International Journal of Scientific & Engineering Research, Volume 4, Issue 12, December-2013 ISSN

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1 833 Polynomal Tme Algorthm (PTA) to generate a survvable rng vrtual topology for Optcal WDM based on Hamltonan Crcut Detecton Heurstcs(HCDH) *Sajal Kanta Das, Department of Computer Scence & Technology, Women s Polytechnc, Hapana,Agartala,Inda. sajalmtechcse@gmal.com Abstract The Routng and Wavelength Assgnment (RWA) problem s known to be NP-hard for general Physcal Topology (PT) n optcal networks. We have analyzed survvablty of optcal network under Survvable Routng and Shared Path Protecton (SPP) for varous topologes and suggested two survvable RWA algorthms whch are shown to perform better under certan performance matrx by smulaton. Genetc Algorthms (GA) also provde an attractve approach to solvng challengng problem of RWA n optcal Wavelength Dvson Multplexng (WDM) networks, because y usually acheve a sgnfcantly low blockng probablty. Avalable GA-based dynamc RWA algorthms were desgned manly for WDM networks wth a wavelength contnuty constrant, and y cannot be appled drectly to WDM networks wth wavelength converson capablty. The polynomal tme Crcut detecton heurstcs, whch acts as backbone of vrtual topology. Due to establsh addtonal lghtpaths n rng to ncrease one-hop traffc enhanced wavelength utlzaton. In Shared Path Protecton(SPP) approach we fnd lmtatons of popular Actve Path Frst heurstc and desgn a new Dsjont Path heurstc, whch s proved to provde dsjont par, f exsts n network. In RWA envronment we use heurstc, whch allocates spare resources for backup path to ensure falure of actve path, we mprove performance of protecton of Path Protecton by an Advanced Search method where routng s ntegrated wth wavelength assgnment part of RWA algorthm and depends on network state. wavelength assgnment algorthm that maxmzes one-hop traffc n a specal type of topology called Lne Network for multple wavelengths per lnk. Snce Rng Topology s an mportant extenson to Lne Network, we desgn anor algorthm usng prevous algorthm, to optmally assgn wavelengths n WDM Rng Networks for multple wavelengths and desgn Survvable Routng n optcal networks. The falure of a sngle fber lnk may cause smultaneous falure of several lghtpaths n WDM networks, and dsconnect vrtual topology. We propose a polynomal tme algorthm to generate a survvable rng vrtual topology based on Hamltonan. Introducton We study dynamc RWA problem[5] n WDM networks wth sparse wavelength converson and propose a novel hybrd algorthm[9] for t based on combnaton of moble agents technque and GA. By keepng a sutable number of moble agents[4] n network to cooperatvely explore network states and contnuously update routng tables, new hybrd algorthm can promptly determne frst populaton of routes for a new request based on routng table of ts source node, wthout requrng tme consumng process assocated wth current GA-based dynamc RWA algorthms. To acheve a good load balance n WDM networks wth sparse wavelength

2 converson, we adopt n our hybrd algorthm a new reproducton scheme and a new ftness functon that smultaneously takes nto account path length, number of free wavelengths, and wavelength converson capablty n route selecton. Our new hybrd algorthm acheves a better load balance and results n a sgnfcantly lower blockng probablty than does FxedAlternate routng algorthm, both for optcal networks wth sparse and full-range wavelength converters and for optcal networks wth sparse and lmted-range wavelength converters. We are movng towards a socety, whch requres that we have access to nformaton at our fngerprnts when we need t, and n whatever format we need t. Ths demand s fueled by many dfferent factors day by day wth networks of hgher capactes, at lower cost. The tremendous growth of Internet and World Wde Web (WWW) has brought more and more users onlne, ncreasng complexty and data transfer rate, consumng large amounts of bandwdth due to hgher data transfer rate. Due to tremendous growth n network traffc and demand for new servces, world s telecommuncaton markets are beng deregulated. Fber optcs technology can be servng demand based servces due to ts potentally lmtless capablty. 834 and Asa, respectvely, as well as a varety of enterprse networks such as FDDI (Fber Dstrbuted Data Interface). 2. Multplexng Technques The ncreasng demand for bandwdth, along wth fact that s relatvely expensve n many cases to lay new fber, mples that we must fnd ways to ncrease capacty on exstng fber. The fundamental way of ncreasng transmsson capacty on a fber s to ncrease bt rate, whch requres hgher speed electroncs. Many lower speed data streams are multplexed nto hgher speed streams at transmsson bt rate by means of hgher electronc Tme Dvson Multplexng (TDM). Optcal TDM(OTDM) and WDM s or approaches that can explot huge optoelectroncs msmatch by requrng that each end user s equpment only operate at electronc rate, but multple WDM channels from dfferent user may be multplexed on same fber. 2. Frst Generaton Networks(FGON) Optcal Optcal fber s preferred medum for transmsson of data at anythng more than a few tens of megabts per second over any dstance more than a klometer. Optcal fber technology s used n all networks purely as a transmsson medum, servcng as a replacement for copper cable, and all swtchng and processng of bts s handled by electroncs. Optcal networks are SONET (Synchronous Optcal Network) and SDH (Synchronous Dgtal Herarchy) networks, whch form core of telecommuncatons nfrastructures n North Amerca and n Europe 3. Second Generaton Networks(SGON) Optcal In recent research, scentsts have realzed that optcal networks are capable of provdng more functon than just pont-to-pont transmsson. Major advantages are to be ganed by ncorporatng some of swtchng and routng functon that was performed by electroncs nto optcal part of network. In frst generaton networks, a node must not handle only all data ntended for that node, but also all data that s beng passed through that node onto or node n network. In second generaton network, ths later data pass through optcal doman and sgnfcantly reduce burden on electroncs doman on that node. 3. Servces It s useful to thnk an optcal layer that offers servces to all hgher layers n networks. Any network can be vsualzed as consstng of many layers, wth each layer performng possbly dfferent functons. Second generaton optcal networks may provde three types of servces to hgher network layers. The frst servce s a lght path servce, applcable for WDM networks. In ndvdual wavelengths are

3 lkely to carry data at farly hgh bt rates (a few Gb/s), and ths entre bandwdth s provded to hgher layer by a lght path. Dependng on capabltes of network, ths lght path could be set up or taken down upon request of hgher layer. Alternatvely network may provde only permanent lght paths, whch are set up at tme network s deployed. 3.2 Physcal Topologes and Logcal The physcal topology of network s physcal set of routng end-nodes and fberoptc lnks connectng m upon one setup lghtpaths between end nodes. lghtpath has been set up from node X to node Y. The physcal degree of a (routng node) s number of or (routng) nodes that t s drectly connected to by fber optc lnks, e.g., physcal degree of all (routng) nodes n Fg. s 2. The logcal out-degree of an end-node s number of lghtpaths that orgnate from that end-node and logcal n-degree of an end-node s number of lghtpaths that termnate n that end-node, e.g., n Fg. 2, logcal n-degree and out-degree of every node s. Ideally n a network wth n nodes, we would lke to set up lght paths between all n (n-) pars. However ths s usually not possble because of two reasons. Frst, number of wavelengths avalable mposes a lmt on how many lght paths can be set up. Secondly each node can be source and snk of only a lmted num number of lghtpaths. Ths s determned by amount of optcal hardware that can be provded (transmtters and recevers) and by amount of nformaton node can handle n total. When t s not possble to establsh lght paths between all pars of nodes, node pars that are not drectly connected va lght paths must use a sequence of lght paths through ntermedate nodes to communcate. At each ntermedate node, packets comng n on a lghtpath must be connected to electronc form, swtched electroncally and n converted back to Fg. Physcal Topology Fg. 2 Logcal Topology correspondng to Fg. A lght path conssts of a path through network between end nodes and a wavelength on that path. Confgurng routng nodes n network wll set up lght paths. Two lght paths that share a same lnk n network must use dfferent wavelengths. As for example, n above fgure, lnk between X and Y node shares 3 wavelengths (W, W2, W3). A lght path provdes a ppe between end nodes wth a bandwdth equal to that of one channel, typcally -2.4 GB/s. The set of all lght paths that have been setup between end nodes consttutes logcal topology. The logcal topology s a graph wth nodes correspondng to end-nodes n network wth a drected edge from node X to node Y f a optcal form and sent out on a dfferent lghtpath route to r destnatons. 4. WDM Archtecture Transmsson capacty of a lnk n today s optcal network has ncreased sgnfcantly due to wavelength dvson multplexng technology (WDM). Optcal wavelength-dvson multplexng (WDM) s a promsng technology to accommodate explosve growth of Internet and Telecommuncaton traffc n wde area, metro area, and local area networks. Wavelength Dvson Multplexng (WDM) s a technque to ncrease transmsson capacty. WDM s essental same as frequency dvson multplexng, whch has been used n rado systems for more than a century. The dea s to 835

4 transmt data smultaneously over multple carrer wavelengths (or, equvalently frequences) over a fber. WDM provdes a way to ncrease transmsson capacty by usng multple channels at dfferent wavelengths. WDM network archtecture can be classfed nto two broad categores: 4. Broadcast and Select Archtecture In broadcast and select archtecture dfferent nodes transmt at dfferent wavelengths. Ths form of a network s smple and sutable for use n local or metropoltan area networks, such as access networks. The number of nodes n ths network s lmted because wavelengths cannot be reused n network. [2]. 4.. Wavelength Routng Archtecture -Ths s a more sophstcated and practcal archtecture used today. The nodes n ths network are capable of routng dfferent wavelengths at an nput port to dfferent output port. Ths enables us to set up many smultaneous usng same wavelength n network; that s, capacty can be reused spatally. Ths archtecture also avods broadcastng power to unwanted recevers n network. Thus se networks are sutable for deployment n metropoltan-and wde-area networks, such as local-exchange and nter-exchange networks. 836 Mn λmax Such that Each logcal lnk n LG corresponds to a lght path and two lght path that share an edge n physcal topology are assgn dfferent wavelengths, The total number of wavelengths used s at most W, Every node n LG has Lµ ncomng edges and Lµ outgong edges, Traffc s routed so that flow of traffc from each source to destnaton par s conserved at each node. b. Wavelength Assgnment to Lghtpaths - From [3], we use followng data structures for our RWA algorthms for ease of mplementatons. We use a MxN matrx called lnk-state matrx S where M s set of wavelengths avalable per lnk and N s set of fber optc lnks n physcal topology Lr The state of a lnk L at any tme can be specfed by column vector Lterature Survey a. Routng and Wavelength Assgnment Problem Statement From [], let s gve a general RWA problem statement for our works. Let Tm = (λpq) be traffc matrx,.e., λpq s arrval rate of packets at p that are destned for q. we assume that traffc s b-drectonal and unformly dstrbuted over multple shortest paths between a par of nodes. We seek to create a logcal topology LG and routng on LG that mnmzes λmax = maxj λj, where λj denotes offer lode on lnk (,j) of logcal topology. λmax s maxmum offer load to a logcal lnk and s called congeston. Let Lr be gven physcal topology of network, Lµ degree of logcal topology and M number of wavelength avalable. An nformal descrpton of logcal topology desgn problem s as follows: T τ = (τ (0), τ (), (τ (2),.., (τ (M-)), where τ (j)= f wavelength λ j s allocated n lnk by some lghtpath and τ (j)= 0 orwse. So lnk-state matrx U= (τ, τ, τ 2 0,.. τ ). Intally all wavelengths are L- avalable n each lnk. So we ntalze S matrx by 0. An nxn matrx VT s mantaned whch stores nformaton of lghtpaths already establshed. The elements of VT are traffc between nodes that has been assgned a lghtpath. The requests for whch lghtpaths cannot be establshed are stored n anor nxn matrx BT. We lne up connecton requests for settng up lghtpaths usng largest-traffc frst scheme. Ths scheme desgns vrtual topology by frst attemptng to set up lghtpath between nodes havng largest traffc. It n attempts to set up lghtpath for nodes havng next largest traffc and so on, constrants beng physcal topology and lmted number of

5 wavelengths per lnk. Intutvely, better performance can be acheved f larger traffc s frst allowed to reach destnaton n one hop. Ths s because t s easer and less loadng for ntermedate nodes to route small traffc ndrectly n multhops. The algorthm s repeated for all avalable wavelengths usng frst-ft scheme. Therefore we sort traffc matrx n nonncreasng order to generate connecton requests for establshng lghtpaths. Let Req be ordered set of source-destnaton pars so that Req={(,j ), (,j ),,(,j ) : T[,j ] T[ k k,j ], k+ k+ 2 2,j n, k k n n k n-}. Connecton requests wll be generated accordng to ths ordered set requred. RWA problem s a NP-hard problem [2] and many researchers have tackled problem of RWA wth a number of effcent heurstc algorthms [], [3], [4]. From [2]-Wavelength assgnment (WA) problem s closely related to graph colorng problem. In above graph [Fg. (2.-a)] s representaton of network L, where vertces of graph represents node of network & edge between two vertces represent fber lnk between two nodes. The route for each lght path correspond to a path n L, and set of routes that have been specfed for lght paths corresponds to a set of paths, say, R. Now consder anor graph, path graph of L, denoted by R (L), whch s constructed as follows. Each path n R correspond to a node n R (L)[Fg. 2.-b], and two nodes n R (L) s connected f re two paths n R share any common edge n L. Solvng WA problem s equvalent to solvng classcal graph colorng problem on R (L), that s we have to assgn color to each node such a way that two adjacent node must be assgned dstnct color and total number of color mnmzed, whch s called chromatc number of graph. Thus mnmum number requred to solve WA problem s chromatc number of R (L). Now n graph L, gven set of node has to be connected by lght paths, whch routes are unquely determned? We have lght path between two nodes and 2, 2 and 3, and 3. Resultng graph R(L) shown n graph. The chromatc number of R(L) s 3 and colorng of R(L) wll be n 3 colors. Thus we need 3 wavelengths to solve WA problem n ths example. Colorng an arbtrary graph s a hard problem that has been ntensvely studed for several decades. In fact, t s n NP-complete problem. However re are several specal classes of graphs for whch frst colorng problem have been found. If R(L) we are nterested n belongs to one of se specal classes, n 5. RWA Algorthm usng Greedy approach In [4] t s stated that n case of a greedy RWA n a physcal network, numbers of avalable wavelengths are gven and once a wavelength s assgned to a lnk t cannot be used agan to that lnk later for anor connecton. Then we have to check wher re are any avalable wavelengths or not. If avalable, n queston does not arse, but n case of unavalablty desred connecton cannot be establshed between source and destnaton node par. Here a traffc matrx between each node par s gven and we have to arrange traffc between node par n decreasng order. Now lnk havng hghest traffc matrx s assgned frst avalable wavelength. If frst wavelength s not avalable n t s tryng through next avalable wavelength orwse t s left wthout assgnng any lghtpath. And procedure s repeated wth lnk havng next hghest traffc untl all lnks are assgned or left due to unavalablty of resources. 837

6 we can found exact soluton to WA problem. Orwse, unless R(L) has only few nodes, we have to content ourselves wth fndng an approxmate soluton to RWA problem. Many fast but approxmate algorthms have been devsed for general graph colorng problem, and se algorthms can be used to fnd good but approxmate soluton to WA problem. Transformaton to a graph-colorng problem does not show that RWA problem s hard or NP complete. To show ths, one needs to perform transformaton n opposte drecton, namely, take an nstance of a graph-colorng problem and convert t nto an nstance of RWA problem. Ths way we can prove RWA ndeed a NP complete problem. 6. Desgn of a Survvable Network attempts we nvestgate problem of routng lght paths on an arbtrary physcal topology, such that vrtual topology remans connected even after falure of a sngle physcal lnk. We call such a routng as survvable routng. To desgn algorthms of survvable Vrtual Topology Desgn, we studed and analyss n [], ntroduced a heurstc polynomal tme algorthm, SemHam, for fndng Hamltonan cycles n random graphs wth hgh probablty. Ths algorthm assumes unt weght on each lnk of gven graph. In [2], a new polynomaltme algorthm for fndng Hamltonan crcuts n certan graphs. It s shown that algorthm always fnds Hamltonan crcuts n graphs that have at least three vertces and mnmum degree at least half total number of vertces (provng Drac s suffcency condton). The algorthm works on graphs wth arbtrary weght on each lnk. In [3], ntroduced bascs of survvable topology desgn, mamatcal formulaton of problem. In [5], ntroduced about Survvablty n Optcal Networks. It dscussed about technques for survvablty n optcal networks; such as Pre-desgned Protecton and Dynamc Restoraton. It also dscussed about Survvablty Technques n WDM Networks such as Mult-layer protecton, Fault detecton and localzaton, protecton from sngle lnk falures etc and Non-WDM Networks such as automatc protecton swtchng, self-healng rng etc. Wth ntegraton of computer and communcaton technologes and rapd maturaton of fber optc communcaton technques, today s telecommuncaton networks can provde fast and hgh-qualty servces to end-users. The servce type has broadened from voce only to a dverse array of multmeda servces. Wth more and more busness users nvolved, nterrupton of servce for even short perods of tme may have dsastrous consequences. As such how to prevent servce nterrupton, and reduce loss of servce to mnmum f nterrupton s nevtable, becomes a crtcal ssue; that s, survvablty must be consdered n desgnng telecommuncaton networks. Optcal fber has become domnant transport medum n telecommuncaton systems because of ts advantages n capacty, relablty, cost, and scalablty. Therefore new multplexng technques such as wavelength dvson multplexng (WDM) have been proposed n order to utlze fber capacty more effcently. The falure of a sngle physcal fber lnk n a WDM network may cause smultaneous falure of several lght paths. Ths may dsconnect vrtual topology. In our 8. Path Protecton n WDM Networks Survvablty of hgh bandwdth optcal networks has emerged as an mportant area of research n recent years due to tremendous mportance as a natonal and nternatonal nfrastructure for movng large volumes of data. Falure of any part of ths nfrastructure, er due to natonal causes or malcous attacks s bound to have a large adverse mpact on economy and securty of country [8]. In WDM networks, end-users can 838

7 communcate wth each or va all-optcal WDM doman called lghtpaths. Because of hgh traffc (up to 50 Tbts/s) a fber carres (because many lghtpaths can route through same fber and each lghtpath s expected to operate at a few Gb/s [5]), t s mperatve to develop approprate protecton and restoraton schemes to prevent or reduce data loss [5]. 9. Survvablty Mechansms The man goal of a survvable network s to be able to perform a rapd restoraton at as small cost as possble (.e. usng mnmum resources). For ths, we have two dfferent survvablty mechansms: ) Pre-desgned protecton where redundant protecton capacty s pre-allocated for use when a lnk fals [4]. Usually t reles on resources (fbers, wavelengths, swtches, etc.) dedcated to protecton purposes from falures at er connecton setup or network desgn tme [7]. ) Anor survvablty mechansm, Dynamc restoraton, mples dscovery of spare capacty dynamcally n network to restore affected servces;.e. protecton s not pre-computed but chosen from avalable resources when falure occurs [7]. In pre-desgned protecton, protecton resources are kept dle when re s no falure. So, use of capacty s not very effcent. On or hand, resource utlzaton s very effcent n restoraton. 839 ) Path protecton entals end-to-end reroutng of all workng lghtpaths that use faled lnk along pre-computed back-up lghtpaths. Here entre route of workng lghtpaths may be changed [4]. In an optcal network wthout wavelength converson capablty, establshment of a lghtpath s subject to wavelength contnuty constrant.e. a lghtpath s requred to be on same wavelength channel throughout ts path n network [5]. 9.2 Dedcated and Shared Protecton Protecton schemes can furr be dvded nto two sectons based on wher backup resources are shared by more than one connecton: ) In Dedcated protecton, each node or lnk can be reserved as a backup resource for at most one connecton [5]. In Fg. 2.3, we have two workng paths, (connecton ) and -2-3 (connecton 2), both usng.. The protecton path for connecton s.2 on and for connecton 2 s Lnk and Path Protecton Protecton mechansms are broadly classfed nto path protecton and lnk protecton, dependng on where protecton swtchng s done. ) In Lnk protecton (also called loopback protecton), alternate paths (dstnct paths for each wavelength, n general), called backup or protecton paths between end ponts of each lnk are pre-computed. Upon a lnk s falure, all of lghtpaths usng lnk (called prmary or workng lghtpaths) are swtched at endnodes of lnks to r correspondng backup lghtpaths. The porton of workng lghtpaths excludng faled lnk remans same [4]. Snce se two protecton paths have common lnk 2-6, and.2 s assgned to protecton path, protecton path 2 has to be assgned a dfferent wavelength (e.g..). [7]. ) In Shared protecton, a lnk or node can be reserved as a backup resource for multple connectons, as long as those connectons do not fal smultaneously [5]. Agan, dedcated protecton requres more network resources but s smpler to mplement, whle shared protecton s more resource effcent but requres more complex sgnalng and network management [5]. 9.3 Shared Path Problem Statement Protecton

8 In our work, we have assumed that we have a connected graph G,.e. number of edges >= n. We study problem n followng way: Consder a WDM network where each fber can carry W wavelengths Λ={λ λ λ }. A, 2,, W lghtpath s establshed between a sourcedestnaton node par when a request for such a node par arrves and approprate resources are avalable. For reasons of survvablty, followng shared path protecton strategy, we try to establsh a prmary (actve) path and a secondary (backup) path. If suffcent resources are avalable at tme of request arrves, actve-backup paths are establshed; orwse call request s blocked. Thus our algorthm provdes WDM protecton. We assume that both actve and backup paths follow Wavelength contnuty constrant, but y can have dfferent wavelengths ndvdually. A path that carres. traffc under normal operaton s known as a workng or actve path (AP). When a workng path fals, traffc s rerouted through protecton or backup path (BP) We llustrate shared path protecton constrants wth an example wth Fg Accordng to C5, APs and -2-3 don t share any lnk. Accordng to C3, lnk 2-6 s shared by two BPs and havng same wavelength λ 2. Agan, followng C4, AP -2-3 and BP wth two dfferent wavelengths, share lnk -2. Two APs have same wavelength λ as per C6. Also, each of, path and f a vertex has no external neghbor n entry s - and f vertces not n path n t s undefned. We assume ntalze Edge (f,t), E where f= head and t= tal of path. Then v[0]=f, v[]=t and length=2, update store path accordngly. Repeat followng steps for (n-2) tmes. Steps: HCDH Algorthms: Hamltonan Crcut Fndng Algorthms(HCFA) : In algorthm s n vertex n undrected graph G(v,e), where vertces are numbered 0 to n-. It performs n number of teratons and each teraton program performs to extend path constructon. In th teraton, algorthm creates - edges wth path of length edges, when t complete teraton cycle and extend path.on Completon of nth successful teraton, Hamltonan Path generated n graph and next teraton t close path whch s called a Hamltonan crcut. If t unable to extend path due to falure of furr teraton (n+), proposed algorthm declare that no Hamltonan crcut exst and no survvable routng path found n physcal topology. a. If external neghbor of head s not n extend path along head to gven external vertex p. b. The new head generated from external vertex complete current teraton orwse goto step 2 2. If tal not - n extend path along tal to gven external vertex p. The external vertex p becomes new tal and complete current teraton orwse go to step If head and tal are joned by an edge, n cycle exst n current path v. We examne path vertces untl fnd a vertex v[] whose external neghbor entry s p -. Such a vertex s guaranteed to exst. Orwse our path would be dsconnected from rest of graph. If step 3 s successful to extend path, and n complete currents teraton, orwse go to step 4. Path extenson usng step and step 2 s called smple extenson and step 3 s called cycle extenson. To buld a new paths we apply steps 4 to 6, by rotatons to orgnal path untl fnd a path er smple smple extenson or cycle extenson n dfferent order. The sze of We defne a structure wth an array v[n] that allocaton path s sze of n2 and at dentfes number of vertces n path begnnng sze s 0. We calculate storage and t stores v[0] head to v[l-],tal. Every sze and number of paths from lst whch are vertex has a smallest external neghbor to

9 84 AP-BP par follows C and C2. calculated by applyng step 4 to Evaluatng all vertces to fnd successve path from lst to establshed new lnk wth teratng vertces, establshed path ncluded n lst and verfy path extenson through prevous steps. 5. Repeat step 4 to add new path and ncrement length lst and check path s extended or not through step 2/3 and complete teraton and go to next step Extendng path and ncrement present lst. G. Hamltonan Crcut Fndng Algorthms(HCFA) 2: We apply heurstc based nearest neghborhood approach n graph G wth n number of vertces and consderng each node as a startng node for Hamltonan crcut for maxmum cost for all vertces else mnmze degree of vertces and perform followng steps: 0. Dsjont Path Algorthms In order to fnd two lnk-dsjont lghtpaths for multple wavelengths, we may consder ntutve two-steps well-known Actve Path Frst (APF) algorthm of complexty 2 O(n ). Even f we have a polynomal tme dsjont par algorthm (Suurballe s algorthm). In APF, graph G and (s,d) par between whch dsjont pars wll be found, Actve Path (AP) and Backup Path (BP), f exst. APF s smple to mplement, runs fast [8] and successfully works n almost all dense graphs whch we consder n DWDM. But soluton fals n trap topologes [5],.e. t fals to fnd AP-BP par even f re s some. In real lfe, trap topology s of less mportance when we Step: Consder a vertces whch are vsted and consder v =p, apply teratvely vsted all vertces and calculate each unvsted neghbors wth mnmum η(c) and extend path untl teratvely t vste last vertex. Fnally t generate a path p0 wth vertces whch has no unvsted neghbors. 0. Shared Constrants Path Protecton In our algorthm, workng lghtpath l w and backup lghtpath l satsfy followng shared path b protecton constrants wth respect to exstng lghtpaths [6]. For same request: C. l and l are lnk dsjont. w b C.2 lw and l bmay have same or dfferent wavelengths. For dfferent requests: C.3 l and l +, where W-, can share both lnks b b and wavelengths on common lnk y traverse. C.4 lw and l b, where W, can share only lnks but not any wavelength on common lnk y traverse. C.5 l and l w + w, where W-, do not share any lnk between m as we want only one request to be affected by a sngle fber-cut. C6 l w and l + are dealng wth MAN. But n mdst of wavelength assgnments to dfferent requests, ntermedate graph may look lke one of trap topologes. 0.2 Path Mechansm Protecton In recovery process for WDM shared path protecton. Upon detectng a fber falure end nodes of faled fber send alarm messages to source node and destnaton node of connecton. Then source node sends a set-up message to destnaton node along backup route (whch s determned at tme of call setup) and confgures cross-connects at each ntermedate node. The destnaton node, upon recevng setup message, sends a w,

10 where W-, can have same or conf rm mess age back to sourc e node, dfferent wavelengths. thus completng recovery process [9][5]. 842

11 A good estmate of recovery tme complexty s provded n [9].. Wavelength Dsjont Paths Assgnment to We are concentratng on shared path protecton wth multple wavelengths. For sngle wavelength networks, a feasble soluton can be found usng Suurballe s algorthm [0]. The total cost of resultng two lnk-dsjont lghtpaths s mnmal among all such path pars. The algorthm runs n 2 O(n logn) tme, where n s number of nodes. For networks wth multple Algorthm. In frst algorthm, two dsjont routes are found usng Suurballe s algorthm and n wavelengths are assgned to m. In second algorthm, frst scan through each wavelength to fnd a par of lnk-dsjont lghtpaths usng Suurballe s algorthm. If Suurballe s algorthm fals search through each par of wavelengths for a par of lnkdsjont lghtpaths on dfferent wavelengths usng a two step approach. In [8], a heurstc called Enhanced Actve Path Frst (APFE) s dscussed where a bg weght M s assgned to Actve path (AP) when correspondng Backup path (BP) s not found. Then cost(ap) s found and compared to cost whch s ntalzed as zero. If t s less, n BP s taken as AP and newer BP s found by shortest path algorthm. It contnues untl ext condton acheves. But none of above papers provde guarantee to success. In [9],[0],[5], dfferent RWA heurstcs are presented wth path protecton. All of m have tred to avod most general but erroneous Actve Path Frst algorthm and so er soluton has become crtcal or can t provde solutons to each possble case of dsjont par. Along wth that, [6] provdes some condtons on mesh network to get dsjont paths wth some modfcatons to mesh network tself. wavelengths, we can apply ths algorthm on every wavelength to fnd same lghtpaths on same wavelength. However, f such paths do not exst, problem s to fnd two lnk-dsjont lghtpaths on two dfferent wavelengths [5]. In [5], t s proven that rrespectve of total cost of two lghtpaths, problem s NP-complete. Also, when we work on shared path protecton, we ll have two separate graphs on whch AP and BP wll be found. So, Suurballe s algorthm wll not work agan, snce t works on sngle graph. In [5], two RWA algorthms are dscussed: Route-Frst algorthm and Wavelength-Scan 2. Greedy Algorthm for Rng Networks Algorthm : Choose an ntal two-dmensonal State matrx (S_MAX [n][w] where n and w sgnfes edge and wavelength) whose all elements are zero. Where one dmenson s node & anor dmenson s wavelength. Take a two dmensonal traffc matrx (T_MAX [n][n]) whose elements are generated randomly keepng all dagonal element zero and upper dagonal element are same wth lower dagonal correspondng element. Take a lner array named Max Traffc (T_ARRY) Array whose elements are arranged n descendng order. We have to assgn se weghts to free path usng any free wavelength and assgn to correspondng path of State matrx. : Repeat up to step 3 for each element of T_ARRAY. 2: Repeat loop up to step 3. 3: Check shortest path and assgned to correspondng poston of state matrx n whch each lnk of path s free. If re s no such path go to step 2 to check wth next wavelength. Orwse go to step. 843

12 4: If re s no element n array n stop. Dynamc Programmng Approach Here connecton requests are ntated n some random fashon. At tme of request dependng upon avalablty of resources t may or may not be suffcent to establsh a lghtpath between sourcedestnaton edge node par. Each tme a request s made t should be examned wher request s feasble to accommodate request, f so, to perform routng and wavelength assgnment. If a request cannot be accepted because of lack of resources, t s blocked. A typcal approach to desgnng an effcent algorthm s to decompose problem nto twosubproblems: routng problems and wavelength assgnment problem. Consequently, most dynamc RWA algorthms for wavelength routed network consst of followng general steps:. Compute a number of canddate physcal paths for each source-destnaton edge node par. 2. Order all wavelengths n a wavelength lst. 3. Startng wth path and wavelengths at top of correspondng lst, search for a feasble path and wavelength for requested lghtpath. Usng Sngle Wavelength It s a specal case of lne network usng multple wavelengths stated below. In case of multple wavelengths number of wavelengths s w, but n case of sngle wavelength, value of w =. Hence algorthm s also same as multple wavelengths algorthm exceptng parameter w havng fxed value. 844 whch holds all traffc between each edge. At each step to establsh lght path between a par of node we take maxmum traffc between ths nodes drectly from traffc matrx or sum up traffcs of ntermedate edges. And we rake maxmum of se two values. To store lght paths already establshed, we take a state matrx S wth wxe, where n denotes number of nodes n network, w denotes number of wavelengths avalable and e denotes number of edges. Algorthm : For each wavelength, do Step 2 and Step 3. 2: Establsh lght path between P and P, where <j<=n; To establsh lght j path we take max T(,j), T(j,j-) + T(j, j-2) + + T(2,)}. If T(,j) s maxmum n store ths nformaton n matrx S only edge (,j) n correspondng row specfyng wavelength current wavelength usage. If sum of traffcs among ntermedate nodes s maxmum, n store ths nformaton n matrx S for all ntermedate edges. 3: Update traffc matrx correspondng to edges such t wll not be consdered for next wavelength. 4: If all wavelengths exhausted or all edges assgned wth lght path, n stop. Usng Multple Wavelengths In lne network, we have set of nodes such as P P P, P. We have to establshed lght, 2, 3, n path between P to P usng ntermedate n nodes. We take traffc matrx T of order nxn, Applcaton of Algorthm for Rng Network Here we propose an algorthm that optmally establsh lghtpaths n an optcal rng network usng a sngle wavelength λ. Assume that Q=p, p p, p..p, p s a rng network of n 2 + n nodes where P s set of nodes n network, traffc matrx s T and a sngle wavelength λ s avalable per lnk. We have to determne a vrtual topology that optmzes one hop traffc. We furr extend our algorthm for multple wavelengths per lnk. Let set of wavelengths avalable per lnk of rng network s M={λ, λ2,.., λw}. So

13 number of wavelengths avalable per lnk s M =w. Assume that rng network s Q and traffc matrx s T. Usng Sngle Wavelength In case of a rng network usng sngle wavelength s a specal case of multple wavelengths stated below. In case of multple wavelengths, number of wavelengths s w, but n case of sngle wavelength, value of w =. Hence algorthm s also same as multple wavelengths algorthm exceptng parameter w havng fxed value. Usng multple Wavelengths In rng network we have a set of nodes P,P 2, P 3,, P where P connected to P,P connected n 2 2 to P and so on and lastly P connected to P to 3 n form rng. Here we use algorthm 4.2. For each wavelength we splt each node P Our RWA algorthm usng dynamc programmng for rng network to maxmze one-hop traffc and smulaton results have shown that our algorthm ndeed provdes optmum one-hop traffc. Then we provded survvablty to a network by two approaches: one by desgnng a survvable vrtual topology and anor by shared path protecton mechansm. We also provde necessary and suffcent condtons both for exstence of survvable vrtual topology and alternate backup path for path protecton, on whch we desgn survvable RWA algorthms. Optcal network s manly used n WAN network, whch operates under DWDM methodology. Ths type of network suffers from multple fber lnks falure smultaneously n practcal.. So our future work conssts of desgnng a survvable RWA algorthm, whch provdes contnuous servce even after multple fber lnks falure. through P to make t a lnear network and n Conclusons apply algorthm 4.2. We note total one hop traffc for each teraton and fnally we consder assgnment of lght path for whch one hop traffc s maxmum. We terate above procedure for each wavelength and ultmately sum up maxmum traffcs. To desgn algorthm we take all assumpton of algorthm. Algorthm 2 : For each wavelength, repeat up to Step3. 2: For each node, splt node and make t a lnear network wth n+ number of nodes, where n denotes number of nodes n network. 3: Call algorthm 4.2 wth number of nodes n+. Make a record of assgnment of wavelength and one hop traffc. Go to Step2. 4: Take maxmum one hop traffc and update nformaton nto S matrx. 5: If all wavelengths are exhausted, n stop. Sum up one-hop traffcs for each wavelength. References. R.Ramaswam and K.N. Svarajan, Desgn for logcal topologes for wavelength routed optcal networks, IEEE journal of selected areas of communcaton, 4(5), June 996, pp R.Ramaswam and K.N. Svarajan, Optcal Networks: A practcal perspectve, Morgan Kaufmann Publsher, A. Mokhtar, M. Azzoglu, Adatve Wavelength Rou\tng n All-Optcal Networks, IEEE/ACM Trans. Networkng, Aprl 998, pp Zhensheng Zhang, Anthony S. Acampora, A Heurstc Wavelength Assgnment Algorthm for Multhop WDM Networks Usng Wavelength Routng and Wavelength Re-Use, IEEE/ACM 845

14 Transacton on Networkng, June 995, pp Ramesh Bhandar, Optmal Physcal Dversty Algorthms and Survvable Networks, IEEE, S. Yuan, Jason p. Jue, Dynamc Lghtpath Protecton n WDM Mesh Networks under Wavelength Contnuty Constrants, IEEE Globecom, C. Ou, J. Ghang, H. Zang, L. Sahasrabuddhe, B. Mukherjee, Near-Optmal Approaches for Shared Path Protecton n WDM Mesh Networks. 7. D. Zhou, S. Subramanam, Survvablty n Optcal Networks, IEEE Netwok, Nov/Dec R. Anderson, F. Chung, A. Sen, G. Xue, On Dsjont Path Pars wth Wavelength Contnuty Constrant n WDM Networks. 9. L. Sahasrabuddhe, S. Ramamurthy, B. Mukherjee, Fault Management n IP-Over- WDM Networks: WDM Protecton versus IP Restoraton, IEEE, Vol-20, No-, January J. W. Suurballe, R. E. Tarjan, A Quck Method for fndng Shortest Pars of Dsjont Paths, Networks, Vol.4, 984. Gabrel Nvasch, Hamltonan Cycles Fndng Algorthm. 2. Ashay Dharwadker, New Algorthm for Fndng Hamltonan Crcuts. 3. N.G.Das, Statstcal Methods. 4. Hongsk Cho, S. Subramanam, H. Cho. Loopback Recovery from Double Lnk Falures n Optcal Mesh Networks, IEEE/ACM Transactons on Networkng, Vol2, No.6, Dec L. Sahasrabuddhe, S. Ramamurthy, B. Mukherjee, Survvable WDM Mesh Networks, IEEE, Vol-2, No-4, Aprl