HIERARCHICAL METHOD OF INTER-AREA FAST REROUTING

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1 Transort and Telecommuncaton Vol. 8 no. 7 Transort and Telecommuncaton 7 volume 8 no Transort and Telecommuncaton Insttute Lomonosova Rga LV-9 Latva DOI.55/tt-7-5 HIRARCHICAL MTHOD OF INTR-ARA FAST RROUTING Olesandr Lemesho Olesandra Yeremeno Olena Nevzorova 3 Kharv Natonal Unversty of Rado lectroncs Deartment of Infocommuncaton ngneerng Kharv Urane 4 Naua Ave. Ph./fa: mal: olesandr.lemesho@nure.ua; olesandra.yeremeno.ua@eee.org; 3 olena.nevzorova@nure.ua In ths aer n order to ncrease the scalablty and fault-tolerance of routng solutons the herarchcal method of nterarea fast reroutng n communcaton networs was resented. The method s based on the decomosed reresentaton of the flowbased routng model wth the ntroducton of the area nteracton condtons to ensure connectvty of the nter-area routes. The model ncludes condtons for border routers rotecton adated for both sngle ath and multath routng. Durng the research t was establshed that the effcency of the roosed method n terms of the seed of the coordnatng rocedure convergence was most nfluenced by the number of border routers and the mlemented routng strategy. Keywords: nter-area routng herarchy fault-tolerance fast reroutng. Introducton A dstnctve feature of any comle system to the class of whch the modern communcaton networs also belong s the herarchy of ts structural and functonal constructon. It s the herarchcal nature of the networ archtecture under the condtons of constant growth n the number and nature of connectons of ts elements swtches routers servers etc. that mamzes the scalablty of rotocol solutons related to the reducton of the amount of servce nformaton crculatng n the networ reducton of the szes of routng tables stored n routers ncreasng effcency of traffc management n networ. It s mortant to note that most modern Qualty of Servce QoS assurance tools have already been adated to the rncles of mult-level traffc management. Ths above all refers to the Herarchcal Queung Framewor Herarchcal Polcng and Herarchcal Shang Csco Networng Academy 4. However the routng rotocols are most senstve to scalablty roblems snce ther man tas s to determne calculate the aths along whch end-to-end QoS requrements would be met whch requres the coordnated oeraton of not one but a number of networ devces. Prncles of herarchcal routng are actvely used n IP Internet Protocol ATM Asynchronous Transfer Mode and MPLS Multrotocol Label Swtchng networs. Ths was esecally evdent n the functonalty of such rotocols as GP order Gateway Protocol OSPF Oen Shortest Path Frst IS-IS Intermedate System to Intermedate System and PNNI Prvate Networ-to-Networ Interface Csco Networng Academy 4; Le Rou et al. 5; Wrght 3. A dstnctve feature of these rotocols s the dvson of the networ nto subnets of dfferent herarchy levels. The uer level s defned by the bacbone through whch low-level subnets echange acets called areas zones or clusters. In IP networs a three-level herarchy can also be suorted when two-level routng s mlemented at the level of an autonomous system. Ths routng s organzed for eamle usng the OSPF rotocol. etween autonomous systems the routng s controlled for eamle by the GP order Gateway Protocol whch determnes the addtonal uer level of the soluton herarchy. At the same tme the boundary between subnets can ass both through routers as n the OSPF rotocol and through the lns accordng to the IS-IS rotocol. An eamle of the structural herarchy s also the dvson of routers nto classes: ntra-area nter-area border and bacbone routers. However under dfferent rotocol solutons the names of routers may dffer as shown n Table Tso and Teare ; Wóc et al. 6. Table. Routers classfcaton n dfferent rotocols Protocol Intra-area routers order routers acbone routers OSPF Internal Routers IRs Area order Router ARs acbone Routers Rs IS-IS Routers Level L Routers Level /Level L/L Routers Level L PNNI Logcal Nodes LNs order Nodes Ns Peer Grou Leaders PGLs 55 Unauthentcated Download Date 7/3/8 5:3 PM

2 Transort and Telecommuncaton Vol. 8 no. 7 Furthermore the ntroduced structural herarchy of routng tas solutons n modern networs s not always suorted by the functonal herarchy. The Dstra and ellman-ford algorthms whch are the bass of most modern routng rotocols do not drectly tae nto account the eculartes of the herarchcal networ constructon. In some cases ths s not a roblem. Ths for eamle s tycal for the scenaro where each area a subnet of the lower level s swtched to the bacbone through one border router whch s the most common soluton n modern networs Tso and Teare. In ths case both the source router and the destnaton router are clearly nown when solvng routng tass n both the areas and the bacbone. Therefore there s no dffculty n coordnatng the fnal solutons of the routng roblems obtaned searately n the areas and the bacbone. It s mortant to note that usng a sngle border router for area and bacbone connecton sgnfcantly reduces the relablty of the networ Ra 5; Yeremeno et al. 6. In the case when the border router s not able to rovde ts functonalty the areas connected through t become bloced wth resect to the bacbone and what s very mortant to other networ areas. And the reasons for ths stuaton can be: falure of the router caused by a breadown; congeston of the border router; comromse of the border router n terms of networ securty. Thus n order to ncrease the relablty of networ solutons n ractce several border routers are used more often to ln searate areas and the bacbone. In case of a falure n one of them the traffc can be transmtted through the worng routers. However n the course of solvng the roblems of routng nter-area flows there s a number of mortant features whch should be taen nto account. The frst feature s related to the fact that when solvng nter-area routng tass t s necessary to foresee the mlementaton of rotecton schemes for border routers wth ther falures due to the reasons gven above. Thus along wth a set of rmary routes t s necessary to calculate a set of bacu aths whch are byassed wth resect to the rotected router. The second feature s that there s ambguty n the order of usng border routers whch s determned on the one hand n the bacbone and on the other hand n the networ areas. When mlementng multath routng ths can be accomaned by a volaton of connectvty of nter-area routes on the bacbone area boundary and under multath routng ambguty can also be manfested n uncoordnated traffc balancng on the border routers. Therefore the tas of ncreasng the coordnaton of routng solutons obtaned n the ndvdual areas and the bacbone s relevant. Ths can be acheved by revson mathematcal models and methods gven n the arorate rotocols of herarchcal routng. To ensure a hgh level of theoretcal ustfcaton for roosed solutons t s necessary to use the roostons rncles and ostulates of the theory of multlevel herarchcal systems roosed by Mesarovc et al. and develoed by Sngh and Ttl 978. Ths aroach has already been aled n solvng herarchcal traffc management roblems by Lemesho et al. 4 6a.. Model of Herarchcal Inter-Area Fast Reroutng Suose that the structure of herarchcal communcaton networ Fg. s resented by the orented grah G M where M s the set of vertces modellng networ routers and s the set of grah ars modellng networs lns. Let K be the set of flows beng crculated n a networ and ~ K K s the cardnalty of set K quanttatvely characterzng the total number of flows n a networ. For every th flow K assumed to be nown ts acet rate whch s measured n acets er second /s. Durng the develong the decomosed model of nter-area routng let us suose that the communcaton networ conssts of n subnetwors or areas nterconnected by rncle of constructng IP networs. Then let every searate р th area n the networ s descrbed by subgrah G M of grah G where M M ; m s the set of р th area routers m s the total number of routers n the area; ; m s the set of lns connectng routers of the р th area n. The number s assgned to the bacbone area resented by the subgrah G M. All other n areas are echangng acets through the bacbone area. 56 Unauthentcated Download Date 7/3/8 5:3 PM

3 Transort and Telecommuncaton Vol. 8 no. 7 Fgure. amle of herarchcal networ Assume that n networ decomoston the boundary between areas asses through the routers le n OSPF rotocol Csco Networng Academy 4. Then based on the ntroduced structural networ model the followng condtons occur M M M M q q q n n; q n q; q. Imlementaton of the condtons system determnes that only the bacbone area may have the common routers wth other areas. Other non-bacbone areas do not have any common routers between themselves. In addton every searate networ ln belongs to only one area. In order to ncrease the fault-tolerance of networ the number of border routers between areas has to be equal to two or more. If one of the routers fals all flows wll be redrected to other border routers. Also for every р th area let us determne the set of border routers M through whch the flows are ncomng or outgong. The whole set of the р th area border routers may be slt nto two subsets where s the subset of border routers through whch the th flow s ncomng to the n р th area; out s the subset of border routers through whch the th flow s outgong from the р th area. For every ln n the р th area ts assocated bandwdth s measured n acets er second out /s. Let us denote M M \ as a set of routers whch are adacent for the router M. Suose that for the networ structure shown n Fg. the source of the th flow s one of the routers of the st area and the destnaton s the router of the nd area. At the same tme the th area s the bacbone. Then the ntroduced sets of transt routers tae the followng form: out ; n M M ; out M 7 M 8 ; M M n. Net we wll wrte down the set of routers adacent for the router M M M. The same router M 4 4 s desgnated as M M 4. routers s the followng: of the st area: M n the th area n whch the set of adacent 57 Unauthentcated Download Date 7/3/8 5:3 PM

4 Transort and Telecommuncaton Vol. 8 no Solvng the roblem of herarchcal routng for every р th area t s necessary to calculate routng varables characterzng the fracton of the th flow rate n the ln. For every router n the р th area t s necessary to fulfl the condton of every th flow conservaton n order to rovde connectvty of calculated nter-area routes n the networ Lemesho et al. 6a. If the р th area s the bacbone area for the th flow these condtons tae the followng form:. ; ; out n The system of equatons must be erformed for every acet flow searately and the frst equaton n the system s ntroduced for all bacbone area routers that the th flow ncomes through to the bacbone area; second equaton n system s ntroduced for all bacbone area routers whch are the transt for the th flow n bacbone area; thrd equaton n system s ntroduced for all bacbone area routers the th flow outgong through from the bacbone area; If the th flow was generated n the р th area and ts source s for eamle the router M for ths networ condton of every th flow conservaton taes the followng form:. ; ; out 3 When the router M n the р th area s the destnaton of the th flow for ths networ the condton of every th flow conservaton taes a followng form:. ; ; n 4 For the case of usng sngle ath routng of flows the net condtons tae lace: 5 and for mlementaton of multath routng strategy the routng varables must satsfy the condtons:. 6 Unauthentcated Download Date 7/3/8 5:3 PM

5 Transort and Telecommuncaton Vol. 8 no. 7 N Routng varables 5 6 are the coordnates of corresondng routng vectors: ~ K 3 m m 7 where s the vector of routng varables determnng the order of flows routng n the networ as a whole; the vector determnes order of flows crculated n the th area; the vector determnes the roblem soluton of the th flow routng n the th area. In dstrbuted decentralzed calculaton of the vectors and wthn each searate th area t s mortant to rovde nter-area connectvty of routes.e. of routes assng through a set of routers n dfferent areas. Smlar to the results obtaned n aer Lemesho et al. 6a ths mles the ntroducton n structure of the model -7 addtonal condtons of nter-area nteracton: С n K 8 С where С m m ; m bacbone areas; s the matr of nterconnecton between the th area and the bacbone wth sze M M m s the number of routers whch are boundary between the th and s the number of coordnates of the vector 3. Condtons of Protectng order Routers under Herarchcal Inter-Area Fast Reroutng When solvng the roblem of nter-area fast reroutng along wth the calculaton of the rmary routes t s necessary to calculate a number of bacu aths. Therefore as shown n Lemesho et al. 6b addtonal routng varables y are ntroduced. y analogy wth eressons 7 the varables y can also be reresented as the coordnates of the corresondng vectors y y and y and condtons of nter-area nteracton 8 must be met for the bacu routes. In ths aer we offer rotecton schemes for a border router by rotectng a set of lns ncdent to the rotected node. Let one of the routers of the th area be the source of the th flow. Then when mlementng sngle ath routng n rotectng a border router M out the followng condtons should hold: y ; where out M M under M M \ 9 when rotectng the ln ; otherwse.. In case of multath routng the followng condtons should be fulflled: y M M under out M M \ where the selecton of values obeys the condton. 59 Unauthentcated Download Date 7/3/8 5:3 PM

6 Transort and Telecommuncaton Vol. 8 no. 7 In notatons of the th area bacbone for the router beng rotected M z n condtons are wrtten as follows: y z ; z z M \ z n the same M M under M. When mlementng the strategy of multath routng we have the condtons: z y z z M M under M M \ z n. 3 If one of the routers of the th area s the destnaton of the th flow then when mlementng the sngle ath routng strategy durng the rotecton of the border router M condtons must be met: y ; n n the followng M M under M M \ 4 where when rotectng the ln ; 5 otherwse. In case of multath routng we have the followng condtons: y M M under n M M \ 6 where the selecton of values obeys the condton 5. In notatons of the th area bacbone for the router beng rotected M z out these condtons are wrtten as follows: y z ; z z M \ z out M M under M. 7 When mlementng the strategy of multath routng we have the condtons: z y z z M \ z out M M under M. 8 If t s necessary to erform reservaton of networ bandwdth and also to revent ossble congeston n the mlementaton of both sngle ath and multath routng strateges the followng condtons are ntroduced nto the model smlar to the results obtaned n Lemesho et al. 6b: K y y 4. Herarchcal Method of Inter-Area Fast Reroutng. 9 Gven the mathematcal model -7 roosed above the bass of the roosed method of herarchcal routng s the solvng of otmzaton roblem durng calculaton of routng varable vectors n K wth fulflment of lmtatons -6 8 durng the usage of the followng otmalty crteron: n t t mn F F H y H y y K where H s dagonal matr of weght coeffcents the coordnates of whch are generally routng t metrcs of the th area lns [] s transose functon of the vector matr. Obectve functon F 6 Unauthentcated Download Date 7/3/8 5:3 PM

7 Transort and Telecommuncaton Vol. 8 no. 7 numercally characterzes total condtonal cost for the organzaton of nter-area routng rocess n communcaton networ. Snce the calculaton of routes n dfferent areas s erformed ndeendently from each other the nter-area route connectvty s not generally ensured.e. the condtons of nter-area nteracton 8 s not fulflled. The ntal choce of routes n each of the areas s dctated by the fact that they are otmal.e. the shortest n the framewor of selected metrcs H. As a rule these routes are on the one hand the most roductve; on the other hand they contan the mnmum number of hos because the addtve crteron s used. The coordnaton whch s carred out on the uer level of herarchy of routng solutons obtaned from searate areas should be drected to the fulflment of the condtons of nter-area nteracton 8. To do ths durng solvng the formulated otmzaton roblem nvolvng wth mnmzaton of eresson wth constrants 6 to rovde fulflment of nteracton condtons 8 the goal coordnaton rncle Mesarovc et al. ; Sngh and Ttl 978 has been used. Then turnng to the uncondtonal etremum roblem: mn F mal y t s necessary to mamze followng Lagrangan by and : L N N t t H y H y K K N С С С y С y K where and are the vectors of Lagrange multlers; and are subvectors of vectors and assgned to each of the vector-matr condtons of nter-area nteracton 8 for rmary and bacu routes resectvely. Under the goal coordnaton rncle the vectors of Lagrange multlers are calculated on the uer level. These multlers are nown values for lower level that s why the eresson can be reresented n the followng decomosed form: L n L t t H y H y L K L K t t H y H y μ С μ С С y q K K K q K С y n where K s the subset of flows ncomng from other networ areas to the р th area whch s the destnaton area for the th flow; K s the subset of flows outgong from the р th area whch s the source area for the th flow K K K. Accordng to the functonal decomoston n eresson all terms are attrbuted to the th area wheren the second thrd fourth and ffth terms n ths eresson are resonsble for the coordnaton of routng order for rmary and bacu routes of outgong and ncomng flows resectvely for th area n the networ. Thus the total roblem of nter-area routng was formulated as a roblem of a herarchcal coordnaton of two-level otmzaton. On the lower herarchcal level there s a calculaton of routng 6 Unauthentcated Download Date 7/3/8 5:3 PM

8 Transort and Telecommuncaton Vol. 8 no. 7 varables resented by vectors n K. The man am of the uer level n the roosed method s a coordnaton of the solutons obtaned from the lower level n order to ensure condtons of nter-area nterworng 8 by modfyng vectors of Lagrange multlers n the mlementaton of the gradent teratve rocedure Sngh and Ttl 978: ; 3 where s the teraton number; accordng to solutons of routng tass each searate area: * and and * are the gradents of functon calculated y n K receved from the lower level n С * С ; y С * y С y. 4 y y On aroachng the values of gradent 4 coordnates to zero the connectvty of nter-area routes wll be rovded. The effectveness of the roosed method of nter-area fast reroutng n terms of effcency and otmalty of the obtaned solutons deends on the coordnatng rocedure convergence rate 3-4. Technologcally the lesser number of teratons s needed to obtan otmal soluton the lesser volume of overhead transmtted between herarchcal levels about the results of calculatons on each of the teratons n the networ s and the lesser tme of solvng the routng roblem n communcaton networ as a whole s. 5. Numercal Study and Analyss of Herarchcal Method of Inter-Area Fast Reroutng 5.. Descrton of Intal Data Let us chec the effcency of the roosed method wth the confrmaton of the adequacy of the mathematcal model assumed n ts bass on a certan numercal eamle. When nvestgatng the soluton of the roblem of herarchcal nter-area fast reroutng wthn the framewor of ths eamle the structure of the communcaton networ shown n Fg. has been chosen. Ths networ conssts of three areas: Area Area and bacbone Area. M 6 M M M 8 M M M 7 M M Fgure. The structure of the networ beng studed 6 Unauthentcated Download Date 7/3/8 5:3 PM

9 Transort and Telecommuncaton Vol. 8 no. 7 Routers that are n the Area Area and Area resectvely can be convenently reresented n the form of the followng sets: M M M M M M ; M M M M3 M4 ; M M M M M M M M M The nteracton between the frst area and the bacbone area s carred out through the routers M M and. In turn the nteracton between the bacbone area and the second area s erformed through the routers M 7 M and M 8 M. Suose that the source node sendng the acets s the router M located n the frst area and the destnaton node s the router located n the second area. Fg. shows ther bandwdth /s n the gas of the lns. Then by analogy wth the 8 values of the routng metrcs that are secfc to the OSPF rotocol the eressons located on the man dagonal of the matr H act as the ln metrc. In the course of the numercal study the ntensty of the transmtted acet flow durng the mlementaton of the sngle ath routng strategy vared from to /s and under multath routng from to /s. 5.. Research of Sngle Path Herarchcal Inter-Area Fast Reroutng Suose that n the networ the structure of whch s shown n Fg. t s necessary to rotect the border router M M located on the boundary of the frst and the bacbone areas. Wth a flow rate 4 rangng from to /s the sngle ath routng has been mlemented. The resultng soluton to the roblem of nter-area fast reroutng reresented by the rmary route s shown n Fg. 3 and by the bacu one n Fg. 4. In ths case the calculated rmary or bacu ath s reresented by a sold lne whle unused lns are shown by semtransarent lnes. In Fg. 3 and Fg. 4 n the gas of the lns a fracton s ndcated where the numerator reresents the ntensty of the transmtted acet flow and the denomnator reresents the caacty of the gven ln. 8 M 6 M M M 8 M M M 7 M M Fgure 3. The resultng coordnated soluton for the roblem of nter-area sngle ath routng of the flow wth the ntensty of /s reresented by the rmary route 63 Unauthentcated Download Date 7/3/8 5:3 PM

10 Transort and Telecommuncaton Vol. 8 no. 7 The calculated rmary ath shown n Fg. 3 ncludes the followng routers of dfferent areas ncludng the border router M M : 4 M M M 7 M M In turn the bacu route s shown n Fg. 4: 4. M M M 7 M M and does not contan the rotected border router: 4 M 6 M M M 8 M M M 7 M M Fgure 4. The resultng coordnated soluton for the roblem of nter-area sngle ath routng of the flow wth the ntensty of /s reresented by the bacu route ach of the calculated routes n accordance wth condton 9 rovdes the transmtted flow wth the necessary bandwdth. Ths soluton was obtaned after the second coordnatng teraton 3 4 snce durng the ntal calculaton the connectvty of the nter-area route was not rovded because the nter-area nteracton condton 8 was not satsfed Research of Multath Herarchcal Inter-Area Fast Reroutng Wth the further ncrease n the ntensty of the same flow u to /s for the same ntal data on the networ structure and bandwdth of the lns Fg. the convergence of the coordnatng rocedure has been already ensured after the thrd teraton and the route solutons have been of the multath nature. The notatons n the gas of the lns are dentcal to those shown n Fg. 3 and Fg. 4. ach of the areas mlements the multath routng because none of the lns can coe wth such a load. Pror to the coordnaton of route solutons receved n the ndvdual areas connectvty of nter-area routes has not been rovded. As before t s needed to rotect the border router M and the resultng soluton to the multath nter-area fast reroutng roblem s shown n Fg. 5 and Fg. 6 for the rmary and the bacu routes resectvely. 64 Unauthentcated Download Date 7/3/8 5:3 PM

11 Transort and Telecommuncaton Vol. 8 no. 7 M 6 M M M M 7 M M 8 M M Fgure 5. The resultng coordnated soluton of the roblem of nter-area multath routng of the flow wth the ntensty of /s reresented by the rmary multath Fgure 5 shows the rmary multath for transmttng the flow /s from the source router to the destnaton router contanng two aths over whch flows wth the same ntensty of /s are transmtted: M M M 6 M 7 M ; M M M M M M M M M M M 6 M M M M 7 M M 8 M M Fgure 6. The resultng coordnated soluton of the roblem for nter-area multath routng of the flow wth the ntensty of /s reresented by the bacu multath 65 Unauthentcated Download Date 7/3/8 5:3 PM

12 Transort and Telecommuncaton Vol. 8 no. 7 The bacu multath used to rotect the border node M also conssts of two aths Fg. 6 over each of whch the flow of the ntensty /s s transmtted: M M M 6 M 7 M ; M M M 7 M. Gven that the ncrease n the set of allowable soluton varants n each of the areas the soluton resented n Fg. 6 has been obtaned after the thrd teraton of the coordnatng rocedure Research of Coordnaton The effectveness of the ractcal mlementaton of the roosed method largely deends on the seed of the coordnaton rocedure convergence 3 4. Mnmzng the number of coordnatng teratons 3 allows frstly to roortonally reduce the volumes of crculatng servce nformaton about the state of the networ; and secondly to ncrease the effcency of solvng the routng roblems n general. The study has found that the seed of convergence of the coordnatng rocedure was nfluenced by dfferent factors: mlemented routng strategy: sngle ath or multath; number of border routers; networ loadng; number of nter-area flows n the networ; area and bacbone structure; area connectvty; number of areas. The resented lst of factors s ordered by the degree of decrease n the nfluence on the seed of the rocedure convergence 3 4. Ths means that the number of coordnatng teratons largely deended on the mlemented routng strategy and the number of border routers and to a lesser etent on the area and bacbone structure as well as the area connectvty. In general when two border routers were used by each of the areas the number of coordnatng teratons n average was - usng the sngle ath routng or -3 wth multath routng Table. If the area structure ncluded three border routers then the average number of coordnatng teratons n rocedure 3 4 ncreased u to for sngle ath routng or to 4 for multath routng. The ncrease n the number of teratons was rovded by the fact that wth the ncrease n the number of border routers and the transton to multath routng whch s sometmes caused by hgh networ load the number of solutons obtaned n ndvdual areas also grew whch must be coordnated wth the hel of the coordnatng rocedure 3 4. Table. The analyss results for the nfluence of the number of border routers and the routng strategy used on the number of teratons of the roosed method coordnatng rocedure 3 4 Number of border routers Number of teratons Sngle ath routng Multath routng Durng the research t was establshed that the sze of the areas and the connectvty of ntra-area routers had no sgnfcant nfluence on the seed of the coordnatng rocedure convergence. 7. Conclusons In order to ncrease the scalablty and fault-tolerance of routng solutons the artcle rooses a herarchcal method of nter-area fast reroutng. The method s based on the decomosed reresentaton of the flow-based routng model -7 wth the ntroducton of the area nteracton condtons 8 to ensure connectvty of the nter-area routes. In addton the model ncludes condtons for border routers redundancy rotecton adated for both sngle ath and multath routng. The roosed method of nter-area fast reroutng s based on the soluton of the otmzaton roblem assocated wth mnmzng the congeston of the networ lns. The roosed method -4 uses the rncle of goal coordnaton to ensure consstency of routng solutons receved by the areas. In the framewor of the eamle consdered the oerablty of the roosed method has been demonstrated n terms of the 66 Unauthentcated Download Date 7/3/8 5:3 PM

13 Transort and Telecommuncaton Vol. 8 no. 7 convergence of the coordnaton rocedure 3 4 and rovson of border routers redundancy n the mlementaton of sngle or multath routng. The use of the roosed method allows to mrove the qualty of solvng routng tass n networs of herarchcal structure namely to sgnfcantly reduce the sze of routng tables and the comutatonal comlety of the solutons obtaned by reducng the dmenson of the otmzaton tas beng solved. Durng the research t was establshed that the effcency of the roosed method n terms of the seed of the coordnatng rocedure convergence 3 4 was most nfluenced by the number of border routers and the mlemented routng strategy. In general the method converged to otmal solutons for - teratons of the rocedure 3 4 under the sngle ath routng for -3 teratons under the multath routng through two border routers; and for 3-4 teratons under multath routng va three border routers. References. Csco Networng Academy d.. 4 Routng Protocols Comanon Gude. Pearson ducaton.. Le Rou J. L. Vasseur J. P. and oyle J. 5 Requrements for nter-area MPLS traffc engneerng No. RFC Lemesho O. Nevzorova O. and Halan A. 4 The ncreasng convergence of coordnaton rocedure n the mlementaton of multath herarchcal routng. In: 4 Frst Internatonal Scentfc-Practcal Conference Problems of Infocommuncatons Scence and Technology Kharv Urane October DOI:.9/INFOCOMMST Lemesho O. Nevzorova O. and Vaveno T. 6a Herarchcal coordnaton method of nterarea routng n telecommuncaton networ. In: 6 Internatonal Conference Rado lectroncs & Info Communcatons UrMCo I Kyv Urane Setember DOI:.9/UrMCo Lemesho O. V. Yeremeno O. S. Tar N. and Halan A. M. 6b Fault-tolerance mrovement for core and edge of IP networ. In: 6 XIth Internatonal Scentfc and Techncal Conference Comuter Scences and Informaton Technologes CSIT I Lvv Urane Setember DOI:.9/STC-CSIT Mesarovc M. D. Maco D. and Taahara Y. Theory of herarchcal multlevel systems Vol. 68. lsever. 7. Ra J. 5 Reslent routng n communcaton networs. Swtzerland: Srnger. DOI:.7/ Sngh M. G. and Ttl A. 978 Systems: decomoston otmsaton and control. Pergamon. 9. Tso J. and Teare D. Desgnng Csco Networ Servce Archtectures ARCH: Foundaton Learnng Gude. Csco ress.. Wóc R. Domżał J. Dulńs Z. Rzym G. Kamsńs A. Gawłowcz P. Jurewcz P. Rząsa J. Stanewcz R. and Wada K. 6 A survey on methods to rovde nterarea multath transmssons. Comuter Networs DOI:.6/.comnet Wrght. 3 Inter-area routng ath selecton and traffc engneerng. Whte aer Data Connecton Lmted.. Yeremeno O. Tar N. & Halan A. M. 6 Fault-tolerant IP routng flow-based model. In: 6 3th Internatonal Conference on Modern Problems of Rado ngneerng Telecommuncatons and Comuter Scence TCST I Lvv-Slavso Urane February DOI:.9/TCST Unauthentcated Download Date 7/3/8 5:3 PM