An algorithm of choosing LSPs in the MPLS network with unreliable links

Transcription

1 Ireneusz OLSZESKI Unversty of Technology an Lfe Scences n Bygoszcz, Faculty of Telecommuncatons an Electrcal Engneerng An algorthm of choosng LSPs n the MPLS network wth unrelable lnks Streszczene. pracy zaproponowano algorytm wyboru śceżek LSPs w secach IP/MPLS o zawone strukturze. Lczba utraconych paketów na uszkozone śceżce LSP zależy o czasu otwarzana uszkozone śceżk na śceżce zabezpeczaące. Aby ogranczyć czas otwarzana, oległość pomęzy węzłam est ogranczona poprzez ogranczene ługośc śceżk aktywne. Rozważany problem obemue ogranczene nałożone na ługość śceżk, merzone lczbą łączy oraz ogranczene prawopoobeństwa uszkozena śceżk. Algorytm rozwązuący sformułowany problem optymalzac przy zaanych ogranczenach wyznacza rozwązane lokalne (Algorytm wyboru śceżek LSP w secach MPLS przy zawone strukturze sec). Abstract. In ths paper an algorthm for choosng LSPs n the MPLS network wth unrelable lnks s propose. The number of lost packets on the fale LSP epens on the restoraton tme of ths LSP on the global backup path. In turn, the restoraton tme epens on the stance between the noe whch etecte falure an the noe responsble for traffc rerecton from fale to global backup LSP. To reuce restoraton tme the stance between these noes s ecrease by length lmtaton of actve LSP. The formulate problem covers lmtaton of the path length etermne by the number of lnks an lmtaton of LSP falure probablty. The algorthm solvng the formulate problem of optmzaton gves a local soluton for gven lmtatons. Słowa kluczowe: Routng, eloprotokłowa Komutaca Etyketowana, struktura sec, Śceżka komutowana etyketowo. Keywors: Routng, Mult Protocol Label Swtchng (MPLS), network structure, Label Swtchng Path (LSP). Introucton A network can be esgne only for assume ntal contons but the loa an traffc characterstcs vary n tme. The network resources also vary because of the network topology changes (noes or lnks falures). An mportant element of the qualty of servce (QoS) s the network relablty. Although most of the problems consere n ths paper concern the network of fferent technologes usng logcal paths concepton, so the further conseratons wll be focuse on IP network wth Mult Protocol Label Swtchng (MPLS). Fault management mechansms n MPLS networks are base on settng up the backup Label Swtchng Path (LSP) [1]. In case of a falure the traffc can be rerecte to the backup path. The backup paths can be statc or ynamc [2]. In the frst case a backup LSP s pre-establshe for each actve LSP. In the secon case a backup LSP s establshe as a result of falure n the network. Many algorthms of choosng LSPs n MPLS networks have been propose so far [3,4,5,6,7,8,9]. All these algorthms mnmze the number of reecte requests or the amount of consume banwth n a network. For ths purpose the nterference of ncomng request of LSP set up wth requests of LSPs set up whch wll come n the future s mnmze [4, 8, 9] or nterference of LSPs alreay set up n a network wth comng request of LSP set up s mnmze [3, 6, 8]. The algorthms of LSPs choce presente n [3,4,5,6,7,8,9] are base solely on the state of lnks occupancy an the number of flows carre by them. Most of these algorthms, however, o not take nto account other aspects, such as lnk falure probablty n the network, packet loss an recovery tme of banwth on the backup path. The mpact of these parameters on the number of lnks requrng local backup on LSP, number of paths for whch falure probablty excees pre-set threshol an number of reecte requests of settng up paths has been shown n [1]. The analyss has been one on the base of k-sp algorthm whch works on k-element set of possble paths between each par of noes. It shoul be notce that fxe k-element set of possble paths for each request of settng up connecton can not be able assure that obtane result wll be near to the optmal soluton. However, for the on-lne routng algorthms (base on ths set) the generaton of a k-element set of possble paths for each request on unrelable topologcal structure s tmeconsumng. Therefore, there s a nee of research on new routng algorthms takng nto account resual banwth on each lnks an other aspects such as lnk falure probablty, packets loss an recovery tme of banwth. In the paper, the algorthm of choosng LSPs n IP/MPLS network whch consers lnk falure probablty an banwth recovery tme has been propose. The paper s organze as follows. In the secon part, the problem of optmzaton has been formulate. In the thr part the heurstcs algorthm solvng ths problem an algorthm whch etermnes the optmal soluton has been propose. In the fourth part of the paper the smulaton results have been gven. In the fnal part the summary an conclusons has been rawn. Formulaton of optmzaton problem Before formulaton of the optmzaton problem n ths paper, the lmtatons occurrng n ths problem an the obectve functon wll be scusse. The frst consere lmtaton s lmtaton of LSP length an the secon the lmtaton of LSP falure probablty. Packets Loss (PL) epens on restoraton tme (RT) an amount of allocate banwth b (n Bts/s) on falure LSP. (1) PL RT b LP where LP s the lost packets n the falure lnk. Tme of restoraton s efne as the tme between falure etecton n the network (noe or lnk) an traffc rerecton (stream of packets) from actve to backup LSP [1]. Ths tme conssts of followng four elements: Detecton Tme (DT), the tme of notfcaton (NT) the noe responsble for swtchover from actve LSP to backup LSP by noe whch etecte the falure; Tme for Backup LSP Setup (TB) an tme of swtchng over packets stream from actve path to the backup path (ST). So: (2) RT=DT+NT+TB+ST It shoul be notce, that f the backup LSP s preestablshe then TB can be omtte. The most mportant element of restoraton tme s notfcaton tme because t s the most responsble for packets loss [2]. Ths tme can be etermne as follows: PRZEGLĄD ELEKTROTECHNICZNY (Electrcal Revew), ISSN , R. 87 NR 2/

2 (3) NT=D(,a)PT where: D(,a) s the stance etermne by the number of lnks from a noe whch etecte falure to noe responsble for swtchover from an actve path to a backup path. PT s propagaton tme of the Fault Incaton Sgnal (FIS) through each lnk. PT conssts of the noe Processng Delay, Buffer Processng Delay an Lnk Delay. In [1] t was shown that n the global backup path protecton RT s rectly proportonal to stance D(,a). For each actve LSP protecte by global backup path D(,a) can be change from to L(LSP).e. L(LSP)> D(,a),where: L(LSP) s the length of falure LSP. For D(,a)= ngress noe of LSP s responsble both for falure etecton an swtchover on the backup path. From (1) t results that to mnmze Packets Loss, the RT nees to be shortene. In turn, the RT epens on NT (see (2)), whereas NT s proportonal to D(,a). Therefore, by lmtng the range of changng of D(,a) by restrcton L(LSP), the PL after falure can be mnmze. The secon parameter whch shoul be taken nto conseraton by the routng algorthm s the probablty of LSP falure, whch s etermne on the bass of probablty of lnks falure n the network. These probabltes can be etermne on the bass of an analyss of fferent statstcs or the network operator experence [1]. As the probabltes of each lnks falure n the network are known, so the probablty of LSP falure can be etermne as the probablty of a complement event. Probablty that LSP s n orer can be etermne as follows: (4) P( LSP s n orer) elsp (1 p ) 1 L( LSP) 1 ( 1) 1 3 e e,..., e LSP 2 3 p p,..., p 2 where: p s the probablty of falure of lnk e. The probablty that LSP s fale can be wrtten as follows: (5) P ( LSP s out of orer) 1 (1 p ) elsp p elsp for aequate small p. Routng algorthm wll choose such LSP for whch probablty of falure s not greater than threshol of p, assume for all LSPs n the network. Lower lmt of probablty of LSP falure causes the lmtaton of number of lnks requrng protecton on LSP. Ths elmnates the fference between possble protecton methos (Local Backup, Global Backup) from the pont of vew of the consume banwth. In general, for the case of a great number of lnks requrng protecton, the global protecton metho s better than the local protecton metho. However, wth a ecreasng number of lnks requrng protecton, the local backup metho becomes more compettve to the metho of global protecton [2]. Both, the lmtaton of path length D(LSP) an lmtaton of value of probablty LSP falure, become constrants of formulate optmzaton problem. After efnng constrants for the optmzaton, the obectve functon stll nees to be efne. In MIRA the LSP between par of noes (s,) wth banwth of b unts s calculate by usng Dkstra algorthm wth the weghts of arcs etermne as follows [4]: (6) w( l) ac ( a, c) P\( s, ) lc ac where C ac - s the set of crtcal arcs for the ngress-egress par (a,c). An arc s crtcal for gven ngress-egress par (a,c) f t belongs to any mn-cut for that ngress-egress par. P-s a set of stngushe noe pars (a,c), whereas α ac s nversely proportonal to θ ac.e. α ac =1/θ ac, were θ ac s the max-flow value between ngress-egress par (a,c). From (6) t results that the weght of lnk w(l) s the sum of reverses of max-flows for these pars of noes (a,c)p\(s,) for whch lc ac. In Constrant Shortest Path Frst algorthm (CSPF) [3], [7], an LSP between par of noes (s,) s calculate by usng Dkstra algorthm n reuce network on the base weghts of arcs n the followng way: (7) 1 w( l) R( l) where: R(l) s the resual banwth of lnk l. The reuce network s forme through elmnaton of all lnks from the graph, for whch the resual banwth s less than b unts of the requre banwth LSP path. eghts of lnks calculate n ths way allow to mnmze the number of reecte request of settng LSPs because CSPF takes nto account the least loae lnks urng choosng LSP. Moreover, another avantage of CSPF, for so etermne weghts, s balancng of the network loa. CSPF avos most loae lnks. A rawback of CSPF s greater consume banwth [7] ue to longer selecte paths n comparson wth MIRA. Takng nto account that amssble lengths of LSPs whch was lmte n the formulate problem of optmzaton, t was assume that the weght of each lnk wll be nversely proportonal to resual capactes of these lnks. Let G( N, E, C) be the network, where N s the set of noes (routers) an E s the set of unrectonal lnks (arcs). C s m vector of banwth of the lnks. Let n enote the number of the noes an m the number of lnks n the network. Let R be an m-vector of resual capacty. Entry n R vector correspons to the resual capacty of arc. Moreover, let current request of settng LSP between par of noes (s,) requres b unts capacty. To smplfy the notaton, we wll often refer to a lnk by (,) nstea l. Formulate problem of optmzaton can be shown as follows: (8) (9) (1) Mn 1 x R (,, x x,, ) xs, x, s (11) 1,, x x (12) p p (, ) E (13) (, ) E R, x x x, 1,, L( LSP), (14) b (, ) E (15) (,1), x The vector x represents the flow on the path between par of noes (s,), where x, s set to 1 f lnk (,) s use n the path. Formula (8) efnes the optmze obectve functon wth weghts, whch are nversely proportonal to 286 PRZEGLĄD ELEKTROTECHNICZNY (Electrcal Revew), ISSN , R. 87 NR 2/211

3 resual capactes of the lnks n the network. Equatons (9) to (11) gve the flow balance for a path. Inequalty (12) s a constrant of probablty of LSP falure, whereas, nequalty (13) s a constrant of LSP length. Equaton (14) states that b unts of banwth have to be sent between noes s an. In general, LSP path selecton problem, whch mnmzes the number of reecte requests of LSP set up s NP-har problem [4]. However, the consere problem, n whch the weghts of lnks are efne, s the nteger lnear programmng problem. Because the algorthm solvng ths problem must work on-lne, a heurstc approach can be consere only. An heurstcs algorthm sub-optmal soluton For a gven vector of weghts whose components w(l), l=1,2,...,m are nversely proportonal to resual capactes w(l)=1/r(l), R(l) b, the shortest path s etermne by Dkstra s algorthm. If probablty of path falure s less or equal to p an length of path (number of lnks) s less or equal to L(LSP) then the obtane result s the optmal soluton. Otherwse, f the obtane path oes not satsfy the assume lmtaton then the sub-optmal soluton s calculate as below. Let s assume that relablty lmtaton s not satsfe (probablty of falure of obtane LSP s grater than p ). In ths case all lnks (,) belongng to LSP are analyse. For each lnk (,)LSP, for whch probablty of lnk falure s equal to p, the cost of bypassng ths lnk s calculate as follows: (16) ( mn w k) ( kn k,, s, k The lnk (,) wth the least cost, (k), for whch p k +p k <p, s replace wth a par of lnks: (,k) an (k,). It means mofcaton of prmary LSP: (s-,,---,,-) to LSP: (s-,,-k--,,-). Ths mofcaton allows to ncrease relablty of the path uner mnmum-ncrease of total weght of path (obectve functon) prove that length of path s not greater than L(LSP). If so obtane path satsfes constrants (12) an (13) then t s accepte as a sub-optmal soluton. Otherwse, f constrant (12) s not satsfe an constrant (13) s satsfe, then next analogous teraton for ths new path s realze. hen the length of path (measure number of lnks) s greater than L(LSP) then the request s reecte. The shown algorthm s lmte enough. To ncrease relablty of LSP any noe k for whch p k +p k <p must exst at least for one lnk (,)LSP. The generalzaton of ths algorthm, whch elmnates ths lmtaton, wll be shown below. (k) w k () s () Fg. 1. The bypassng path for lnk (,) an the path between par of noes (s,) Let be the shortest path tree roote at s etermne by Dkstra s algorthm for weght of arcs w(l)=1/r(l), R(l) b. Let () be the weght of the shortest path from noe s to noe. Moreover, let L() enote the length of path from noe s to noe (etermne by number of lnks) on the bass of obtane tree. Let P() enote the probablty of falure of k w k w () ) () the path between noe s an noe, etermne on the same tree. If etermne LSP between the par of noes s an wth weght () satsfes relablty lmtaton (P() p ) an path length lmtaton (L() L(LSP)) then ths LSP s an optmal soluton. Otherwse, for each lnk (,) of LSP the bypassng path s etermne. Fgure 1. shows a bypassng path (enote as contnuous lne) for lnk (,) of LSP (s---) an the path between par of noes (s,) (enote as ashe lne), whch contans ths bypassng path. The estmaton of weght of path () from noe s to noe, takng nto conseraton bypassng cost for lnk (,), can be wrtten as follows: (17) ( ) mn ( k k N, s, ( k) w k ( ( ) ( )) Smlarly, the probablty of path falure P () an length path L (), takng nto account the bypassng cost lnk (,), for the same path can be wrtten as follows: (18) P ()=P(k)+p k +P() -P() (19) L ()=L(k)+1+L() -P() Snce the man goal s mnmzaton of summarze weght of path, lnk (,) assurng the least value of estmaton of path () s remove (w := ). In the case when for several lnks (,)LSP estmatons of costs () are equal, then the estmaton of path falure probablty P () s consere an the lnk (,) wth the least P () s reecte. Fnally, n the case when for two or more lnks estmatons of costs () are equal an estmatons of falure probablty P () are equal then the lnk (,) assurng the least length of path L () s remove. After removng so etermne lnk, the next shortest path of tree roote at noe s wth weght of arc w on lnk (,) s etermne. If etermne LSP between the par of noe s an wth weght () satsfes constrants (12) (13) (P() p, L() L(LSP)) then t s a suboptmal soluton. Otherwse, analogous teraton for ths new path s realze Below, an algorthm solvng the formulate problem of optmzaton s shown. Ths algorthm s enote as CSPF_U(p ; L(LSP)), (Constrant Shortest Path Frst wth Unrelable lnks). Algorthm CSPF_U(p ; L(LSP)); 1: begn {begn CSPF_U()} 2: for (,)E o 3: f b R then w :=1/R else w := ; 4: conton:=true; 5: whle conton o 6: begn 7: :=GetSPTree(s); { Shortest Path Tree rote at s} 8: LSP:=GetPath(, ); {Get path to from s n } 9: ol ():= ; L ol ():= ; 1: P ol ():=P(); 11: f (P() p ) an (L() L(LSP)) then 12: begn 13: conton:=false; {LSP satsfes (12) an (13)} 14: UpateMatrx(R); 15: en 16: else for (,)LSP o 17: begn 18: f ()< ol () then 19: begn 2: (u,v):=(,) 21: ol ():= (); 22: en; PRZEGLĄD ELEKTROTECHNICZNY (Electrcal Revew), ISSN , R. 87 NR 2/

4 23: f ( ()= ol ()) an (P ()< P ol ()) then 24: begn 25: (u,v):=(,); 26: P ol ():= P (); 27: en; 28: f ( ()= ol ()) an (P ()= P ol ()) an (L ()< L ol ()) then 29: begn 3: (u,v):=(,); 31: L ol ():= L (); 32: en; 33: en; 34: f ol ()< then {Next teraton} 35: w uv := ; 36: else conton:=false; {Request s reecte} 37: en; 38: en; { begn CSPF_U()} The contons from lne 18 an lne 23 can be substtute by conton f ( () ol ()) an (P ()<P ol ()) then. However, the request wll be remove f there s not lnk (,), (,)LSP for whch the bypassng path causes growth of LSP relablty. Therefore, n ths case lnk (,), (,)LSP, whch wll assure possbly the least growth of the obectve functon for the path n the next teraton (lne 18), s remove from the LSP. The last conton (lne 28) causes choosng the path wth the shortest length. Complexty of the computng functon of CSPF_U() for sngle teraton s O(n 2 ); The tme of choosng the shortest LSP whch satsfes constrants (12) (13) epens on the number of teraton. An exact algorthm optmal soluton An algorthm etermnng the optmal soluton, enote as LM(p ; L(LSP)) for a gven request between the par of noes s an generates all possble paths wth length less or equal to L(LSP) for reuce network wth weght w(l)=1/r(l). The shortest LSP whch satsfes relablty constrant (12) s chosen by LM() from all generate paths. To generate all possble paths wth length constrant (13) Latn Multplcaton [11] was apple. Because of the number of paths between a gven par of noes s very huge (grows exponentally), therefore, LM() gvng the optmal soluton can serve to verfy other algorthms only. Obtane results A stuy of the consere algorthms has been performe for the mesh structure network wth fferent number of noes (an lnks). In ths paper the obtane results for network wth 15 noes an 56 unrectonal lnks are shown. The topology structure of the examne network s shown n fgure 2 [4]. Each ege n fgure 2 represents a par of arcs of opposte recton. The banwth of 38 lnks s 12 unts (thn lne) an other 18 lnks s 48 unts (thck lne). The values of lnk falure probablty p for each lnk (,) are shown on arcs of the graph. In ths paper t was assume, smlarly as n [4] an [1], that there exsts a set of pars of noes, for whch probablty of LSP path reecton s smaller than probablty of LSP path reecton for remanng pars of noes. Therefore, even n the general case, when every noe can be an ngress-egress router, a certan subset of noe pars wll be more essental then the remanng noe pars n the network. The stngushe par of noes S -D are: 1-13, 5-9, 4-2 an A request of choosng LSPs between par of ngress-egress routers arrve ranomly an each request s unformly strbute between 1 an 4 unts. It was assume that 5 requests arrve between the stngushe par of noes. Each par s chosen ranomly. In ths paper, t s assume that p =,8 an L(LSP)=6,7,8 epens on experment. Fg. 2. Topology structure of the consere network Each experment for all consere algorthms was performe for the same stream of request. It shoul be notce that the length of shortest paths between the stngushe par of noes are: Length(1-13)=3, Length(5-9)=4, Length(4-2)=2, Length(5-15)=4. Fgure 3. shows epenence of the network banwth consumpton on the number of requests of LSP set up. The fgure shows that the consume banwth for MIRA s less than the consume banwth for other algorthms (CSPF, CSPF_U(.8,8) an LM(.8,8)). It results from the fact that for MIRA, weghts of lnks whch belong to the set of crtcal lnks, are calculate on bass of (6), whereas, the weghts of other lnks for whch R b assume small postve values. It assures mnmzaton of the path length etermne by the number of hops an mnmzaton of the consume banwth. hereas, n the case of all other algorthm weghts of arcs (,), for whch R b are etermne as w =1/R. So etermne weghts cause a slght ncrease of length of paths an an ncrease of the consume banwth n the network. Network Banwth Consume 5,E+4 4,5E+4 4,E+4 3,5E+4 3,E+4 2,5E+4 2,E+4 1,5E+4 1,E+4 5,E+3,E Request Number MIRA - CSPF - CSPF_U(,8; 8) - LM(,8; 8) Fg. 3. Network banwth consume vs. request number Fgure 4 shows the number of reecte requests n the epenence on the number of ncomng requests for all consere algorthms. It can be notce that MIRA, CSPF an algorthm LM(), base on Latn Multplcaton, reects almost the same number of requests. CSPF_U() reects a slghtly greater number of requests for p =8 1-4 an L(LSP)=8. Fgure 5 shows the number of lnks n the epenence on loa of lnk (n %). For CSPF an LM(), base on weghts of lnk etermne by (7), the number of 288 PRZEGLĄD ELEKTROTECHNICZNY (Electrcal Revew), ISSN , R. 87 NR 2/211

5 loae lnks from 8% to1% s smaller than for MIRA. For CSPF_U(), whch chooses paths satsfyng lmtatons (L(LSP)=8 an p =8 1-4 ) the number of loae lnks from 8% to1% s the same as for MIRA. Fgure 6. shows the consume banwth n the network obtane after usng the consere algorthms for 1 fferent experments. The stream of requests for each experment s the same for all the consere algorthms. It results from the fact that the consume banwth n the network for MIRA s comparable wth the consume banwth for LM(,8, 8). The consume banwth for two other algorthms (CSPF an CSPF_U(,8, 8) s comparable, too (except 4th experment), however, greater than the optmal soluton. Number of Reecte Requests Fg. 4. Number of reecte requests vs. request number Number of Lnks Fg. 5. Number of Lnks vs. loa of lnk Request number - MIRA - CSPF - CSPF_U(,8; 8) - LM(,8; 8) %-2% 2%-4% 4%-6% 6%-8% 8%-1% Loa of Lnk - MIRA - CSPF - CSPF_U(,8; 8) - LM(,8; 8) Exactly, the consume banwth for CSPF_U() s from.9 % to 1.4 % greater (except 4th experment) than the consume banwth for LM(). Fgure 7. shows the number of reecte requests by the consere algorthms for the same 1 experments. It shoul be notce, that MIRA reects more requests than CSPF. An CSPF_U(), whch satsfes relable lmtaton an length of path lmtaton reects from 1.9% to 12.9% requests (for 5th experment) greater than LM(). Fgure 8. shows the runnng tme of algorthms for the same 1 experments. It shoul be notce, that the tme of choosng paths s crtcal for each on-lne routng algorthm. The obtane results prove that CSPF s much faster than MIRA. The complexty functon for CSPF s O(n 2 ), whereas for MIRA s On m 4 [4]. CSPF_U(), whch satsfes constrants (12) (13) s also much faster then MIRA. The obtane results prove that the weghs of lnk n the propose optmzaton algorthm (CSPF_U()), whch takes nto account relable lmtaton an the length of path lmtaton are efne properly. It shoul be note that n the propose algorthm other weghts are also consere, such as those use n the ILIOA [8]. Network Banwth Consume Experment Number - MIRA - CSPF - CSPF_U(,8; 8) - LM(,8; 8) Fg. 6. Network banwth consume for 1 experments Number of Reecte Request Experment Number - MIRA - CSPF - CSPF_U(,8; 8) - LM(,8; 8) Fg. 7. Number of reecte requests for 1 experments Tme [s] Experment Number - MIRA - CSPF - CSPF_U(,8; 8) Fg. 8. The runnng tme of algorthms for 1 experments. However, both, the number of reecte requests an the volume of the occupe banwth, was greater than n the case of lnk weghts consere for the same value lmtatons. The shown results were obtane (by CSPF_U()) for p =8 1-4 an L(LSP)=8. Fgure 9 shows the number of reecte requests for CSPF_U() an LM() for fferent lengths of paths: L(LSP)=6,7,8. It can be notce that for L(LSP)=7,8 the number of requests reecte by CSPF_U() s comparable to the number of requests reecte by LM(). However for L(LSP)=6 CSPF_U() reects from 63% to 127% more request than LM(). Such a great number of reecte requests results from the fact that CSPF_U() n next teratons, blocks the lnks (,), whch for a mnmal ncrease of the path weght assure an ncrease n the path relablty. Therefore, wth large lmtaton of the path length comparable to the shortest length of the path between a PRZEGLĄD ELEKTROTECHNICZNY (Electrcal Revew), ISSN , R. 87 NR 2/

6 gven par of noes (see Fg. 2.), CSPF_U() o not choose LSP, whch satsfes constrants (12) (13). Fgure 1. shows the consume banwth for CSPF_U() an LM() for the same constrant length of paths L(LSP)=6,7,8. Together wth the ncrease n the number of requests reecte by CSPF_U() the amount of banwth consume by LSPs ecreases. Number of Reecte Requests Experment Number - CSPF_U(,8; 8) - LM(,8; 8) - CSPF_U(,8; 7) - LM(,8; 7) - CSPF_U(,8; 6) - LM(,8; 6) Fg. 9. Number of reecte requests for 1 experments Network Banwth Consume Experment Number - CSPF_U(,8; 8) - LM(,8; 8) - CSPF_U(,8; 7) - LM(,8; 7) - CSPF_U(,8; 6) - LM(,8; 6) Fg. 1. Network banwth consume for 1 experments Summary an Conclusons In ths paper an algorthm of choosng LSPs n the IP/MPLS network wth unrelable network structure was propose. Ths algorthm has been compare to algorthm gvng optmal soluton. The consere problem concerns relablty of paths lmtaton an length of paths lmtaton. The constrane length of path causes a ecrease of lost packets n the network through shortenng tme of restorng of falure path on the backup path. In turn, the relablty lmtaton ecreases the probablty of falure of chosen paths. The accepte weghts of lnks n the obectve functon are nversely proportonal to resual banwth of lnks n the network. CSPF_U() solvng the formulate problem of optmzaton for gven lmtatons etermnes a sub-optmal soluton. To verfy ths algorthm, an algorthm base on Latn Multplcaton was apple. The obtane results prove that the propose CSPF_U() balances the loa of lnks as well as MIRA. For ths algorthm the number of reecte requests s slghtly greater an chosen paths consume a slght greater banwth than for the exact algorthm. However, paths etermne by the propose algorthm satsfy the assume lmtatons. CSPF_U() works well at reasonable values of lmtatons. For path length lmtaton comparable to the length of the shortest path, ths algorthm reects much more requests. Therefore, further works shoul etermne the maxmum length of paths n a epenence on the graph ameter an the number of the network lnks. REFERENCES [1] Autenreth A., Krstäter A., Engneerng En-to-En IP Reslence Usng Reslence-Dfferentate QoS, IEEE Communcatons Magazne, January (22). [2] Calle E., Marzo Jose L., Urra A.: Protecton Performance Components n MPLS Networks, Computer Communcatons Journal, 27 (24), 12, [3] Bagula A.B., Botha M., Krzesńsk A. E.: Onlne Traffc Engneerng: The Least Interference Optmzaton Algorthm, Communcatons, 24 IEEE Internatonal Conference on, 2 (24), [4] Koalam M., Lakshman T.V.: Mnmum Interference Routng wth Applcatons to MPLS Traffc Engneerng, Proc. IEEE INFOCOM 2, Mar. (2), [5] Kott A., Hamza R., Boulemen K., Benwth Constrane Routng Algorthm for MPLS Traffc Engneerng. Thr Internatonal Conference on Networng an Servces, ICNS, (27). [6] Krachonok P., Constrant Base Routng wth Maxmze Resual Banwth an Lnk Capacty-Mnmze Total Flows Routng Algorthm for MPLS Networks. Ffth Internatonal Conference on Informaton, Communcatons an Sgnal Processng, (25), [7] Olszewsk I., The Algorthms of Choce of the LSP path n the MPLS networks, Kwartalnk Elektronk Telekomunkac, 5 (24), n.1, [8] Olszewsk I., The Improve Least Interference Routng Algorthm. Paper accepte for the 2 n Internatonal Conference on Image Processng & Communcatons, (21), Bygoszcz, Polan. [9] Zhu M., Ye., Feng S., A new ynamc routng algorthm base on mnmum nterference n MPLS Networks. 4th Internatonal Conference on reless Communcatons, Networkng an Moble Computng. COM '8, (28). [1] Calle E., Marzo Jose L., A. Urra A., Vlla P.: Enhancng MPLS QoS routng algorthms by usng Network Protecton Degree paragm, Proceengs of IEEE Global Communcatons Conference, GLOBELCOM (23), San Francsco. [11]Kaufmann A.: Graphs, Dynamc Programmng an Fnte Games, Acaemc Press, (1967), Author: r nż. Ireneusz Olszewsk, UnwersytetTechnologczno- Przyronczy, yzał Telekomunkac Elektrotechnk, Al. Prof. S. Kalskego 7, Bygoszcz, E-mal: [email protected] 29 PRZEGLĄD ELEKTROTECHNICZNY (Electrcal Revew), ISSN , R. 87 NR 2/211