 2 3 = r : 2 falure tate node = { } 3 falure tate 2 channel : { } 4 falure tate channel and node = { t } 5 falure tate З channel: = { } 4 5 Ung model of an actve envronment, t poble to defne probablty of each tate { } For example, f the tate of channel, ( r falure then ( = ( Г, r, Г r,, (4 ( r, ( r, where Г r, a probablty of the afe tate of channel ( r,, Г r, - probablty of a channel ( r, falure In work [2] the algorthm of an etmaton of urvvablty ndcator of MLS network ha been uggeted We calculate the general ntenty of a flow n falure tate for all clae of ervce:

3 Internatonal Journal "Informaton Theore & Applcaton" Vol5 / (, (2,, 2 We mulate varou falure tate: 5 For each of them we calculate probablte accordng to (3 ( ( ( (, 2, 3, 4, ( 3 We fnd the value of the maxmum flow for all the clae n a condton : ( k, z k =, For th purpoe we ue algorthm of a fndng of the maxmum flow whch have been pecally developed n the dertaton 4 We calculate a complex urvvablty ndex for each cla of ervce: for the frt cla ( ( = (, (5 { } where ummaton n (5 performed for all for the k th cla { ( k ( k } = uch that ( ( (, (6 ( where ummaton n (6 performed for all tate :, ( k r ( k ( k ntenty of flow of k th cla n faultle tate of network (k - actual ntenty of a flow of a cla k n cae of falure, r =(5 %, k =, ( where uch: that ( r k ( r Let u contruct the receved dependence n co-ordnate { ( k} ( (, (2 (2 ( k - r { } { } { ( k } % Statement of MLS network optmzaton problem by urvvablty ndcator Durng degnng network by reult of the analy of t urvvablty ndcator a problem of mantenance of demanded urvvablty level appear It natural, that th problem can be olved by reervaton of t channel and node, tructural optmzaton of a network and need addtonal expene Therefore, further we wll conder tatement of the network tructural optmzaton problem by urvvablty ndcator [3] Let there be MLS network whch decrbed by the orented graph G = { X, E} where X = { x } a et of network node, E = {(, r} et of communcaton channel (КС μ r - capacty of a channel Let u aume, that n the network flow clae are tranferred (To =, 6 (CoS accordng to matrxe of requrement, k ( = h ( k =, N ( =, N Mbt/ For each cla k the qualty of ervce ndcator (QoS n the form of the value of an average delay k T ср, k et up Let proceedng from a network functonal purpoe the followng value of urvvablty ndcator for the k th cla flow are ( k ( k ( k etablhed k зад, зад,, 5 зад It requred to defne uch tructure of a network for whch for all clae followng retrcton on urvvablty level wll be provded: ( { ( k ( k } kзза and addtonal expene would be thu mnmum, r = (5 %, k =, (7

4 256 Internatonal Journal "Informaton Theore & Applcaton" Vol5 / 28 We hall provde achevement of demanded level of urvvablty by ntroducton of correpondng reervaton of the mot reponble element of a network (channel and node For an etmaton of effcency of channel and node reervaton the followng ndcator uggeted: Δ ( а for channel, α r = (8 Cr where - a falure tate of the channel ( r Δ ( - change of probablty of the tate after reervaton, The value Δ etmated by the followng formula: рез ( ( = ( ( отк r = ( 2 отк r Г r, ( r, отк r Г r, ( r, = ( Cr отк r Г r, ( r, отк r ( the cot of uch reervaton = (9 The mlar formula ued for an etmaton of node reervaton Let u notce, that at falure of node, all ngong and outgong channel fal multaneouly The ndcator ued for a choce of prme element (channel and node for reervaton In work the followng algorthm of MLS network optmzaton by urvvablty ndcator offered Algorthm of MLS network optmzaton by urvvablty ndcator The algorthm cont of the ame teraton, on each of whch the next element - the channel or node reerved t teraton For all channel and node we calculate an ndcatorα by formula (8 2 We chooe channel ( r *, * uch that ( r r α r maxα * * = 3 We reerve channel ( r *, * and recalculate urvvablty ndcator for all clae after reervaton by the followng formula: ( ( * { ( k } = { ( k } + Δ( r α r, ( * where Δ( a change of probablty tate after reervaton of the channel ( r *, * 4 Check up condton ( (retrcton on urvvablty: ( ( k { ( k } r, r =(5 %, k,, зад = ( If retrcton ( are fulflled for all r and all clae then the end, otherwe we go to the 2nd teraton We repeat the pecfed teraton untl the condton ( wll be held for all k and r A on each teraton the value of urvvablty ndcator rae, and ther ze lmted from top by value the algorthm converge for a fnal number of teraton Expermental reearche The analy of entvty of the receved decon to a varatont ср All experment were held for factor of readne of the channel dtrbuted normally at the nterval 9 95, and for factor of readne of the node dtrbuted normally at the nterval 95 99

5 Internatonal Journal "Informaton Theore & Applcaton" Vol5 / In the frt ere of experment entvty of urvvablty ndcator of the frt cla to a varaton of retrcton on an average delay T ср wa etmated Correpondng reult are preented n table and on fg Table T ср =, T ср =,5 T ср =,5 T ср =,7 (%,352779,389927,444,43244 (9%,352779,389927,444,43244 (8%,482439,52454,539737, (7%,483985,525,54752, (6%,484394,525,543298,56656 (5%,484394,525,545879,56656 In the gven ere of experment entvty of urvvablty to a varaton T ср for the econd cla wa etmated Correpondng reult are preented on fg 2 A well a for the cla traffc, the varaton T ср trongly enough nfluence on urvvablty ndcator, and at the further ncreae of Tср the gnfcant mprovement of urvvablty ndcator not oberved In the followng ere of experment entvty of urvvablty to a varaton for T ср for the thrd cla wa etmated Correpondng reult are preented on fg 3 Fg Fg 2 Fg 3 The analy of entvty of the receved oluton to a varaton of node and channel readne factor In the gven ere of experment wa etmated entvty of urvvablty ndcator to a varaton of relable charactertc of network element factor of readne of channel and node Experment Factor of readne of node are dtrbuted normally on an nterval [,95,99], factor of readne of channel [,9,95]

6 258 Internatonal Journal "Informaton Theore & Applcaton" Vol5 / 28 Experment 2 Factor of readne of node are dtrbuted normally on an nterval [,95,99], factor of readne of channel [,85,9] Experment 3 Factor of readne of node are dtrbuted normally on an nterval [,9,95], factor of readne of channel [,85,9] Experment 4 Factor of readne of node are dtrbuted normally on an nterval [,9,95], factor of readne of channel [,9,95] Reult for the traffc of cla are preented on table 4 Table 4 Exper Exper 2 Exper 3 Exper 4 (%,37938,2295,3787,283 (9%,37938,2295,3787,283 (8%,47672,244787,6623,32938 (7%,477463,24499,6623,32938 (6%,478882,24499,66299,33238 (5%,47982,24553,66557,33238 Concluon The problem of the analy of urvvablty ndcator of MLS network, n cae of falure of t elementchannel and node, formulated Indcator of network urvvablty are defned and the algorthm of ther etmaton conderng the pecfcty of MLS network offered 2 The problem of optmzaton of network by urvvablty ndcator formulated and the algorthm of t oluton, allowng reachng preet value of urvvablty ndcator uggeted at the mnmum addtonal expene 3 Expermental reearche of the offered analy algorthm and optmzaton of MLS network are performed Bblography Зайченко ЮП, Мохаммадреза Моссавари Анализ показателей живучести компьютерной сети с технологией MLS // Вісник національного технічного універсітету КПІ Інорматика, управління та обчислювальна техніка- 43,25,с Зайченко ЮП, Мохаммадреза Моссавари Оптимизация компьютерных сетей с технологией MLS по показателям живучести в случае активной внешней среды // Вісник національного технічного універсітету КПІ Інорматика, управління та обчислювальна техніка-45,26,с ЮП Зайченко, АС Аникиев, Мохаммедреза Моссавари, Ашра Абдель-Карим Хилал Абу-Аин Синтез структуры глобальних компьютерных сетей с технологией MLS при ограничениях на показатели качества и живучести // Электроника и связь- 26-N 2 - с 68-7 Author' Informaton Yur aychenko profeor, hd, Inttute of Appled Sytem Analy NTUU oltechnchekaya Str 4, ev, Ukrane phone: +8( , e-mal: zaych@comua, bakervl@volacablecom Mohammadreza Moavar hd Student, Dept Appled Mathematc, NTUU, rop obedy 37 phone