Joint Design on Load Balancing and Survivability for Resilient IP Networks

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1 Joit Desig o Load Baacig ad Survivabiity for Resiiet IP Networks Po-Kai Tseg ad Wei-Ho Chug * Abstract Natura or artificia disasters ofte etwork service iterrutios as we as acket ad reveue osses. To aeviate the imact of faiures o IP etworks, may IP Fast ReRoute (IPFRR) aroaches have bee reseted. I tue-based IPFRR schemes, uo the occurrece of a ik faiure, the odes adjacet to the faied ik are activated to ecasuate ad reroute the affected traffic to the edoit aog the shortest ath. Oce the edoit receives the affected traffic, it decasuates ad deivers the ackets to the origia destiatio aog the shortest ath. These shortest aths are comuted based o ik weights. The goa of this aer is to determie a set of ik weights i a tue-based IPFRR system to joity cosider the two most sigificat issues: () oad baacig ad (2) survivabiity, i.e., coverage. We first formuate this robem as a mixed iteger rogrammig (MIP). Due to the NP-hard roerty of the MIP, a Joit Load baacig ad Coverage for Tue-based (JLCT) faut recovery heuristic is roosed to aroximate the soutio of the MIP. Numerica resuts deieate that the roosed scheme efficiety imroves covetioa tue-based aroaches o the rate of faut recovery ad effectivey baace ik utiizatios i the o-faiure state. Idex Terms IP Fast ReRoute (IPFRR), Load baacig, Tueig, Resiiet IP Networks. I. INTRODUCTION Network faiures ofte cause service iterrutios ad tremedous acket osses i the moder high data-rate etwork [], [2]. To shorte the recovergece time, may IP fast reroute (IPFRR) aroaches have bee reseted. The Loo-Free Aterate (LFA) scheme [3] is oe of the most ceebrated IPFRR techiques. The goa of the LFA is to re-comute a aterate oo-free ext ho. I the evet of rimary ext ho faiure, the affected ackets are immediatey redirected to the re-comuted aterate oo-free ext ho so that the acket osses ca be mitigated. Tue-based fast IP oca recovery is aother famous IPRFF techique. I Tue-based faut recovery scheme [4], [5], [6], whe a router detects the adjacet ik faiure, the router seects a itermediated router (i.e., tue edoit) as temorary destiatio, ecasuates the affected ackets ad forwards these affected ackets by the reguar routes (i.e., shortest aths) to the itermediate router to byass the faied ik, where the edoit is comuted i advace. Oce the itermediate router receives the ecasuated ackets, it decasuates these ackets ad forwards them by the reguar routes to the corresodig destiatios. The tueig techique ca be imemeted through the stadard IP ecasuatio withi IP (IP-i-IP) Research Ceter for Iformatio Techoogy Iovatio, Academia Siica, Taiei City 529, Taiwa. * Corresodig author: Wei-Ho Chug, Emai: [email protected] This work was suorted by Natioa Sciece Couci of Taiwa, uder grat umber E rotoco [7]. The mai desig cocet is to seect a avaiabe tue edoit so that those affected ackets coud be rerouted to the tue edoit without traversig the faied ik. A router is cosidered as a avaiabe tue edoit if the affected traffic ca be rerouted to the router via orma forwardig without traversig the faied ik ad formig routig oos. A ightweight backu ath seectio agorithm, termed Fast Tue Seectio (FTS), was reseted for tue-based fast IP oca recovery [8]. The FTS agorithm seects some odes to be the edoits for rotectig the corresodig comoets, e.g., ik or ode. The shortest ath from the seected ode to the other side of the faied comoet does ot ass the faied comoet. FTS agorithm rovides a fast tueig edoit seectio oeratio ad thereby reduces the shortest ath tree comutatio overhead. The FTS agorithm has bee aied o LFA [3], U-Tur [9], ad Not-Via Address [5] aroaches. The existig Tue-based fast recovery schemes have either focused o fidig the avaiabe edoit to rotect ik or doube-ik or ode faiures [4], [5], [6], or devote to aeviate the comexity of comutig tueig edoit [8]. Most existig Tue-based fast recovery schemes focus o mitigatig faiures ad recoveries. The joit cosideratio of oad baacig ad faiure recovery has ot bee addressed i the ast. Faut recovery ad oad baacig are the two most sigificat issues for IPFRR. I this aer, we cosider a coectioess destiatio-based ure IP routig etwork. We focus o otimized desig of joity cosiderig oad baacig ad faiure recovery i the tue-based IP fast oca recovery system. To the best of our kowedge, this work is the first oe to joity cosider oad baacig ad faut recovery i the tue-based IPFRR. The goa of this aer is to offie determie a set of ik weights i the tue-based fast IP oca recovery system to joity achieve oad baacig i the o-faiure state ad rotectio of arbitrary sige ik faiure without icurrig ay ik overoad durig the faut recovery. This robem is formuated as a mixed iteger rogrammig (MIP) with the objective of miimizig the weighted differece betwee the maximum ik oad ad rate of faut recovery. The MIP determies routig ad ik weights such that each sige ik faiure ca be rotected (i.e., fidig avaiabe edoit for each sige ik faiure case) with satisfyig ik caacity costraits. Owig to the NP-hard roerty of the MIP, we roose a Joit Load baacig ad Coverage for Tue-based (JLCT) faut recovery heuristic to aroximate the soutio of the MIP. I the simuatios, the roosed JLCT is aied o the most famous tue-based aroach, e.g., tues [4]. 579

2 The remaider of this aer is orgaized as foows. We first demostrate the robem formuatio i Sectio II. I Sectio III, the roosed JLCT is described i detai. I Sectio IV, the exerimeta resuts are show ad erformace comarisos to other we-kow schemes are coducted. Fiay, we discuss reated work i Sectio V, ad cocudig remarks are made i Sectio VI. II. PROBLEM FORMULATION We formuate the oad baaced fast oca rotectio with IP tueig as a mixed iteger rogrammig (MIP). Give a hysica etwork tooogy ad the demad voume for a source-destiatio (SD) airs, the robem is to comute the ik weights for workig routig ad determie avaiabe edoits for tueig uder sige ik faiures. Notatios are defied i the foowig. Notatios: L: Set of etwork iks. N: Set of etwork odes. C : Physica caacity o ik. Ψ: Set of source-destiatio (SD) airs. P ψ or P (a,b) : Cadidate ath set for SD air ψ or SD air (a,b). src : Source ode of ik, e.g., ode a is the source ode of ik (a,b). dest : Destiatio ode of ik, e.g., ode b is the destiatio ode of ik (a,b). t ψ : Traffic demad for SD air ψ. δ : =, if ath icudes ik ; = 0, otherwise. ς : =, if ath icudes ode ; = 0, otherwise. M: A arge eough umber. α: A weight for objective fuctio, 0 α. Decisio variabes: v: Utiizatio o the most cogested ik. a : Lik weight for shortest ath routig. x : =, if ath is used to be a workig ath; = 0, otherwise. y : = 0, if the ode ca be the avaiabe tue edoit for the faied ik ;, otherwise. w : Workig caacities aocated o ik. b : Backu caacities aocated o ik. z : = 0, if ik ca be rotected; =, otherwise. Probem(MIP): subject to: Pψ L mi αv (-α)( P ψ L L L x = ψ x = or 0 x δ a L a δ q z ) () Ψ (2) P ψ, ψ Ψ (3) q P ψ, ψ Ψ (4) + a Z L (5) P ( src, ) x δ t = ψ Ψ Pψ x ς N k P w dest + xς src = y y (, dest ) k P ( k src, ) M z L k P (, k dest ) L (6) N, L (7) (8) w / C v L (9) ( y )( w x δ + w x δ ) b N,, k L, k (0) w + b C L () b 0 L (2) z = or 0 L (3) We wat to meet two objectives: miimizig the maximum ik utiizatio i the o-faiure state whie simutaeousy maximizig the rate of faut recovery. Hece the objective fuctio is desiged as equatio (), where the first term is the maximum ik utiizatio mutiied by costat α, the secod term is the rate of faut recovery mutiied by costat -α, the L meas the amout of iks i the etwork. The umerator of secod term is the umber of iks which ca be rotected. The costat α is a tradeoff arameter used to tue the imortace betwee miimizig the maximum ik utiizatio i the o-faiure state ad maximizig the rate of faut recovery. I our tue-based rotectio system, oy oe workig ath is aowed to carry traffic demad for each source-destiatio (SD) air, i.e., the ECMP is disabed. That is because if the ECMP is aowed, each SD air may use mutie workig aths to deiver traffic demad. Such mutie workig aths wi reduce the chace of rotectig ik faiures sice usig mutie workig aths icreases the risk of assig faied ik. Costraits (2) ad (3) determie a workig ath for each SD air. Decisio variabe a o the eft had side of Costrait (4) (together with (2) ad (3)) is the routig metric of the shortest ath for SD air ψ. The right had side of (4) is the cost of ath q P ψ. Costrait (4) maitais that, for each SD air, the seected ath is guarateed to be a shortest ath with resect to the ik cost metric a. Costrait (5) maitais that the ik metric is a ositive iteger. For OSPF, the ik weight rages from to 65,535. I Costrait (6), w deotes the aggregate workig traffic o ik. Costraits (7-8) maitai the rotectio criteria of tueig. We give a more detaied iterretatio for Costraits (7-8) i the ext aragrah. Costrait (9) uses variabe v to fid the utiizatio o the most cogested ik. The backu caacity is comuted at Costrait (0). The first term of eft had side of Costrait (0) is to determie whether ode ca rotect ik k or ot. If ode caot rotect ik k, the vaue of eft had side of Costrait (0) equas to 0; otherwise, the workig traffic carried o ik k (i.e., w k ) is rerouted to the workig aths of air (k src,) ad air (,k dest ). If ik is o the rerouted aths, the backu caacities of ik (i.e., b ) shoud be greater tha or equa to the rerouted traffic w k. Fiay, Costrait () is the caacity costrait for each ik. I the tue-based IP fast reroute aroach, a ik is 580

3 Agorithm JLCT:. Give: 2. A cur : iitia ik weights. 3. ρ: a variabe. 4. : weight for equatio (). 5. T: temerature. 6. : reduce ratio for temerature T. 7. MAXIterTem: termia criteria for outer for oo. 8. MaxIteratio: termia criteria for ier whie oo. 9. begi 0. A * := A cur ;. Cacuate workig routes usig Dijkstra(A cur); 2. Cacuate w (i.e., costrait (6) i MIP); 3. ru tues to cacuate z (i.e., costraits (7-8) i MIP); 4. Cacuate Objective (i.e., eq. ()); 5. Obj cur:= Objective; 6. Obj * :=Obj cur; 7. for (iter tem =; iter tem MAXIterTem; iter tem ++) 8. for (k=; k MaxIteratio; k++) 9. Radomy ick a iteger withi iterva [-ρ,ρ]; 20. Radomy ick a ik from set L; 2. A ext ={a, a 2,, a +,, a L }; 22. Cacuate workig routes usig Dijkstra(A ext ); 23. Cacuate w (i.e., costrait (6) i MIP); 24. ru tues to cacuate z (i.e., costraits (7-8) i MIP); 25. Cacuate Objective (i.e., eq. ()); 26. Obj ew := Objective; 27. := Obj ew Obj cur ; 28. if ( 0) 29. A cur := A ext ; 30. if (Obj cur < Obj * ) 3. Obj * := Obj cur ; 32. A * := A cur ; 33. ese if (rad(0,) < ex(- /T)) 34. A cur:= A ext; 35. T:= T ; 36. If (ρ > ) the ρ:= ρ/2; 37. retur (Obj *, A * ) ; 38. ed. Figure. Pseudo code for the JLCT agorithm. rotected if there exists a avaiabe edoit to reroute affected ackets. For rotectig ay sige ik faiure, say ik, a ode woud be the avaiabe tue edoit if dest SP( src,) ad src SP(, dest ), where SP(a,b) reresets the shortest ath from ode a to ode b. Accordig to such coditio, the Costraits (7-8) are derived. The eft had side of Costrait (7) is to check whether ode is a avaiabe tue edoit for rotectig ik. If there exists a avaiabe tue edoit, the vaue of the eft had side of Costrait (7) equas to 0. Costrait (8) uses variabe z to determie whether the ik is rotected or ot. If the vaue of eft had side of Costrait (8) is 0, z = 0; otherwise, z =. The vaue of M ca be set as the amout of odes i the etwork. Eve though this robem ca be etirey formuated as the MIP mode, the comutatio of the soutio is highy comicated due to the huge umber of decisio variabes ad NP-hard roerty [0]. For this reaso, we reset a heuristic scheme to fid the soutio of Probem(MIP) i the ext sectio. III. PROPOSED JOINT LOAD BALANCING AND COVERAGE FOR TUNNEL-BASED FAULT RECOVERY ALGORITHM Our heuristic is based o the Simuated Aeaig (SA) [] method. Simuated aeaig is a stochastic search agorithm for obtaiig a good aroximatio to the goba otima soutio of the otimizatio robem i a arge search sace. SA uses a temerature to cotro the robabiity of accetig a disadvatageous soutio whereby the otima soutio is evetuay obtaied whe temerature is cooig. I this sectio, we roose a Joit Load baacig ad Coverage for Tue-based (JLCT) faut recovery heuristic to aroximate the soutio of Probem(MIP). The JLCT adots the cocet of simuated aeaig to tue ik metric reeatedy such that the objective of MIP ca be achieved ad satisfy costraits. The JLCT scheme is show i Figure. Iitiay, the curret ik weights A cur is assiged to curret otima ik weight set A *. A iitia feasibe soutio is geerated at ies -6. We use Dijkstra agorithm to cacuate workig routes accordig to curret ik weights A cur. The, the ik oad w ad tues aroach [4] are used to comute the curret vaue of objective (equatio ()). I erformig the tues aroach, the P-sace ad Q-sace are comuted to search avaiabe tue edoit for each sige ik rotectio, where the P-sace icudes a avaiabe tue edoits ad Q-sace icudes a ossibe reease oits. The reease oit reresets the router which ca reach the reair ath target (the reair ath target ca be the ode j or the eighbors of ode j if the faied ik is (i,j)) via orma forwardig without assig faied ik. Besides, the cocet of direct forwardig of tues is aso used to aow the tue edoit to exted the tue by oe ho. We defie a edoit is avaiabe for a rotected ik if the fows carried o rotected ik ca be successfuy rerouted to the tue edoit ad further arrived the corresodig destiatios without icurrig ik overoad i the duratio of faut recovery. The mai oeratio of JLCT is ocated i the ested oo from ie 7 to ie 37. The outer for oo is to cotro the temerature T ad shrik the give variabe ρ, whie the ier for oo (ies 8-34) is to reeatedy seect a ik ad tue its weight such that the vaue of objective (i.e., equatio ()) is miimized, ad the costraits, that maximum ik oad ad ay sige ik faiure is rotected, is cacuated. The give variabe ρ is the boud of the seected iteger λ at ie 9. The variabe ρ is shruk by the factor of 2 uo the cometio of each ier for oo. I each iteratio of the ier for oo, we first radomy ick a ik, tue its weight, comute ik oad for each ik (i.e., w ), ru Tue-based fast reroute aroach to examie rotectio of each ik (i.e., z ), ad cacuate the vaue of objective (i.e., equatio ()) (see ies 9-25). We the cacuate the differece betwee Obj ew ad Obj cur ad assig the vaue to Φ. If Φ is ess tha or equa to 0, A cur is udated by A ext. If Obj cur is ess tha Obj *, Obj * is udated by Obj cur ad A * is udated by A cur. Otherwise, we comute the exoetia of -Φ/T ad geerate a radom rea umber withi (0,). If the exoetia of -Φ/T is arger tha the geerated rea umber, the A cur is udated by A ext eve though the vaue of Obj ew is a disadvatage soutio. That avoids covergig to a oca miimum. The outer for oo is termiated whe iter tem is greater tha MAXIterTem whie the ier for oo is stoed whe k is greater tha MaxIteratio. Oce the roosed JLCT scheme termiates, we 58

4 (a) Srit IP Figure 2. Bechmark etworks for erformace evauatio, (a) Srit IP backboe (6 odes, 68 iks), (b) EON (9 odes, 76 iks). obtai the otima ik weights for baacig workig traffic ad the edoits for ay sige ik rotectio. For each iteratio, the workig routes ad maximum ik utiizatio are cacuated by ruig Dijkstra s agorithm at ies of Figure. The comexity of Dijkstra s agorithm is O( N 2 ). The Tue-based fast reroute aroach is ru to sed O( L N ) comutatioa comexity for examiig each ik rotectio at ie 24 of Figure. Hece the comexity of JLCT is O( L N ) for each iteratio sice O( N 2 + L N ) O( L N ). To reduce the amout of cacuatios of JLCT, the we-kow icremeta SPF (ispf) agorithm was used i searchig the tue edoit. IV. EXPERIMENTAL RESULTS The goa of the roosed JLCT scheme is to joity miimize utiizatio o the most cogested ik ad maximize coverage o the tue-based IP fast faiure recovery scheme. Hece, i the foowig exerimets, we comare the erformace betwee roosed JLCT ad the most famous tue-based IP fast faut recovery aroaches, e.g., tues [4]. Note that we disabe ECMP i erformig JLCT because the emoymet of mutie equa cost aths icreases the risk of assig faied ik. We simuatig the most ofte ecoutered sige ik faiure [2], [3] to measure two erformace metrics: coverage rate ad maximum ik utiizatio o the two rea-word tooogies show i Figure 2. I each test etwork, a ik icudes two oosite directioa iks. For simicity, we assume each ik has equa caacity. The rea-word traffic demad matrix for the EON etwork is adoted from [4] ad the reaistic traffic demad matrix for the Srit IP backboe etwork is based o the Gravity Mode [5]. For each erformed scheme, each simuatio resut takes the best resut from 0 trias. For each tria of JLCT, the iitia weight of each ik i each test etwork is set as the commoy recommedabe iverse of the ik caacity [6]. We emhasize that JCLT does ot rey o ay secific tooogy. It ca be erformed o arbitrary tooogy or grah. The arameters of JCLT are give as foows: iitia ik weights as iverse of the ik caacity, ρ = iitia ik weight σ, σ =, T = 0, ε =, MAXIterTem = 0, ad MaxIteratio = 0000 for each bechmark etwork. A. Coverage Rate I the first exerimet, we observe the coverage rate (rate of faut recovery), which is defied as the ratio of the tota umber of successfuy rotected iks to the amout of iks i the etwork. A successfuy rotected ik meas the a affected Coverage rate Coverage rate Maximum ik utiizatio Maximum ik utiizatio E Tues ivca Tues rad Lik caacity (Mb) (a) Srit IP backboe E Tues ivca Tues rad Lik caacity (Mb) Figure 3. Coverage rate imrovemet for tues E Tues ivca Tues rad Lik caacity (Mb) (a) Srit IP backboe E Tues ivca Tues rad Lik caacity (Mb) Figure 4. Maximum ik utiizatio imrovemet for tues. traffic carried o the rotected ik ca be successfuy rerouted to corresodig destiatios without occurrig ik overoad aog with rerouted aths. A route here is regarded as a IP acket stream traversig a source-destiatio (SD) air. The simuatio resuts of erformig JLCT o tues are draw i the Figure 3. I the egeds of Figure 3, the Tue-rad ad Tue-ivCa rereset cases of usig tues [4] to reair 582

5 ik faiures with each ik weight seected radomy withi [,65535] ad seected by the iverse caacity, resectivey. The JLCT-0-Tu, -0.-Tu, -0.5-Tu, -0.9-Tu ad --Tu rereset the JLCT oeratig o tues with α = 0, 0., 0.5, 0.9, ad, resectivey. Besides, JLCT--Tu-E reresets the JLCT oeratig with α = o tues with eabed ECMP. The Y-axis shows the coverage rate. The X-axis reresets the ik caacity ad the uit is megabytes (Mb). The ik caacity is 00Mb meas each ik has equa ik caacity 00Mb. As show i Figure 3, for each scheme, the coverage rate icreases with the icrease of ik caacity. That is because a higher ik caacity settig woud reduce the chaces of icurrig ik overoad durig the faut recovery. Tues-ivCa has higher coverage rate tha Tues-rad. Due to the objective fuctio, i.e., the equatio (), the coverage rate of JLCT icreases with the decrease of α. JLCT-0-Tu has better rate of coverage tha Tues-ivCa u to 7%-04% ad 5%-29.26% o Srit IP backboe ad EON etworks, resectivey. The resuts idicate that the roosed JLCT scheme ca efficiety ehace coverage rate for the tue-based IP faiure recovery aroach. The resuts aso demostrate that the set of good ik weights ca achieve better coverage rate ad use ess etwork resources. B. Maximum Lik Utiizatio I this subsectio, we imemet JLCT ad tues to observe the maximum ik utiizatio i the o-faiure state. We articuary examie the maximum ik utiizatio i the o-faiure state because the etwork oerates at o-faiure state durig most oeratio time ad JLCT rotects faiure without meetig ik overoad durig faiure recovery. The ik utiizatio is defied as the ratio of the oaded traffic to the hysica caacity o a ik. The maximum ik utiizatio is to seect the utiizatio o the ik whose utiizatio is the argest. A sige ik faiures were cosidered, comuted, ad draw i Figure 4. For each scheme, the maximum ik utiizatio decreases with the icrease of ik caacity. With the desig of the objective fuctio i JLCT, the maximum ik utiizatio of JLCT decreases with the icrease of α. Tues-ivCa uses iverse caacity as the ik weight to baace ik oad. Hece, Tues-ivCa has ower maximum ik utiizatio tha Tues-rad. JLCT--Tu-E has the owest maximum ik utiizatio due to the eabed ECMP routig. JLCT--Tu has ower maximum ik utiizatio tha Tues-ivCa u to 32%-40% ad 0%-8.92% o Srit IP backboe ad EON etworks, resectivey. To joity cosider coverage ad oad baacig, we erform JLCT with α = 0.5 o tues to observe the erformace. Whe JLCT with α = 0.5 is erformed o tues, the JLCT-0.5-Tu reaches higher coverage rate tha Tues-ivCa u to 0%-67% ad 0%-5.2% o Srit IP backboe ad EON etworks, resectivey. The JLCT-0.5-Tu has maximum ik utiizatio ower tha Tues-ivCa u to 20.4%-47.29% ad 0%-8.9% o Srit IP backboe ad EON etworks, resectivey The resuts idicate that the erformace of commo tue-based IPFRR aroaches ca be imroved if the coverage rate ad oad baacig are cosidered joity; the erformace imrovemet ca be achieved i both ow ad high avaiabe etwork resources (ik caacity). V. CONCLUSION I this aer, we joity cosider oad baacig ad faut recovery i the tue-based fast IP oca recovery system. We reset a mixed iteger rogrammig (MIP) to formuate the joit robem ad further roose a simuated aeaig based heuristic to aroximate the soutio of MIP. The roosed scheme determies a set of ik weights to baace workig fows ad simutaeousy determie avaiabe tue edoit to rotect ay sige ik faiure so as to miimize the maximum ik utiizatio i the o-faiure ad maximize the rate of faut recovery. Exerimeta resuts demostrate that the roosed scheme ca imrove coverage rate by 0%-30% ad reduce maximum ik utiizatio by 5%-5% for covetioa tueig aroach. REFERENCES [] A. Basu ad J. G. Riecke, Stabiity Issues i OSPF Routig, i Proc. ACM SIGCOMM, , Aug [2] D. Watso, F. Jahaia, ad C. Labovitz, Exerieces with moitorig OSPF o a regioa service rovider etwork, i Proc. IEEE ICDCS, , [3] A. Atas ad A. Zii, Basic secificatio for IP fast reroute: oo-free aterates, RFC 5286, Set [4] S. Bryat, C. Fisfis, S. Previdi, ad M. Shad, IP fast reroute usig tues, IETF Iteret Draft, draft-bryat-ifrr-tues-03, Nov [5] M. Shad, S. Bryat, ad S. Previdi, IP fast reroute usig ot-via addresses, IETF Iteret Draft, draft-ietf-rtgwg-ifrr-otviaaddresses- 07, Ar. 20. [6] S. Kii, S. Ramasubramaia, A. Kvabei, ad A. F. Hase, Fast recovery from dua-ik or sige-ode faiures i IP etworks usig tueig, IEEE/ACM Trasactios o Networkig, vo. 8, o. 6, , Dec [7] C. Perkis, IP ecasuatio withi IP, RFC 2003, Oct [8] Y. Yag, M. Xu, ad Q. 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