Computer Commuicatios 30 (2007) 1331 1336 wwwelseviercom/locate/comcom Recovery time guarateed heuristic routig for improvig computatio complexity i survivable WDM etworks Lei Guo * College of Iformatio Sciece ad Egieerig, Northeaster Uiversity, Sheyag 110004, Chia Key Lab of Broadbad Optical Fiber Trasmissio ad Commuicatio Networks, Uiversity of Electroic Sciece ad Techology of Chia, Chegdu 610054, Chia Received 20 October 2006; received i revised form 5 December 2006; accepted 14 December 2006 Available olie 22 December 2006 Abstract I this paper, we ivestigate the protectio for survivable WDM optical etwork ad propose a ew algorithm called Quick Heuristic Routig (QHR) to tolerate the sigle-lik failure I QHR, each coectio request will be assiged to oe primary path ad multiple segmet-backup paths to guaratee the recovery time i the worst case Compared to previous algorithm, QHR ca yield sigificat improvemets i computatio time ad blockig probability Simulatios are show to be promisig Ó 2006 Elsevier BV All rights reserved Keywords: Optical etworks; Protectio; Segmet-backup path; Recovery time; Time complexity 1 Itroductio I Wavelegth-Divisio-Multiplexig (WDM) optical etworks, each wavelegth chael has the much high trasmissio rate ad the cosequece is that the fiber lik failure may lead to a lot of traffic blocked Therefore, the survivability is a key issue i WDM optical etworks ad also has bee studied for may years [1] Sice the siglelik failure is domiat i WDM optical etworks, previous papers mostly focus o studyig this failure sceario I order to improve the resource utilizatio ratio ad reduce the blockig probability, previous papers have proposed the shared protectio scheme [2,3], i which the backup resources/paths ca be shared if the correspodig primary resources/paths are lik disjoit I shared protectio scheme, the Shared Path Protectio (SPP) algorithm has the best resources utilizatio ratio while has the slowest recovery time, ad the Shared Lik Protectio (SLP) algorithm has the fastest recovery time while has the * Tel: +6 2 53601343 E-mail address: haveball@263et worst resources utilizatio ratio Therefore, i order to yield fast recovery time meawhile obtai satisfactory resources utilizatio ratio, previous papers have proposed the Shared-Segmet Protectio (SSP) algorithm [4 ] I SSP, each coectio request will be first assiged to oe primary path Secod, the primary path will be divided to several u-overlapped segmet-primary paths Fially, each segmet-primary path will be, respectively, assiged to oe lik disjoit segmet-backup path Therefore, the recovery time ca be faster tha SPP ad the resources utilizatio ratio is also better tha SLP; that is, SSP ca make trade-offs betwee SPP ad SLP It is obvious that if we choose proper segmet-primary paths ad segmet-backup paths, the recovery time required by the coectio request ca be guarateed meawhile the resource utilizatio ratio also ca be satisfied However, the flaw of SSP is the much high time complexity sice i the worst case may potetial segmet-backup paths may be computed ad checked for guarateeig the recovery time High time complexity will restrict the efficiet computatio for dyamic coectio requests ad the cosequece is that some coectio requests may be blocked if the computatio time exceeds the establishmet time costraits 0140-3664/$ - see frot matter Ó 2006 Elsevier BV All rights reserved doi:101016/jcomcom200612014
1332 L Guo / Computer Commuicatios 30 (2007) 1331 1336 I this paper, we focus o the solvig this problem of SSP ad propose a ew algorithm called Quick Heuristic Routig (QHR) to achieve fast computatio for dyamic coectio requests Compared to SSP, the improvemet of QHR is to obtai multiple segmet-backup paths by ru oe time of Dijkstra s algorithm while SSP oly ca obtai oe segmet-backup path by ru oe time of Dijkstra s algorithm Therefore, QHR ca save sigificat computatio time for fidig the proper segmet-backup paths to guaratee the recovery time The rest of this paper is orgaized as follows Sectio 2 presets the etwork model, recovery time computatio, ad routig selectio method i SSP ad QHR Sectio 3 describes the heuristic process of QHR Sectio 4 presets the simulatio results Sectio 5 cocludes this paper 2 Problem statemet 21 Network model Assume the etwork has V odes ad L liks, ad each lik has W wavelegths Assume each coectio request arrives at the etwork orderly, ad there is oly a coectio request arrives at a time Assume the badwidth of each coectio request is oe wavelegth chael The shortest path algorithm, ie, Dijkstra s algorithm, is applied to compute the routes The followig otatios are itroduced j: fiber lik i the etwork c j : cost of lik j; it is determied by the curret state of etwork fw j : umbers of free wavelegths o lik j pw j : umbers of primary wavelegths o lik j bw j : umbers of backup wavelegths o lik j cr : coectio request p : primary path for cr b : backup path for cr sp s;dðcþ sb s;dðcþ : segmet-primary path of p from ode s to ode D(c) that is with c hops distat to the destiatio ode; especially, D(0) deotes the destiatio ode : segmet-backup path for sp s;dðcþ RTC: recovery time costrait; if the RTC caot be guarateed, the coectio request will be blocked ETC: establishmet time costrait; if the coectio request caot be established withi ETC, it will be blocked jxj: umber of elemets i set X 22 Recovery time The recovery time is defied as the time betwee the failure of the primary/segmet-primary path ad the time that the correspodig backup/segmet-backup path begis to work [3] The followig otatio is itroduced: D, the message processig time at a ode is 10 ls, correspodig to 1 GHz CPU time P, the propagatio delay o the lik, is 400 ls, correspodig to a lik legth of 0 km X, the time to cofigure, test, ad set up a OXC (Optical Cross-Coect) is 10 ls F, the time to detect the lik failure, is 10 ls I Fig 1, assume the segmet-primary path A B C D traverses the failed lik B C, the umber of hops from ode B to the segmet source ode A is k, ad the umber of hops of the backup path A E D is m The recovery procedure is preseted as follows If lik B C fails, the ed odes of lik B C, ie, lik source B ad lik destiatio C, sed failure messages to the segmet source ode A ad the segmet destiatio ode D, respectively The, the segmet source ode A seds a setup message to the segmet destiatio ode D alog the segmet-backup path A E D ad cofigures the OXCs at each itermediate ode alog the segmetbackup path A E D, because i shared protectio, at the time of the coectio setup, wavelegths are reserved for the backup path but OXCs are ot cofigured After receivig the setup message, the segmet destiatio ode D seds a cofirmatio message back to the segmet source ode A alog the segmet-backup path A E D, thus completig the recovery procedure Therefore, the recovery time ca be writte as T ¼ F þ kp þðk þ 1ÞD þ 2mP þ 2ðm þ 1ÞD þðm þ 1ÞX I order to tolerate ay sigle-lik failure, we should cosider the worst case; that is, the failure of the lik whose lik destiatio is the segmet destiatio ode Therefore, i the worst case k = h 1, where h deotes the total hops of the segmet-primary path, ad the recovery time ca be writte as T ¼ F þðh 1ÞP þ hd þ 2mP þ 2ðm þ 1ÞD þðm þ 1ÞX ð2þ I Eq (2), if T 6 RTC ca be satisfied, the recovery time required ca be guarateed It is obvious that smaller h ad m will lead to less T, ie, faster recovery time Therefore, if the curret recovery time caot be guarateed, we ca choose the shorter segmet-primary path ad A B E Fig 1 Illustratio of recovery time for shared protectio C D ð1þ
L Guo / Computer Commuicatios 30 (2007) 1331 1336 1333 segmet-backup path to reduce the T for guarateeig the recovery time 23 Routig selectio i SSP The process of SSP ca be briefly preseted as follows [4 7]: 1 Compute the primary path p 2 Compute the lik-disjoit backup path b If the recovery time ca be guarateed by p ad b, retur p ad b Else, letc 1,s source ode, ad go to step3 3 If D(c) s, choose the segmet-primary path sp s;dðcþ ad compute its correspodig backup path sb s;dðcþ If the recovery time ca be guarateed by sp s;dðcþ sb s;dðcþ, record sp s;dðcþ ad sb s;dðcþ If c = 0, retur the solutio Else, let s D(c), c 0, ad go back to step3 Else, let c c + 1 ad go back to step3 Else, o solutio ca be foud ad retur NULL ad Note that, i the process of SSP, if the computatio time exceeds the ETC costraits, the process will be stopped ad the coectio request will be blocked Accordig to the process of SSP, for the coectio request from source ode A to destiatio ode D i Fig 2, first, SSP computes the primary path A B C D through ruig oe time of Dijkstra s algorithm Secod, SSP computes the backup path A E F G D through ruig oe time of Dijkstra s algorithm Third, sice the recovery time caot be guarateed by the curret primary path A B C D ad backup path A E F G D, SSP computes the segmet-backup path A E F C through ruig oe time of Dijkstra s algorithm for the segmet-primary path A B C Fially, sice the recovery time caot be guarateed by the curret segmet-primary path A B C ad segmet-backup path A E F C, SSP computes the segmet-backup path A E B (two hops) through ruig oe time of Dijkstra s algorithm for the segmet-primary path A B (oe hop) that ca guaratee the recovery time Therefore, SSP will ru three times of Dijkstra s algorithm to obtai the first solutio with segmet-primary path A B ad segmet-backup path A E B Based o the same pricipal, SSP will ru two times of Dijkstra s algorithm to obtai the secod solutio with segmet-primary path B C ad segmet-backup path B F C, ad will ru oe time E F G of Dijkstra s algorithm to obtai the third solutio with segmet-primary path C D ad segmet-backup path C G D Therefore, the total times of ruig Dijkstra s algorithm to establish this coectio request for guarateeig the recovery time is seve (oe is for primary path ad six is for segmet-backup paths) 24 Routig selectio i QHR Compared to SSP, the mai advatage of QHR is that it has lower time complexity to obtai the same solutios with SSP I Fig 2, to fid the solutio with the segmet-backup path A E B for guarateeig the recovery time, SSP will ru three times of Dijkstra s algorithm However, the process of SSP is ot efficiet sice the three routes A E F G D, A E F C ad A E B ca be obtaied through ruig oe time of Dijkstra s algorithm First, QHR computes the primary path A B C D through ruig oe time of Dijkstra s algorithm Secod, after deletig the liks o the primary path SPP computes all routes (A E F G D, A E F C ad A E B) from the ode A to all other dowstream odes (B, C ad D) through ruig oe time of Dijkstra s algorithm, ad choose the segmet-primary path A B ad segmet-backup path A E B for guarateeig the recovery time With the same pricipal, QHR will ru oe time of Dijkstra s algorithm to obtai the secod solutio with segmet-primary path B C ad segmet-backup path B F C, ad will ru oe time of Dijkstra s algorithm to obtai the third solutio with segmet-primary path C D ad segmetbackup path C G D Therefore, the total times of ruig Dijkstra s algorithm to establish this coectio request for guarateeig the recovery time is four (oe is for primary path ad three is for segmet-backup paths) It is obvious that QHR ca save more computatio times tha SSP; that is, QHR is more efficiet tha previous SSP 3 Proposed heuristic algorithm 31 Process of QHR Iput: etwork iformatio; a ew cr from source ode s to destiatio ode d Output: the solutio for guarateeig the recovery time; or NULL if o solutio is available Step1: adjust the costs of all liks accordig to (3) Ru Dijkstra s algorithm to compute the least-cost primary path p from the source ode s ad the destiatio ode d If p has bee foud, go to step2 Else, block this coectio request ad retur NULL A B C Fig 2 Illustratio for routig selectio i SSP ad QHR; assume the recovery time ca be guarateed by the segmet-primary path with oe hop ad the segmet-backup path with two hops D >< þ1; If fw j ¼ 0 c j ¼ W þ 1 fw j =W ; other >: ð3þ
1334 L Guo / Computer Commuicatios 30 (2007) 1331 1336 Step2: adjust the costs of all liks accordig to (4) Ru Dijkstra s algorithm to compute the least-cost routes from the source ode s to all other odes o p If the route from the source ode s to the destiatio ode d has bee foud, record this route as backup path b If the recovery time ca be guarateed by p ad b accordig to (2), update the etwork iformatio ad retur p ad b Else, let c 1 ad go to step3 Else, let c 1 ad go to step3 þ1; If ðj 2 p Þ or ðfw j þ bw j < v >< j Þ c j ¼ v j þ 1 bw j =W ; other >: ð4þ Step3: check the ode D(c) If D(c) s, choose the segmet-primary path sp s;dðcþ ad the segmet-backup path sb s;dðcþ obtaied i step2 or step4 If the recovery time ca be guarateed by sp s;dðcþ ad sb s;dðcþ accordig to (2), record sp s;dðcþ ad sb s;dðcþ If c = 0, update the etwork iformatio ad retur the solutio Else, let s D(c),c 0, ad go to step4; Else, let c c + 1 ad go back to step3 Else, o solutio ca be foud ad retur NULL Step4: Ru Dijkstra s algorithm to compute the leastcost segmet-backup paths from ode s to all other dowstream odes o p Go back to step3 primary path cotais V odes, the total umber of all potetial segmet-backup paths is V(V 1)/2 Thus, the time complexity of SSP is approximately O(V 2 + V 2 V(V 1)/2) = O(V 2 +(V 4 V 3 )/2) sice it will ru oe time of Dijkstra s algorithm to compute the primary path ad ru V(V 1)/2 times of Dijkstra s algorithm to compute the backup path ad all potetial segmet-backup paths However, QHR ca ru oe time of Dijkstra s algorithm to compute the primary path ad ru (V 1) times of Dijkstra s algorithm to compute the backup path ad all potetial segmet-backup paths Therefore, the time complexity of QHR is approximately O(V 2 + V 2 (V 1)) = O(V 3 ) It is obvious that the differece of time complexity betwee QHR ad SSP is expoetial, so that QHR is much faster tha SSP Therefore, i QHR more coectio requests ca be established withi ETC ad the cosequece is that QHR has lower blockig probability tha SSP 4 Simulatio results ad aalysis We simulate a dyamic etwork eviromet with the assumptios that coectio requests arrival accordig to a idepedet Poisso process with arrival rate b, ad the coectios holdig time is egative expoetially a 0 1 2 3 Note that, i the process of QHR, if the computatio time exceeds the ETC costraits, the process will be stopped ad the coectio request will be blocked I Eq (3), we ca see that the liks that have more free resources (ie, fw j ) will have smaller lik-cost, ad the the primary paths will be favorable for traversig these liks ad the cosumed resources ca be more uiformly distributed to all liks Therefore, the load may be more balace I Eq (4), v j ¼ maxfjve jj; e 2 Lg that deotes the reserved backup resources o lik j We ca observe that the liks that have more reserved backup resources (ie, bw j ) have less lik-cost, so that the backup paths will be favorable for traversig these liks, ad the fewer ew backup resources eed to be assiged Therefore, the resource utilizatio ratio ca be improved b 9 0 1 7 10 4 14 11 7 6 12 13 12 11 16 4 5 15 17 1 32 Compariso of QHR ad SSP 2 5 13 I Sectios 23 ad 24, we ca see that QHR ad SSP ca obtai the same solutio for guarateeig the recovery time, ad the advatage of QHR is the lower time complexity From the process of SSP, i this worst case all potetial segmet-backup paths eed to be eumerated If the 6 9 19 14 3 10 Fig 3 Test etworks: (a) US Natioal etwork ad (b) ARPANET
L Guo / Computer Commuicatios 30 (2007) 1331 1336 1335 a ACT 6 76 66 56 46 36 26 16 06 Network Load i Erlag b ACT 9 7 6 5 4 3 2 1 0 Network Load i Erlag Fig 4 Performace of ACT i (a) Natioal etwork ad (b) ARPANET a 2% 24% b 30% 25% BP 20% 16% 12% % BP 20% 15% 10% 4% 5% 0% 0% Network Load i Erlag Network Load i Erlag Fig 5 Performace of BP i (a) Natioal etwork ad (b) ARPANET distributed 1/l, the, the etwork load is b/l Erlag I simulatio, we assume l = 1 ad each required badwidth is oe wavelegth chael We assume there are o waitig queues i the etwork, so if a coectio request was blocked, it would be abadoed immediately The test etworks are US Natioal etwork ad ARPANET show i Fig 3, where each ode-pair is itercoected by a bi-directioal fiber lik that has 16 wavelegths ad each ode has the wavelegth coversio capacity Assume each lik legth is 0 km, the recovery time costrait (RTC) is 2 ms ad the establishmet time costrait (ETC) is 6ms The computer used i simulatio is cofigured with 1 GHz CPU ad 512 M RAM We compare the performaces of QHR ad SSP We first test the performace of Resource Utilizatio Ratio (RUR), which is the rate of the total backup resources to the total primary resources We fid that the values of RUR of QHR ad SSP are both about 70 9% The reaso for this is that QHR ad SSP ca fid the same solutio for guarateeig the recovery time (see Sectios 23 ad 24), ad the oly differece betwee them is the time complexity We secod evaluate the performace of Average Computatio Time (ACT) that is defied as the rate of the total times of ruig Dijkstra s algorithm for successfully establishig the coectio requests to the total umbers of successfully established coectio requests Smaller ACT meas faster computatio time I Fig 4, we ca see that the computatio time of QHR is much improved compared to SSP, ad the improvemet ratios are up to 92% ad 5% i Natioal etwork ad ARPANET, respectively The reaso for this is that QHR ca compute multiple segmet-backup paths by ruig oe time of Dijkstra s algorithm while SSP oly ca obtai oe segmet-backup path by ruig oe time of Dijkstra s algorithm Therefore, QHR ca save more computatio times to fid the proper segmet-backup paths for guarateeig the recovery time tha SSP We fially evaluate the performace of Blockig Probability (BP) that is defied as the rate of the total coectio requests blocked by ETC costraits to the total coectio requests arrived o the etwork I Fig 5, we ca see that the BP of QHR is sigificatly improved compared to SSP, ad the improvemet ratios are up to 53% ad 44% i Natioal etwork ad ARPANET, respectively The reaso for this is that QHR has much faster computatio time tha SSP ad the cosequece is that more coectio requests ca be established withi ETC Therefore, QHR has lower blockig probability tha SSP 5 Coclusio This paper has ivestigated the problem of survivable routig i WDM optical etwork ad proposed a ew algorithm called Quick Heuristic Routig (QHR) to tolerate the sigle-lik failure Compared to previous algorithm, QHR ca yield sigificat improvemets i computatio time ad blockig probability
1336 L Guo / Computer Commuicatios 30 (2007) 1331 1336 Ackowledgmet The authors thak reviewers for valuable commets Refereces [1] G Maier, A Pattavia, SD Patre, et al, Optical etwork survivability: protectio techiques i WDM layer, Photo Netw Commu 4 (2002) 251 269 [2] P Ho, H Mouftah, Shared protectio i WDM mesh etworks, IEEE Commu Mag 42 (2004) 70 76 [3] S Ramamurthy, L Sahasrabuddhe, B Mukherjee, Survivable WDM mesh etworks, J Lightwave Techol 21 (2003) 70 3 [4] P Ho, J Tapolcai, T Cikler, Segmet shared protectio i mesh commuicatios etworks with badwidth guarateed tuels, IEEE/ ACM Tras Netw 12 (2004) 1105 111 [5] D Xu, Y Xiog, C Qiao, Novel algorithms for shared segmet protectio, IEEE J Sel Areas Commu 21 (2003) 1320 1331 [6] L Guo, L Li, H Yu, J Cao, Dyamic survivable routig heuristic for shared protected WDM optical etworks, IEEE Commu Lett 10 (2006) 676 67 [7] C Ou, Hui Zag, N Sighal, et al, Sub-path protectio for scalability ad fast recovery i optical WDM mesh etworks, IEEE J Sel Areas Commu 22 (2004) 159 175 [] J Cao, L Guo, H Yu, L Li, A ovel hop costraied sub-path protectio routig algorithm i WDM etworks, Opt Commu 260 (2006) 155 163 Lei Guo was bor i Sichua, Chia, i 190 He received the PhD degree i commuicatio ad iformatio systems from School of Commuicatio ad Iformatio Egieerig, Uiversity of Electroic Sciece ad Techology of Chia, Chegdu, Chia, i 2006 He is curretly a Associate Professor i College of Iformatio Sciece ad Egieerig, Northeaster Uiversity, Sheyag, Chia His research iterests iclude survivability ad GMPLS/WDM etwork techology Dr Guo was the recipiet of the Best Paper Award from the Iteratioal Coferece o Commuicatios, Circuits ad Systems (ICCCAS 04) Dr Lei Guo is a member of IEE ad a member of OSA