Scholars Journal of Engneerng and Technology (SJET) Sch. J. Eng. Tech., 2015; 3(4A):343-350 Scholars Academc and Scentfc Publsher (An Internatonal Publsher for Academc and Scentfc Resources) www.saspublsher.com ISSN 2321-435X (Onlne) ISSN 2347-9523 (Prnt) Research Artcle Fault-Tolerant Uncast, Multcast and Broadcast Routng Flow-Based Models Olexandr V. Lemesho, Knan M. Arous, Olesandra S. Yeremeno. Telecommuncaton Systems Department, Kharv Natonal Unversty of Rado Electroncs, Urane, 61166. *Correspondng author Olexandr V. Lemesho Emal: alexere@ur.net Abstract: Flow-based models of uncast, multcast and broadcast fault-tolerant routng n telecommuncaton networs were proposed. The novelty of models s a descrpton of multproduct case, as well as n consderaton of flowng nature of modern networ traffc, allowng to mplement prevously nown condtons for communcaton lns overload preventon for the case of uncast, multcast and broadcast routng type. The models represented by a system of lnear equatons and nequaltes, whch maes them effectve n terms of algorthm mplementaton. As part of the proposed models tass of uncast, multcast and broadcast routng are focused on solvng optmzaton problems. Numercal examples showed effcency of the proposed models n terms of servng multple flows wth dfferent characterstcs concurrently and adaptaton to changes of networ parameters (e.g. channel capacty). The proposed model can be used for solvng the uncast, multcast and broadcast routng problems, and the mathematcal descrpton of more complex processes and problems, such as those assocated wth the desgn of telecommuncaton networs (selecton of topology and bandwdth of communcaton lns). Keywords: Flow-based model, Fault-tolerance, Routng, Bacup scheme, Uncast, Multcast, Broadcast flows INTRODUCTION Routng protocols s a sgnfcant part n provdng the qualty of servce (QoS) n modern communcaton systems whch prmarly based on IP and MPLS (MultProtocol Label Swtchng) technologes. It s mportant to note that the man source of QoS degradaton s the occurrng of networ overload. Unfortunately the majorty of routng protocols provde the recalculaton of routes n a perod of tens seconds. Thus they don t provde an effcent response on the networ overload. So, to ncrease the effcency of response on the possble denals of pacets servng caused by overloads n lns and routers buffers the fault-tolerant routng s used (e.g. MPLS Fast ReRoute technology). Routng protocol has to satsfy a number of mportant requrements such as provdng networ elements reservaton (protecton of ln, node and path) and adaptaton for sngle/multpath routng. Thus an approach as flow-based model that satsfes these requrements s offered. Modern networs are multservce,.e. they provde several servces concurrently on the bass of one transport platform. In addton to transmt traffc pacets of IPTV servce, dstance learnng, database replcaton, Web servces multcast routng s used. In order to mprove QoS dfferent schemes of fault-tolerant uncast, multcast and broadcast routng are used, whch n partcular are also based on provsons of the Fast Reroute concept. Represented schemes demonstrate an approach proposed n [1-3], and they are based on nonlnear flow model n whch the condtons for ln overload preventon are modfed for the case when only some flows can swtch to bacup routs but not all of them. Fault-Tolerant Routng Models Mathematcal Model for Uncast Flows Routng Let us descrbe a networ structure as orented graph Г ( V, E), where V v, 1, m s a set of vertces nodes (routers) of the networ and ( E s a set of graph arcs modelng networ lns. Let E ( :ln goes from to j be the set of lns. For each ln (, t s specfed the throughput, and wth each -th traffc flow the set of parameters assocated: r, s and d rate of -th flow, source node and 343
Lemesho OV et al., Sch. J. Eng. Tech., 2015; 3(4A):343-350 destnaton node respectvely. Quantty ( E of prmary path. x s the control varable, whch characterzes the part of -th flow of the ln For the purpose of preventon of networ nodes overload t s necessary to meet the condton of flow conservaton [4]: E E E x j j, ) E x j j, ) E x j j, ) E Condtons of multpath routng realzaton for prmary path are next 0; K, 1; K, 1; K, 0 1 s, d s ; d. ; (1) x. (2) Condtons of sngle path routng realzaton for prmary path are x 0;1. (3) Besdes, the model s supplemented by condtons of QoS assurance [5] that s very mportant for multservce networs. Mathematcal Model for Multcast/Broadcast Flows Routng In developng of multcast routng model let us use the same concept as for uncast. Each -th flow connected wth several parameters: an average flow rate at the networ entrance r ; source node s ; * 1 2 m d d, d,..., d (4) set of destnaton nodes, where m s the number of recevers of -th flow. In broadcast routng model every -th flow s connected wth an extended (n comparson to (4)) set of destnaton nodes Where all the networ nodes except for s are ncluded. ** d d,..., 1 2 m 1, d d, (5) Whle solvng the problem of multcast routng t s necessary to calculate a set of Booleans (3). Each of them characterzes the proporton of ntensty of -th flow n the ln the networ. and also Routng varables (3) are lmted by several constrants [6]: Each transt node v j V E :( E ( E ; K, where K denotes a set of flows n 1 f K, v s, (6) * ; v j d 1 f K. (7), whch can be any node, except for the source, s gven by the followng condtons: 344
Lemesho OV et al., Sch. J. Eng. Tech., 2015; 3(4A):343-350 :( E x jp, K; v s. (8) j The fulfllment of these condtons allows to have a flow n any communcaton ln (( j, p) E ) comng from the transt node only n that case when ths flow comes on the gven node at least va one ncomng ln ( ( E ). where In order to prevent cycle formng condtons added nto the proposed model: ( E E s a set of arcs formng -th cycle accordng to ther orentaton; x E, (9) E denotes power of the set E. The fulfllment of the condton (9) guarantees that the number of arcs used n multcast routng, composng any cycle s always smaller than the total number of arcs n ths cycle. Ensurng of the Fault-Tolerance Routng Condtons In order to mprove fault-tolerance routng together wth prmary path havng a root n the source node ( s ), we have to determne a bacup path wth the same root. From the mathematcal pont of vew n order to determne the bacup (reserved) path t s necessary to calculate addtonal varables ln ( E of the bacup path wth arguments (3), (6)-(9). x characterzng a part of the -th flow n the However wth the purpose of preventng the prmary and bacup paths overlappng wth realzaton of dfferent bacup-schemes we add several addtonal restrctng condtons that connect routng varables to calculate the prmary and bacup path trees. For example, whle mplementng protecton scheme of ( -ln the offered model (3), (4), (6)- (9) obtans such condtons [7,8]: x x 0. (10) bacup. The fulfllment of these condtons guarantees the usng of ( -ln by the sngle path, ether the prmary or In realzaton of the protecton scheme for -th node the model s added by the followng term: :( E x x 0. (11) The fulfllment of the gven condton guarantees the usng of -th node (.e. all ncdents to t lns) by ether the prmary or bacup path. To provde protecton for the prmary path the followng equalty condton must be added to the model x x 0, (12) ( E Whch guarantees the meetng of requrements regardng the absence of any common lns n the prmary or bacup path? OVERLOAD PREVENTION CONDITIONS Usng the proposed model let s consder followng two varants of ts applcaton, whch characterzed by the ablty to prevent the overload of networ lns by flows whch run through prmary and bacup routes. In the frst case, when consder only prmary paths flows, condton of the lns overload preventon has the form: r x ; ( E. (13) K 345
Lemesho OV et al., Sch. J. Eng. Tech., 2015; 3(4A):343-350 Then the requred lns throughput of the bacup paths flows are not guaranteed and the addtonal restrctons on varables x are not applcable. Then followng condtons entered: n case of one path routng realzaton (3). r K 1, ( E, (14) Durng the calculaton of varables x and x whle solvng the problem of fault-tolerant routng n networ t s reasonable to mnmze the followng objectve functon: F c c, (15) K( E K( E where c and c are lns metrcs whch used n calculaton of the prmary and bacup paths respectvely. As a result of mnmzaton of the equaton (15) varables x and x are calculated what n practce means the determnaton of the two types of paths between a nodes (source and destnaton) the prmary and bacup. More over the order of usng these routes by flows determned n the same tme wth ther calculaton. Besdes n [7,8] the necessty to mplement the condtons establshed: c x c x. (16) K( E K( E The fulfllment of ths condton guarantees that the prmary path wll be always more effectve n rate, pacet delay,.e. «shorter» than the bacup one wthn the chosen routng metrcs c and c. Whle mplementng of faulttolerance n multcast flows the optmzaton tas (15) wth the constrants (1)-(14) and (16) belongs to the class of nonlnear programmng. NUMERICAL EXAMPLES Let us consder an example of mplementaton of the proposed schemes (1)-(16) whle solvng the problem of sngle path fault-tolerant uncast routng n the networ the topology of whch s presented on the Fgure 1. The networ conssts of fve nodes (routers) and seven lns wth the throughput (pacet per second, 1/s) shown on the graph arcs. For frst flow: the source node s, destnaton node s Nodes 5. The rate of frst flow s 80 1/s. For second flow: the source node s Node 2, destnaton node s Nodes 4. The rate of second flow s 60 1/s. Let us assume that wthn the gven example we mplement uncast routng wth mnmzaton of the number of hops ( c 1). It s needed to represent the scheme of protecton of the (1, 3) ln. 120 100 90 120 180 110 Node 2 60 Node 4 Fg-1: The example of MPLS-networ topology 346
Lemesho OV et al., Sch. J. Eng. Tech., 2015; 3(4A):343-350 120 100 а The prmary path for frst flow 60 b The prmary path for second flow Fg-2: Set of prmary paths for two flows 90 110 Node 2 60 Node 4 Fg-3: The bacup path for frst flow wthout usng the condton (14) 180 90 120 Node 2 Fg-4: The bacup path for frst flow usng the condton (14) Whle solvng a problem t was determned that prmary path for frst flow s consst of two hops whch nclude 135 nodes. The prmary path for second flow ncludes just one ln 24. In realzng the protecton scheme of the (1, 3) ln wthout condton (7) the bacup path for frst flow wll contan 3 hops and nclude 1245 nodes. But usng the ln (2, 4) by both frst and second flows wll cause ts overload due to addtve flow ntensty of 140 1/s. It s possble to avod the overload n the case of usng the overload preventon condton (7). Then the bacup path for frst flow wll consst of 1235 nodes wthout networ overload. Let us consder an example of mplementaton of the proposed schemes (10)-(14) whle solvng the problem of sngle path fault-tolerant multcast routng n the networ the topology of whch s presented n the Fgure 5. The networ conssts of sx nodes (routers) and eght lns wth the throughput (pacet per second, 1/s) shown on the graph arcs. For frst flow: the source node s, destnaton nodes are Nodes 3, 5 and 6. The rate of frst flow s 100 1/s. For second flow: the source node s Node 2, destnaton nodes are Nodes 4 and 6. The rate of second flow s 200 1/s. Let us assume that wthn the gven example we mplement multcast routng wth mnmzaton of the number of hops ( c 1). 347
Lemesho OV et al., Sch. J. Eng. Tech., 2015; 3(4A):343-350 Fg-5: The example of MPLS-networ topology Fg-6 shows an example of the problem-solvng for fault-tolerant routng n the networ wth (2, 4)-ln protecton. Then as the prmary path for frst flow we tae the soluton presented n Fgure 6 a), and the "length" of the gven path s mnmal and conssts of 3 hops. Then soluton for prmary path for second flow presented on Fgure 6 b), and the "length" of the gven path s mnmal and t conssts of 2 hops. а The prmary path for frst flow b The prmary path for second flow Fg-6: Set of prmary paths for two flows If only condtons (13) used for mplementaton of (2, 4) ln protecton scheme, the bacup path for second flow (Fgure 7 a) ncludes 3 hops and does not contan any ln (2, 4) n accordance wth the mplemented protecton scheme. 348
Lemesho OV et al., Sch. J. Eng. Tech., 2015; 3(4A):343-350 a The bacup path for second flow usng the condton (13) only b The bacup path for second flow usng condtons (14) only Fg-7: Implementaton of (2, 4)-ln protecton scheme Bacup path (Fgure 7 a) s shortest and conssts of 3 hops, but has throughput of 200 1/s, because of the (5,6)- ln throughput. Thus due to presence of two flows wth the rates of 100 and 200 1/s an overload wll occur n ths ln. Usng the condton (14) the soluton shown on Fgure 7 b wll be used as the desred bacup path. Ths bacup path (Fgure 7 b) has 4 hops,.e. overload does not occur, because shared lns (3, 5) and (5, 4) have throughput larger than 300 1/s. The above examples demonstrate the advantages of usng the proposed condtons (13) and (14) for the lns overload preventon. In the consdered case for multcast routng the fault of (2, 4)-ln has not caused a change n the transmsson route for frst flow. However, t s not a rule, sometmes n order to prevent networ overload under fault of one of ts elements (node, ln, or path) wthn the proposed soluton, reroute can smultaneously nclude several but not all flows wthn the networ. CONCLUSION The schemes for protecton of node, ln and path under fault-tolerant uncast, multcast, and broadcast routng are presented for a multflow case. The schemes demonstrate an approach proposed n [7,8], and they are based on a nonlnear flow model n whch the condtons for ln overload preventon (14) are modfed for the case when only some flows can swtch to bacup routes, but not all of them. Ths approach ncrease the effcency of practcal realzaton of solutons related to uncast, multcast and broadcast fault-tolerant routng n modern multservce networs and can be used n MPLS Fast ReRoute technology. Effcency of updatng routng nformaton ncreased by the proposed soluton, and allows reducng the tme of updatng to tens of mllseconds, whle current solutons suppose to have tmers of 60 90 seconds. Functonalty of proposed bacup schemes s demonstrated by the numercal examples wth proven effectveness for the multflow case. REFERENCES 1. Haryawan MY; Comparson Analyss of Recovery Mechansm at MPLS Networ. Internatonal Journal of Electrcal and Computer Engneerng (IJECE), 2011; 1(2): 151-160. 2. Sundarrajan A, Ramasubramanan S; Fast Reroutng for IP Multcast Under Sngle Node Falures. Global Communcatons Conference (GLOBECOM 2013), 2013; 1: 2076 2081. 3. Tam AS-W, Kang X Chao HJ; A Fast Reroute Scheme for IP Multcast. Global Telecommuncatons Conference, 2009; 1: 1-7. 349
Lemesho OV et al., Sch. J. Eng. Tech., 2015; 3(4A):343-350 4. Lee Y, Seo Y, Cho Y, Km C; A Constraned Multpath Traffc Engneerng Scheme for MPLS Networs. Proc. IEEE ICC 2002, 2002; 1: 2431-2436. 5. Lemesho AV, Evseeva OYu, Garusha SV; Research on Tensor Model of Multpath Routng n Telecommuncaton Networ wth Support of Servce Qualty by Greate Number of Indces. Telecommuncatons and RadoEngneerng, 2014; 73(15): 1339-1360. 6. Lemesho OV, Arous KM; The flow-based model of multcast routng. Mcrowave and Telecommuncaton Technology (CrMCo), 23rd Internatonal Crmean Conference, 2013; 1: 523-524. 7. Lemesho O, Romanyu A, Kozlova H; Desgn schemes for MPLS Fast ReRoute. XIIth Internatonal Conference the experence of desgnng and applcaton of cad systems n mcroelectroncs, Polyana-Svalyava, 2013; 1: 202-203. 8. Lemesho OV, Kozlova HV, Romanyu AA; Flow-based model of fault-tolerant routng n MPLS-networ. Mcrowave and Telecommuncaton Technology (CrMCo), 2013 23rd Internatonal Crmean Conference, 2013; 1: 509-510. 350