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Link-State Routing in Networks with Unidirectional Links LICHUNBAO J.J.GARCIA-LUNA-ACEVES [email protected] [email protected] ComputerEngineeringDepartment ComputerEngineeringDepartment UniversityofCalifornia UniversityofCalifornia SantaCruz,CA95064 SantaCruz,California95064 NetworkingandSecurityCenter SunMicrosystemsLaboratories PaloAlto,California94303 Abstract—Itisshownthataunidirectionallinkofanetworkcanbeused and various concepts and notation used throughout this paper. forroutingonlyifithasaninclusivecycle,whichisapaththatcancarry SectionIIIdescribesULP.SectionIVprovesthecorrectnessof routing updatesfromthedownstreamnodetotheupstreamnodejoined ULP. Section V addresses ULP’s performance, and Section VI bytheunidirectionallink.Anewroutingalgorithmfornetworkswithuni- directionallinksisthenpresented,whichincrementallydisseminateslink- presents the results of simulations ona network with 20nodes stateinformationandselectively utilizesunidirectionallinksinnetworks. used to compare ULP with topology broadcasting; the results Thenewalgorithmisverifiedtobecorrectanditscomplexityisanalyzed. showthatULPisamoreefficientapproachtosupportingrouting Simulationsona20-nodeunidirectionalnetworkshowthatthenewalgo- innetworkswithunidirectionallinks. rithmismoreefficientthantopologybroadcasting. II. NETWORK MODEL I. INTRODUCTION (cid:0)(cid:2)(cid:1)(cid:4)(cid:3)(cid:6)(cid:5)(cid:8)(cid:7)(cid:10)(cid:9)(cid:12)(cid:11) Anetworkismodeledbyadirectedgraph ,where Although many routing protocols and algorithms have been (cid:5) includes a set of nodes (routers) with a unique ID number, proposedandimplementedinthepast,thevastmajorityassume (cid:9)(cid:14)(cid:13)(cid:15)(cid:5)(cid:17)(cid:16)(cid:18)(cid:5) and isthesetofdirectedlinks. Abidirectionallink networkswithbidirectionallinks. However,unidirectionallinks between two nodes is represented by two unidirectional links. mayoccurinwirelessnetworksbecauseofradiolinkcharacter- (cid:3)(cid:20)(cid:19)(cid:21)(cid:7)(cid:23)(cid:22)(cid:24)(cid:11)(cid:26)(cid:25)(cid:27)(cid:9) (cid:22) Link if and only if can receiveinformation from isticsandinmixed-medianetworkswhen,forexamplesatellite (cid:19) . Weassumethelinklayerprotocoliswelldesignedsuchthat transponders are used. This paper focuses on routing in net- information can propagate through a link with positive proba- workswithunidirectionallinks. (cid:19) bility. Node is called the head or upstream node of the link McCurley and Scheider [5] presented a routing protocol for (cid:22) (cid:0) and is called the tail or downstream node. A cycle in is a networkswithunidirectionallinksbasedoncompletetopology directedpathwithdistinctnodesexceptforthestartingandend- information. The IETF working group on unidirectional link ingnodes. Aninclusivecycleforalinkisacyclethatcontains routing (UDLR) copes the unidirectional property of links in thelinkonitspath. the network by encapsulating and tunneling IP packets in the WeusethenotationintroducedinTableItorepresenttopolo- link layer, which migrates some routing functionalities to the gies,datastructuresandoperations. link layer and complicates the linklayer [1]. However,UDLR assumes that a detour for a unidirectional link exists to tunnel TABLEI IP packet in the reverse direction when the link is discovered. NOTATIONS In a mobile network in which every link can change in each direction, it is hard to guarantee that the detour for a unidirec- (cid:28)(cid:30)(cid:29) (cid:31) (cid:28)(cid:24)"(cid:6)(cid:31)$#&%(’ tionallinkexistorbenoticedatthetimetheunidirectionallink )+,.* -/ PLhinyksisctaaltelinokf(cid:28)0! (cid:29) (cid:31) reporte.dby1. isdiscovered.Therefore,UDLRcanonlysolvespecificcasesin 2 ,.* -/ Inclusivecyclefor(cid:28)0(cid:29) (cid:31) foundat1. whichthenetworkisstronglyconnectedandrelativelystable. 3 4 *,.-/ Discoverypathfor(cid:28)0(cid:29)(cid:23)(cid:31) at1. ErnstandDabbous[2]proposedacircuit-basedlink-stateap- 16587:9 Apathfrom1 to9 . proach for unidirectional routing. To find out a route to a des- 16) %;<>=:9 Theshortestpathfrom1 to9 .) 1(cid:24)5?7:9 Pathfrom1 to9 containslink . tination, a circuit including both source and destination is first @(cid:28)0(cid:29)(cid:23)(cid:31) @ (cid:28)0(cid:29) (cid:31) Thecostoflink . @ @ @ @ detected, thenvalidatedbysendinga validationmessagealong 1(cid:24)587A9 TC he cost of p@(cid:28)0at(cid:29)(cid:23)h(cid:31) @1B5?7 9 , i.e. 1B5?7 9 5 thecircuit. Ifavalidationsuccessfullygoesthroughthecircuit, ,>-/ED *GFIHKJ . L(cid:21)M abidirectionalcommunicationcanthusbeestablishedbetween * Thesetoflinkstatesaboutthenetworktopologyknown source and destination, using paths on the circuit. However, N6O L * Sbyhonrotedset1p.athroutingtreeofnode1 builtonL(cid:21)M *. P0M when the network grows larger, the number of circuits main- * Partialtopologygraphatnode1 forfindingdiscoverypath. L NQO L P0M tainedinthenetworkbecomesformidableandthealgorithmhas R * Shortestpathgraphofnode1 builton *. * Thesetof1’supstreamnodes. toresorttoadditionalmechanismsinordertoscale. P * Thesetof1’sdownstreamnodes. 4TSVUW48X 4(cid:24)S 4YX Inthispaper,weproposeandverifyULP(unidirectionallink Concatenationoftwopaths and . Z Z stateprotocol),alink-stateroutingalgorithmfornetworkswith =B[ implies[ . Z]\ Z [ isassignedthevalueof[ . unidirectional links. Section II introduces the network model ThisworkwassupportedinpartatUCSCbytheDefenseAdvancedResearch ProjectsAgency(DARPA)undergrantF30602-97-2-0338. Alinkstate^‘_8ab containsthefollowingparametersinaddition Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 3. DATES COVERED 1999 2. REPORT TYPE 00-00-1999 to 00-00-1999 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Link-State Routing in Networks with Unidirectional Links 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION University of California at Santa Cruz,Department of Computer REPORT NUMBER Engineering,Santa Cruz,CA,95064 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S) 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited 13. SUPPLEMENTARY NOTES 14. ABSTRACT 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 18. NUMBER 19a. NAME OF ABSTRACT OF PAGES RESPONSIBLE PERSON a. REPORT b. ABSTRACT c. THIS PAGE 6 unclassified unclassified unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 totheidentifiersoftheheadandtailofthelink: cycleisbrokenandnootherinclusivecycleisfoundforthelink, )),>-/>cd Linkcostoflink(cid:28)0(cid:29)(cid:23)(cid:31) ,),>* -/ cd 5 @(cid:28)0(cid:29) (cid:31) @. the head ofthe linkwould simply reset ^ (cid:129)(cid:130)E(cid:131) (cid:1) ˜ which starts ,>-/ cd(cid:10)e Inclusivecyclesize; ),>-/ ce(cid:23)f Sequencenumberofthelinkstate; anothersearchfortheinclusivecycleofthelink. ),>-/>cZEgEh Theageofthelinkstate; ) ) ,>-/>cijf Thesetofneighborsreporting ,>-/ . III. ULP Foranyroutingprotocoltoworkinanetwork,itisnecessary Recentroutingalgorithmsbasedonlink-stateinformation[3], foratwo-waypathtoexistbetweenanysourceanddestination [4]avoidtheoverheadofbroadcastingcompletetopologiesand ofroutinginformation.Therefore,foragivenunidirectionallink (cid:19)lk (cid:22) (cid:22) (cid:19) (cid:19) aresuchthatarouterpropagateslinkstateupdatesforonlythose ,theremustexistapathfrom to inorderfor toreceive (cid:22) links that it uses to reach destinations. ULP adapts the link- routinginformationfrom . (cid:19)mk(cid:24)(cid:22) vector algorithm (LVA) [3] to operate in networks with unidi- The inclusive cycle for link is the shortest path from (cid:22) (cid:19) rectionallinks.WithLVA,eachroutermaintainsitsownrouting to that can be defined for the link, and is represented by n (cid:1)o(cid:19)pk8(cid:22)(cid:26)qr(cid:22)tsuwvx(cid:19)A(cid:1)y(cid:19)zk.(cid:22){suwvx(cid:19) n treeandreportstoitsneighborslinkstateupdatesforthoselinks _8ab . That is, _8ab is the (cid:19)(cid:18)k|(cid:22) (cid:22) (cid:19) itusestoreachdestinations,aswellasforthoselinksitstopsus- concatenationoflink andapathfrom to . Incaseofa n (cid:1):(cid:19)}kI(cid:22)(q~(cid:22)lkE(cid:19)(cid:127)(cid:1)(cid:15)(cid:19)(cid:128)k$(cid:22)lkE(cid:19) inginitsroutingtree. bidirectionallink,wehave _8ab . ULP consists of three parts: Neighbor Protocol (NBR), Net- Itisobviousthatadownstreamnodeshouldnotbeusedasa work Routing Control Algorithm (NET) and Retransmission next-hop in routing if the inclusivecycle of the link is broken, Protocol(RET).NBRprovidesmechanismsforanodetodetect becauseoftheresultinguncertaintyregardingthelink. Theex- upstreamneighbors,updatecyclesizesofdownstreamlinks,and istenceofaninclusivecycleforalinkisindicatedbythecycle- propagatelinkstatesthatsatisfy(1). NETcalculatestheshortest size property of the link, which is the summation of link costs (cid:1)(cid:133)(cid:132)n (cid:132) pathtree(SPT)basedonDijkstra’salgorithmandsendschanges ontheinclusivecycle,i.e. ^_8ab?(cid:129)(cid:130)$(cid:131) _8ab . in SPT to upstream neighbors. RET keeps a list of packetsfor To find out the inclusive cycles for links, cycle discovery retransmissionupontimeout,untilitreceivesacknowledgments paths for each link are maintained and propagated in the net- fromtheirdestinationsordestinationsbecomenon-neighbors. work. A cycle discoverypath is the shortest path from the tail (cid:1)(cid:137)(cid:22)(cid:138)suVv(cid:140)(cid:139) ofthelinktothecurrentnode,denotedby (cid:134)E(cid:135)w(cid:136)_8ab for (cid:19)(cid:141)kI(cid:22) (cid:139) (cid:139) A. NeighborProtocol link atnode . Linksondiscoverypathsatnode compose (cid:0) (cid:139) (cid:25) (cid:0) (cid:0) discoverygraph(cid:142) of . Formally,^_8ab (cid:142) ifitsatisfies: Three data structures, (cid:142) , ¯ and (cid:142) , are maintained by (cid:136) (cid:136) (cid:136) (cid:136) (cid:136) NBR.¯ containsstatisticsfordetectingandmaintainingincom- (cid:132) (cid:132)6(cid:143) (cid:136) (cid:134)E(cid:135) (cid:136)_8ab ^_8ab?(cid:129)(cid:130)$(cid:131) (1) ing links. (cid:142) monitors outgoing (downstream) links and rec- (cid:136) (cid:19)(cid:144)k?(cid:22) ommendstheselinksforroutingaslongastheyhaveinclusive Suppose a link has cycle size ^‘_8ab (cid:129)(cid:130)E(cid:131) . It is enough to (cid:0) (cid:22) cycles. (cid:142) keeps link states that satisfy Eq. (1) to find their leteverynodewithinaradiusof^_8abT(cid:129)(cid:130)E(cid:131) from maintainacycle (cid:136) (cid:19)(cid:145)kG(cid:22) (cid:19) inclusivecycles. discoverypathfor sothattheheadofthelink, ,isinformed of the link state eventually. The cyclesize of the link is deter- A.1 LinkDetection mined by algorithm (2) when the link state with its discovery pathgetstothehead: WithNBR,anodeperiodicallybroadcastsaHELLOpacketto informneighborsofitsexistence. However,ifotherpacketsare (cid:3) (cid:132) _ (cid:132)$q (cid:11) if ^_8ab?(cid:129)(cid:130)E(cid:131)W(cid:146) (cid:134)$(cid:135) _8ab ^_8ab?(cid:129)(cid:130) sentoutduringtheintervalofHELLOpackets,thenextHELLO (cid:132) _ (cid:132)Eq (2) then ^‘_Yab (cid:129)(cid:130)E(cid:131)(cid:148)(cid:147) (cid:134)$(cid:135) _8ab ^‘_8ab (cid:129)(cid:130)(cid:30)(cid:149) packetissuppressed.UpondetectionofHELLOpacketsfroma (cid:19) (cid:139) (cid:19)˘kj(cid:139) (cid:19) neighbor bynode ,alink issetupand becomesoneof Fig. 1(a)showsanetworkwithunidirectionallinksandFig. ¯ . Withoutlossofgenerality,thecostofanactivelinkissetto (cid:136) (cid:1)(cid:14)˙ (cid:139) 1(b)showsthediscoverygraphfornoden9inthatnetwork. 1(^_8a (cid:129)(cid:130) ). Ifthelinkdisappears,^_8a (cid:129)(cid:130) issetto˜ by . (cid:136) (cid:136) (cid:150)(cid:154)(cid:153) (cid:150)(cid:6)(cid:153) (cid:150)(cid:6)(cid:155) (cid:150)(cid:6)(cid:155) A.2 CycleSize (cid:150)(cid:6)(cid:156) (cid:150)(cid:6)(cid:156) (cid:150)j(cid:151) (cid:150)j(cid:151) In ULP, both the head and tail of a link can originate link- (cid:150)j(cid:151)(cid:152) (cid:150)j(cid:151)(cid:152) state updates for the link. The cycle size of a link state is de- (cid:150)(cid:6)¡ (cid:150)(cid:6)(cid:157) (cid:150)(cid:6)¡ (cid:150)(cid:154)(cid:157) cided by the head of the link. The differences in link state at (cid:150)(cid:6)(cid:158) (cid:150)(cid:6)(cid:158) head and tail is resolved with the following algorithms. For a (cid:150)(cid:6)(cid:160) (cid:150)(cid:154)(cid:159) (cid:150)(cid:6)(cid:160) (cid:150)(cid:6)(cid:159) link (cid:19)(cid:127)k>(cid:22) , (cid:19) detects the inclusivecycleand determines ^_8ab?(cid:129)(cid:130)$(cid:131) , ¢£¥⁄(cid:20)ƒ¤§“'“«w‹“›flfi(cid:21)(cid:176)(cid:23)–†£G‡(cid:181)·G¶fl§ ¢•E⁄(cid:10)‚†„G”‘»G‹“…†§“›fl‰&(cid:190)†›¿£¿·fl(cid:192)(cid:181)£`'8´(cid:10)ˆ while (cid:22) accepts any change on cycle size made by (cid:19) for ^‘_8ab and generates a new link state with higher sequence number. Fig.1. DiscoveryGraph //Found2 ,.-/ inP0M , at(cid:28) . //Received)`,>, -/ . @2 , @.¨ ), ), ¨ )/ thrIonuitgihaloluyt, ^t_8heab?(cid:129)n(cid:130)Ee(cid:131) twisosrekt.toW˜hensoittshaintctlhuesilvinekcsytcalteeipsrofopuangdateast if()),.,.,, --//,>cc-d(cid:23)e(cid:23)/ef \5\ @,>)2,.,-,>,/-/-c/d(cid:23)ce e@;f)U(cid:18)(cid:201) ˚ ; if()),>,>// ,>--//-/ccd(cid:10)e(cid:23)cd(cid:10)ef e\\5 ),.,,>--// ccd(cid:23)d(cid:10)ee;)(cid:201) its hea(cid:22) d, the link state only propagates within a radius ^‘_8ab (cid:129)(cid:130)E(cid:131) ¸ propagate),>, -/ ; max(),., -/)`/ce f ,),>/ -/ ce(cid:23)f )+1; from . A link can be used for routing by its head only if the propagate ,>-/ ; ¸ cyclesizepropertyissettoafinitenumber,whichimpliesthat the head is able to know the state of that link. If the inclusive Procedureat(cid:28) Procedureat(cid:31) A link is used for routing by its head node or an upstream meansthattheoutgoinglinkdisappears. OutgoinglinksinIN- node only if the link has associated with it a finite cycle size. VALID and DISCONNECTING state cannot be used for rout- Therefore,thedecisionofcyclesizebytheupstreamnodeper- ing. mits the node to enact a correct response when the inclusive A.4 Link-StatePropagation cycleofthelinkisbrokenandtheupstreamnodehasnoinfor- mationaboutthestateofthelink. InsectionIV, weprovethat (cid:19) The set(cid:19)of lin(cid:21)ks(cid:20) that satisfy Eq. (1) at node (cid:139) is denoted by (cid:23)(cid:22) (cid:1) $(cid:19)(cid:138)k (cid:22)z(cid:132)(cid:18)(cid:132) (cid:132)(cid:209)(cid:143) theupstreamnodeanddownstreamnodeholdequivalentviews (cid:142) ,i.e., (cid:142) (cid:134)E(cid:135)w(cid:136)_Yab ^(cid:154)_Y(cid:136) ab (cid:129)(cid:130)E(cid:131) . Thissetoflinks (cid:136) (cid:136) about the link between them (Lemma 1). That is, they either and other links on the discovery paths of these links compose reliably exchange link-state updates in NBR and NET, or stop º(cid:148)Ø(cid:236)Œ(º (cid:136),i.e(cid:24).,(cid:20) (cid:19) (cid:26)(cid:25)(cid:28)(cid:27) (cid:19) coordinatinglink-stateinformation. (cid:22) (cid:1) (cid:132)(cid:24)(cid:3) (cid:25) (cid:11) T(cid:19)}kE(cid:22)(cid:128)(cid:25) (cid:3) (cid:25) (cid:11) º(cid:12)Ø(cid:236)Œ(º ^ ^ (cid:142) (cid:142) ^ (cid:134)$(cid:135) (cid:136)_8ab (3) (cid:136) (cid:136) (cid:136) A.3 NeighborStates The collection of discovery paths from upstream nodes is comThinegulpinstkrse.aTmhneosdtaetetasbolfea¯n(cid:136)uaptstnroeadme (cid:139)niesiguhsbeodrtaoremiollnuisttorratiend- ic.ael.l,edthediscoverygraph,whichwedenoteby(cid:142) (cid:0) (cid:136) fornode(cid:139) , inFig. 2. (cid:30)(cid:29) (cid:31) (cid:0) (cid:1) (cid:204)$˝˛jˇ(cid:209)—6(cid:210) (cid:142) (cid:31)! (cid:1)"(cid:1)# º(cid:12)Ø(cid:236)Œ(º (4) (cid:136) WAITING (cid:204)$˝˛jˇ(cid:209)(cid:211).(cid:212)‘(cid:213)(cid:214)ˇ(cid:216)(cid:215)(cid:6)˛ INVALID (cid:0) (cid:217)`˛†(cid:218)‘(cid:219)(cid:220)j(cid:221)(cid:20)˝(cid:222)¿(cid:215) (cid:142) (cid:136) ispropagatedt(cid:0)ofindinclusivecyclesoflinks.Dijkstra’s (cid:223)j(cid:224) (cid:218)‘(cid:219)(cid:215) (cid:217)G˛j(cid:218)‘(cid:219)(cid:220)†(cid:221)(cid:20)˝(cid:222)¿(cid:215) (cid:204)$˝˛jˇ algorithmisrunon(cid:142) tofindtheshortestpathstothetailsof (cid:231)$(cid:213)(cid:6)(cid:220)†˛j(cid:226) (cid:223)j(cid:224) (cid:218)‘(cid:219)(cid:215)T(cid:211)>(cid:212)‘(cid:213)(cid:214)ˇ(cid:216)(cid:215)(cid:214)˛ (cid:211).(cid:212)‘(cid:213)(cid:214)ˇ(cid:216)(cid:215)(cid:214)˛ linksandtodecidewhe(cid:136)therlinkssatisfy(1)sothatupdatesfor theselinksarepropagated. NEW Æ (cid:215)(cid:214)˛j(cid:226) (cid:223) (cid:213)(cid:6)ª&(cid:210)(cid:10)(cid:219)(cid:215)(cid:214)(cid:228)+(cid:215) Æ†(cid:229)$(cid:230) CONNECTED Changes in º(cid:148)Ø(cid:236)Œ(º (cid:136) are broadcast to downstream nodes and all CONNECTED downstream nodes are required to acknowl- edge the update; otherwise, the update packet is retransmitted Fig.2. StateTransitionsofUpstreamNode byRET.Sincethesetofdownstreamnodeschangesfrequently The WAITING state of an upstream node (cid:19)(cid:2)(cid:25) ¯ indicates inamobilenetwork,linksthatsatisfyEq.(1)andtheircomplete thatthelink(cid:19)KkŁ(cid:139) hasbeendetectedby(cid:139) butisstillunno(cid:136)ticedby(cid:19) . discoverypathsarealwayspackedintothesamepackettoavoid AWAITINGnodebecomesNEWwhenn _8a isfoundby(cid:19) and fragmentedviewofdiscoverypathsbynewdownstreamnodes. thenewlinkstatewithfinite^‘_8a (cid:129)(cid:130)E(cid:131) isreceive(cid:136)dby(cid:139) ,whosendsa TheformatofNBRpacketisdepictedbyFig. 4,andalink-state completeØKŒ(º to(cid:19) .Then,the(cid:136)stateof(cid:19) switchesfromNEWto entryisillustratedinFig. 5. (cid:136) CONNECTEDandstaysinthatstateasfarastheinclusivecycle (cid:143) is maintained (^_Ya (cid:129)(cid:130)$(cid:131) ˜ ). Updates in Ø(cid:236)Œ(º are sent to an Transmitter ID Packet Seq # (cid:136) (cid:136) upstreamnodereliablyonlyifitisinCONNECTEDstate. An Dest # Link State # upstream nodein CONNECTEDstategoes backto WAITING Destinations state if the inclusive cycle is broken. An upstream node (cid:19) in Link States (cid:19)(cid:128)kE(cid:139) INVALIDstatemeansthelink disappears. Fig.4. PacketFormatsforNeighborProtocol (cid:237)`(cid:238)†(cid:239)‘(cid:240)æj(cid:242)(cid:20)(cid:243)(cid:244)¿ı (cid:246)(cid:216)(cid:247) (cid:239)‘(cid:240)ı?ł$ø(cid:214)æj(cid:238)†œ ß(cid:255)(cid:1)ı(cid:214)(cid:0)(cid:238)jœ(cid:254)+øT(cid:246) (cid:254)(cid:6)ø(cid:10)(cid:5)j(cid:9)(cid:11)ı(cid:8)(cid:3)(cid:10)(cid:7)$(cid:240)ı(cid:214)(cid:253) N(cid:254)+(cid:243)ı(cid:240)EW(cid:237)G(cid:246)j(cid:238)j(cid:247)(cid:239)‘(cid:239)‘(cid:240)(cid:240)æjıT(cid:242)(cid:154)ł$(cid:243)(cid:244)¿ø(cid:214)ıæj(cid:238)jœ (cid:12)(cid:17)(cid:13)‘ø(cid:10)(cid:15)(cid:216)(cid:252)$ı(cid:214)(cid:238)(cid:243)(cid:238)(cid:16)(cid:15) INVA(cid:252)$(cid:12)(cid:14)L(cid:243)I(cid:13)(cid:238)(cid:18)D(cid:10)(cid:15)(cid:15) Head ID Tail ID$&A%(’(cid:4)g)+e *(cid:14)C,.o-.s,0t/213C’(cid:4)yc,046l5e SizeLS Seq# ‘ø (cid:216)ı(cid:6)(cid:238) Des78t/(cid:8) 9(cid:10)I,0D%(’:-(cid:18)N,0e%<;=x’>t 13H’(cid:4)op,046 5ID CONNECTED (cid:237)G(cid:238)j(cid:239)‘(cid:240)æj(cid:242)(cid:154)(cid:243)(cid:244)¿ı DISCONNEC(cid:1)T(cid:0)ING (cid:12)(cid:14)(cid:246)j(cid:13)(cid:247)(cid:10)(cid:239)‘(cid:15)(cid:240)ı (cid:2)(cid:4)(cid:3) ß ı(cid:214)(cid:238)jœw(cid:252)$(cid:253)(cid:23)(cid:6)(cid:242)(cid:20)(cid:5)(cid:254)$(cid:8)(cid:255)(cid:7) ‘ø (cid:216)ı(cid:214)(cid:238) (cid:10)œ(cid:10)(cid:253) (cid:254)+ıT(cid:254)+øT(cid:254)jı $(cid:253) (cid:243)(cid:240) Fig.5. EntriesinNeighborPacket Fig.3. StateTransitionsofDownstreamNode B. RoutingAlgorithms A downstream node table (cid:142) is also maintained for outgo- (cid:136) inglinks(Fig. 3). AdownstreamnodeisinitializedINVALID, InULP,theshortestpathtree(Ø(cid:236)Œ(º )ofthenetworkiscom- (cid:139) (cid:139) andentersNEWstateiftheinclusivecycleisfoundat ,when puted using Dijkstra’s algorithm on the topology graph. Any (cid:0) sendsacomplete(cid:142) tothatdownstreamnodereliably. After- change in Ø(cid:236)Œ(º is updated reliably at its CONNECTED up- (cid:136) wards, the downstream node becomes CONNECTED and the stream neighbors. An operation code (OpCode) is affixed to downstream link in CONNECTED state is given to NET for each link-state entry in the update packet, If the link state is routing. If the inclusive cycle of the outgoing link is broken, added or updated in the routing tree, the OpCode is set UP- theCONNECTEDdownstreamnodeenterstheDISCONNECT- DATE.Ifalinkstateisdeletedfromroutingtree,theOpCodeis ING state, until another inclusive cycle is found to change the setDELETEtoindicatetoupstreamnodesthatthelinkstateis nodebacktoNEWstate. AdownstreamnodeinINVALIDstate nolongerusedforrouting. B.1 TopologyGraph B.2.a LinkCostChanges:. Thecostofalinkismonitoredby thetailofthelinkinNBR.Linkcostchangesarepropagatedin For the purpose of routing, NET maintains a topological (cid:0) ? (cid:0) (cid:139) NBRreliablybecausetheupstreamlinkispartofº(cid:12)Ø(cid:236)Œ(º accord- graph(º )andaroutingtable( )ateachnode. º atnode (cid:136) ing to Eq. (1) and changes in º(cid:148)Ø(cid:236)Œ(º are propagated to CON- containsthe Ø(cid:236)Œ(º sofitsdownstreamnodesandinformationin (cid:0) NECTEDdownstreamnodesreliably. Thenewlinkstatekeeps (cid:142) (cid:136) ,i.e., (cid:29) (cid:31) &B propagatingaslongasthelinksatisfiesEq.(1), andeventually (cid:0) (cid:1)(cid:14)(cid:3) (cid:11) (cid:0) º (cid:31)@ (cid:23)A:# Ø(cid:236)Œ(º (cid:142) (5) the head of the link is informed of the new link state by NBR. (cid:136) (cid:136) (cid:0) (cid:0) (cid:0) Because (cid:142) is part of º by Eq. (5), º also receives the (cid:139) (cid:0) newlinkstate, whichcausesanothercalculationof Ø(cid:236)Œ(º using Node uses (cid:142) (cid:136) tosenditscomplete Ø(cid:236)Œ(º (cid:136) toDaC&nE upstream Dijkstra’s algorithm. Modifications to Ø(cid:236)Œ(º at a node are sent nodeinNEWstate,sincelinkstatesontheinclus(cid:31)ivecyclemay reliablytoallCONNECTEDupstreamroutersofthatnode,and (cid:139) (cid:7) :(cid:25) nuosetdbfeorrerpoourttiendgbtoyno’sdedsouwnnrsetarcehamablneobdyes(cid:142). (cid:0)Ø(cid:236)Œ(. º (cid:142) (cid:136) is everynodeusing^_8a(cid:136) isnotifiedofthemostrecentlinkstate. (cid:136) (cid:139) The shortest path routi(cid:0)ng tree Ø(cid:236)Œ(º (cid:136) of node is not repre- B.2.b Cycle Size:. The cycle size of a link is monitored by sentedseparatelyfromº (cid:136); itis(cid:0)indicatedbyanonTreetagin itsheadinNBR.Modificationsto (cid:142) (cid:0) resultinre-inspectionof eachlinkstatedatastructureofº (cid:136). Theroutingpathtoades- everydQoEwnstreamlinktoseeifits(cid:31)cycRleEsizechanges. Consider tinationmustuseadownstreamneighborasthenext-hoponlyif (cid:139)0k (cid:1) (cid:137)suwv (cid:139) lin(cid:31)k , the discovery path (cid:134)E(cid:135)w(cid:136) a and li(cid:31)nk cost thedownstreamneighborreportstheremainingpathtothesame E (cid:0) =E (cid:136) ^(cid:154)(cid:136)a (cid:129)(cid:130) in (cid:142) are combined to decide the cycle size ^(cid:154)(cid:136)a (cid:129)(cid:130)E(cid:131)(cid:31). If destination. Ø(cid:236)Œ(ºF(cid:136) i(cid:20)srepresentedby (cid:132)(cid:26)(cid:136) su(cid:209)v (cid:139)I(cid:132)IqA(cid:132)(cid:139)(cid:136) k ¤(cid:132)(cid:24)(cid:143) ˜ andisdifferentfromtheoldon(cid:136)e,^ a (cid:129)(cid:130)E(cid:131) (cid:136) Ø(cid:236)Œ(G º (cid:27)(cid:4)G(cid:136) E(cid:138)(cid:1) C(cid:25) IH(cid:142)^ (cid:25)J(cid:132)(cid:136) ^(cid:3)(cid:20)E(cid:141)(cid:139)(cid:236)(cid:1):suVsuwv(cid:19)}v kI(cid:22)w(cid:22)˘(cid:22) (cid:7)(cid:1)AKH (cid:139)(cid:25) k@E˘suwv (cid:31) B(cid:19)(cid:128)kE(cid:22) (cid:0) (cid:11) (cid:22) is(cid:132)sE{traessuwasmvxignn(cid:139)Ieo(cid:132)8ddq(cid:133)eths.e(cid:132)(cid:139)]nIk(cid:1)feE¤wth(cid:132)(cid:236)ei(cid:1)nicnlc˜ulsuivsîeva(cid:31)ce(cid:129)y(cid:130)Ecc(cid:131)pylec(cid:147)lseizfeõranlaidnndkpraô(cid:136)(cid:136)npa(cid:31)oatgihsaetbrerdsoetkoaerdnco,hwi.feon.r-, ^ ^ Ø(cid:236)Œ(º (cid:142) (cid:136) inclusivecyclebeginsinthe(cid:136) network. B.2.c LinkDeletion:. Adownstreamnodeindicatesthedele- Transmitter ID Source ID tion of a link state by setting the cost of the link to ˜ . The Packet Seq # newlinkstateispropagatedbyNBRtoallCONNECTEDdown- Dest # Link State # streamnodesreliably,andgetstotheheadofthelinkeventually. Destinations Because no updates to a deleted link will be generated there- Link States after,thelinkstateiserasedfinallyfromalltopologygraphsby aging.Thedeletionofalinkstateduetoagingisnotpropagated Fig.6. PacketFormatsforRoutingPacket toneighboringnodes. Whenadownstreamnodeisdeleted, all linkstatesreportedbythatnodeshouldbedeleted.Thedeletion Whenever Ø(cid:236)Œ(º changes, a routing packet containing the of a link state reported by a specific node simply deletes that (cid:136) routing changes with operation codes is sent to all upstream node from reporting the node set of the link. A link ^ is com- (cid:139) (cid:0) neighbors of inCONNECTED state. Therouting packetfor- pletelyerasedfromº whenitsreportingnodesetisempty.If (cid:136) mat is presented in Fig. 6. Since ¯ may contain several up- thedeletionofalinkcauses Ø(cid:236)Œ(º tochange,thosechangesare (cid:136) stream nodes and an update packet takesseveral hops to reach reportedtoupstreamnodesinCONNECTEDstate. theseupstreamnodes,asingleupdatepacketisconstructedwith destination and next-hop information. Only those downstream C. RetransmissionProtocol nodes whose address is one of the next-hop addresses in the packetprocessorforwardthepacket.Thepacketlatersplitsinto Update packetsof both NET and NBR require reliable trans- severalpacketsonthewaytoupstreamnodesbecause pathsto mission to CONNECTED upstream nodes and CONNECTED these upstream nodes may divergeat some points. This mech- downstream nodes, respectively. The retransmission protocol anism avoids that every downstream node tries to forward the (RET)providesthemechanismtokeepthesetwotypesofpack- packettoupstreamnodesandmultiplecopiesbegenerated. ? (cid:139) etsandretransmitthemtoneighboringnodesiftheyarenotac- Therouting table atnode isa vectorofentriescontain- (cid:136) ML knowledgedupon time-outs. The time-out value is set propor- ingfollowingi=nLformationderivedfromN ØKŒ(º (cid:136): destination (cid:134) (cid:131) , tional to the cycle size of the link between neighbors in CON- distance(cid:134) to(cid:134) (cid:131) andnext-hopaddress . NECTEDstate. (cid:0) (cid:0) Giventhatlinkstateskeepchanginginº and(cid:142) ,packets B.2 InformationProcessing (cid:136) (cid:136) inRETonlyspecifylink-stateidentifiers,whichare(head,tail) Most link-state algorithms use sequence numbers to decide pairs. Destination entries of packetsare also saved in the RET which link state updates are up to date. In ULP, we assume packetlist,aslongasthosedestinationsareCONNECTED.Ifa a simple sequence number scheme for updating link states. A neighborturnsintoastateotherthanCONNECTED,thatneigh- (cid:25) (cid:0) liPnkO state ^ is coNnsidered moNre recent than the one in º if borisdeletedfromdestinationentriesofpacketsintheretrans- (cid:25) (cid:0) (cid:0) (cid:136) (^ º ^ (cid:129)“(cid:131) (cid:146) º (cid:129)^ (cid:129)“(cid:131) ). Anewlinkstateisupdatedin missionlist. Ifapacketwaitingforretransmissionhasnodesti- (cid:0) (cid:136) (cid:136) º accordingtothethreecasesdiscussedbelow. nation,itisremovedfromretransmissionqueue. (cid:136) IV. CORRECTNESS OF ULP Theorem4: WhenULPstabilizes,thereisnoloopinnetwork routing. Lemma1: Theknowledgeaboutthe linkat its head and tail Proof: We prove the claim by contradiction. Assume that isequivalent. (cid:139) U (cid:139) (cid:19) (cid:22) there exists an implicit loop at in routing to . Since runs Proof: Considertwonodes, and ; therearefourpossible !E (cid:139)(cid:21)(cid:16)suwE v Dijkstra’salgorithmbasedonlocaltopologyinformation, cases to consider, based on the link cost ^‘_Yab (cid:129)(cid:130) and cycle size U (cid:25) E (cid:139)(cid:181)suwv JU (cid:1):E (cid:139) k (cid:141)suwv U (cid:7) (cid:18)(cid:25) 1^_8.ab?^(cid:129)_8(cid:130)Ea(cid:131)b8(cid:129)o(cid:130) f(cid:143)aliñksGtate(cid:27) ^n_8_8abab: (cid:25)(cid:2)(cid:0) , which means an inclusive cy- (cid:142) (cid:136),(cid:26)Ø(cid:236)Œ(su(cid:209)vº (cid:136) cU o(cid:25)ntaØ(cid:236)(cid:139)inŒ(sXº n(cid:31)Vo. lSoionpc.eA(cid:139) s(cid:25)(cid:127)Osu(cid:139)(cid:21)msu(cid:209)ev U ,(cid:27) (cid:139) (cid:25)k<OV (cid:141)(cid:25)WsuVE(cid:141)v suVvU . U tcolegeextitsotstfhNoeroththeelrinokn.eCbhyaNngBeRs,tsoin^c_8eab (cid:22)atNacbcoethpts(cid:19) â_8_nabd(cid:129)(cid:130)E(cid:22) (cid:131) arreegaabrdle- (cid:139) (cid:25)OA(cid:135)sasuVsvsumU ebdu,t(cid:139)(cid:30)ssu(cid:209)tv(cid:25)ay˘sUosuwn(cid:1)v arUo.uk(cid:23)tBVzinesuwgcavluosoeUp,the(cid:135) algorithmsta,bwilihzeerse, less ^_8_ ab (cid:129)(cid:131) and always increases ^_8abT(cid:129)(cid:131) . Because (cid:19) updates we know(cid:139)(cid:8)(cid:25)thatsuw(cid:135) v U (cid:135) by(cid:139)its(cid:25)O defisuwnv itiUon, whicTh ^_8ab only if there is a differencebetween ^_8ab?(cid:129)(cid:130)$(cid:131) and the actual implies (cid:135) . Thiscontradictswith (cid:135) . inclusivec(cid:143) ycle,(cid:19)G annd(cid:22)Sg(cid:25)AOetc(cid:0) onsistent^_8ab inthiscase. V. PERFORMANCE EVALUATION 2. ^‘_8ab (cid:129)(cid:130) ˜ _8ab , which means the link exists but theinclusivecycleisbroken. Sincethebrokenlinkpropagates The communication complexity of NBR can be analyzed downthepathoninclusivecycleandgetsto (cid:19) ,(cid:19) resetsthecy- probabilistically. Assume the probability of link-state changes clesizeandpropagatesthenewlinkstateto(cid:22) . (cid:22) becomesDIS- atanytimeforeverylinkis(cid:135) ,thecommunicationcomplexityof CONNECTING downstream node of (cid:19) and (cid:19) is a WAITING NBRwithY inatimeunitintermsofnumberoflinkstatespropa- upstream neighbor of (cid:22) . RET at (cid:19) keeps sending the new link gatedis: (cid:22) (cid:22) (cid:14)] ] stateto forlimitedtimestoinsurethat getthenewlinkstate Z(cid:23)[(cid:10)\ becauseacknowledgmentfrom (cid:22) isunabletoreach (cid:19) . (cid:19) and (cid:22) (cid:1) (cid:135) k (cid:1)^ #g!hi ‘_g!hi!lmDn (cid:132)(cid:134)$(cid:135) (cid:136)_8ab (cid:132) (6) stopcoordinatingG li(cid:27)nk-stateupdatesafterafinitetime. (cid:136) acbdfe _(cid:145)a(cid:23)bb=j>k (cid:1) n (cid:25) (cid:0) 3. ^‘_8ab (cid:129)(cid:130) ˜ _Yab ,whichmeansthelinkisbroken. Inthiscase,thenewlinkstateispropagateddowntheinclusive (cid:19) Forexample,supposeeverylinkhaslinkcostof1andinclu- cycleinNBR,and getstoknowthelinkstatewithinfinitetime (cid:19) (cid:22) sivecyclesizeof3,everynodehasin-degreeof2andeverytwo afterthelinkdisappearance. Both and areinINVALIDstate nodeswithintwohopsaredistinct,thenthelinkstateispropa- ateachot(cid:1)her. G n (cid:25)(cid:18)O (cid:0) gatedwithinlimitedpdoriqstJanocesso(cid:23)btyvNuBRs,o(cid:14)awndthexcomu(cid:14)ymunication 4. ^_8ab8(cid:129)(cid:130) ˜ _8ab ,whichmeansthelinkisbrokenand complexityis(cid:135) kj(cid:3)(cid:23)˙](cid:16) Qq (cid:30)(cid:16) Vq (cid:148)(cid:16) $(cid:11)6kI(cid:132)(cid:9) (cid:132)8(cid:1) (cid:145)k(cid:135) kI(cid:132)(cid:9) (cid:132) for the inclusive cycle also breaks before the new link state prop- (cid:19) (cid:19) thenetwork,becausenewlinkstateswiththeirdiscoverypaths agates to . In this case, since knows the exact information (cid:22) (cid:19) (cid:19) arepropagatedwithintwohops. about ^‘_8ab (cid:129)(cid:130)E(cid:131) , is i(cid:22)n D(cid:19) ISCON(cid:22) NECTINGstateat and is in ThecommunicationcomplexityofNETisdifficulttoestimate INVALID state at . and do not coordinate link-state up- T whenthenetworkroutingisalreadyestablishedandlinkstates dates. change randomly. However, the overall communication com- Lemma2: An upstream node reliably gets the shortest path plexityoftheroutingalgorithmatnetworkstart-upcanbeesti- treeofitsdownstreamnodesinCONNECTEDstate. matedbyEq.(7),becausethedownstreamnodeofalinksends Proof: In NBR, an upstream node is CONNECTED at the itscompleteØKŒ(º throughpathontheinclusivecycletotheup- downstreamnode if the linkhas a finite inclusivecycle, which streamnodewhentheinclusivecycleofthelinkisfoundatthe Y impliesthatitisadownstreamnodeatitsupstreamnode. Since (cid:5) upstreamnode,andeachroutingtreeØKŒ(º contains entries. bothupstreamnodeanddownstreamnodeholdequivalentlink ] Z(cid:23)z0{ state about the link between them (Lemma 1), they are both in (cid:1)(cid:133)(cid:132)(cid:5)(cid:138)(cid:132)|k k (cid:23)_ a(cid:1)k lmDn j}| (cid:3) ^ (cid:129)(cid:130)E(cid:131) u ^ (cid:129)(cid:130) (cid:11) (7) CONNECTED state at each other. Thus, link-state updates in the Ø(cid:236)Œ(º of the downstream node are transmitted to the upstreamnode. ByRET,theupdatepacketkeepsbeingtransmit- Tocomparetheefficiencyofdatacommunicationinthenet- ted,untilitisacknowledgedbytheupstreamnodes. Therefore, work,weintroducetheconceptofroutingweighttocomparethe the upstream node reliably receives updates of Ø(cid:236)Œ(º from iTts data traffic cost that results from different routing algorithms. downstreamnodesinCONNECTEDstate. Theroutingweightisthesummationoffinitedistancestoother Theorem3: ULPstabilizeswithinafinitetimewhenthenet- nodes at every node in the network. It provides a comparable worktopologystopschanging. metricfor efficiencyofbidirectionaland unidirectionalrouting Proof: After any sequence of topology changes in the net- algorithms when the network has the same connectivity from (cid:127)~ (cid:127)~ work,boththeheadandtailofalinkkeepequivalentlinkstate both bidiqrectionaq l anqd unidiretctionalt point ts of view. Two net- (cid:0) (cid:1)(cid:27)(cid:4)(cid:128)(cid:130)(cid:3)(cid:6)(cid:5)(cid:129) (cid:7) (cid:11) (cid:0) (cid:1) (cid:3)(cid:6)(cid:5) C (cid:7) (cid:11) (cid:128) by Lemma 1, and every upstream node receives link-state up- works q antd havqe the same con- (cid:128) &(cid:5) v (cid:5) w(cid:19)(cid:21)(cid:7)(cid:23)(cid:22)z(cid:25)t(cid:5) (cid:181)(cid:3)(cid:20)(cid:22)(cid:24)(cid:11) dates from its CONNECTED downstream nodes by Lemma 2. nectivityif t suchthat , isreachq - (cid:181)(cid:3)(cid:20)(cid:19)&(cid:11) (cid:0) (cid:22) (cid:19) (cid:0) Since a node stops propagating a link state once it already has ablefrom in ifandonlyif isreachablefrom in . up-to-date link-state information, the propagation of an up-to- A higher routing weight indicates that longer paths are used, date link state happens only once at each node. By our finite which is less efficient. By enabling the use of unidirectional modelofanetwork,itisfinitetimetostabilizecoordinationof links into a network routing protocol, we can shorten the dis- link-stateupdatesbetweenneighboringnodes. Thatis,thetime tancefordatatrafficfromsourcetodestinations. Ifweassume forstabilizingthedistributedalgorithmisfinite,andULPstabi- eachnodegeneratesequaltraffictoeveryothernodeswithuni- T (cid:131) lizeswithinafinitetime. formrate , thecost ofnetworkdatacommunication withina Y timeunitwouldbe: 600 800 d(cid:18)(cid:132) { (cid:132) (cid:1) (cid:131) k I(cid:133)](cid:134) (cid:1)^ ? (cid:134)(cid:136) (cid:129)(cid:134) (8) # New LS240000 UEOLPSPF # Packets460000 (cid:136) 0 200 whichisproportionaltotheroutingweightofthenetwork. 0 10 20 30 40 50 0 10 20 30 40 50 Link Addition Link Addition 100 800 Fig. 7isasamplenetworkwithunidirectionallinks. Within tthioenanletlwinokrsk,soa sthpaatnnLiVnAg tcreaencwoonrnkecctosrarellctnlyodienstwhiisthnbeitdwiorerck-. # New LS 468000 # Packets460000 If any link on this bidirectional links breaks, LVA is not com- 20 200 parable with ULP. Therefore, we only illustrate the advantage 0 10 20 30 40 50 0 10 20 30 40 50 Link Deletion Link Deletion of ULP overLVA bycalculating routing weightswhen nolink 100 700 borfeLaVkAs.iAss1s8u9m8,inwgheilveetrhyelirnokuthinagswaeuingihttcoofstU,tLhPeirso1u5ti3n0g;wheenigchet, New LS 50 Packets560000 efficiencyisimproved20%overLVA. # # 400 Ingeneral,assumingthesamenumberoflinksinthenetwork, 0 300 0 10 20 30 40 50 0 10 20 30 40 50 unidirectionallinkdecreasesnetworkloadbyshrinkingthedis- Link Cost Increased by 1 Link Cost Increased by 1 1000 1000 tancefromonenodetotheotheraccordingtoEq.(8). However, tnheetwcoomrkmisunmicoaretiothnaonvtehrahteoafdboindiNreBcRtioannadlNnEetTwionrkundiudeirteoctlioonnga-l # New LS 500 # Packets 468000000 haulneighboringrelationshipasimpliedbyEqs.(6)and(7). 0 200 0 5 10 15 20 0 5 10 15 20 Node Addition Node Addition VI. SIMULATIONS 300 800 ingOlbovnigo-uhsalyu,lUnLePighcobnosrurmeleastimonosrheinpestwthoarnkrtreasnosuirtcioensamlarionuttaiinng- # New LS120000 # Packets246000000 algorithms that operate over bidirectional links only, where a 0 0 node’sneighborhoodlieswithinonlyone-hopdistance. 0 5 10 15 20 0 5 10 15 20 Node Deletion Node Deletion We simulated an ideal link-state algorithm based on OSPF, Fig.8. SimulationResultsona20-NodeUnidirectionalNetwork called EOSPF (extended OSPF), whose neighbor protocol in- corporates unidirectional links like ULP does. The difference betweenULPandEOSPFisthatEOSPFusesfloodingtoprop- VII. CONCLUSION agate link-state updates to all CONNECTED upstream nodes, Our contribution in this paper is the introduction of the whileULPselectivelysendlink-stateupdatestoCONNECTED inclusive-cyclesizepropertyofalinkstate, whichisanimpor- upstreamnodesifthelink-stateupdatesresultindifferentrout- tant criterion in routing and link-state maintenance. We also ingpaths. (cid:135)(cid:10)(cid:148) definedtheconceptofroutingweightasameasureforevaluat- (cid:135)(cid:10)(cid:136) ingtheefficiencygainedwithroutingalgorithmsthatcanincor- (cid:135)(cid:18)(cid:137)(cid:146) (cid:135)(cid:16)(cid:137)(cid:140) (cid:135)(cid:16)(cid:137)(cid:136) porate unidirectional links over similar algorithms that require (cid:135)(cid:16)(cid:137) (cid:135)(cid:10)(cid:141)(cid:142)(cid:135)(cid:10)(cid:143) (cid:135)(cid:18)(cid:137)(cid:138) bidirectionallinks. (cid:135)(cid:18)(cid:137)(cid:143) (cid:135)(cid:18)(cid:137)(cid:141) Although ULP requires less overhead than EOSPF in net- (cid:135)(cid:18)(cid:137)(cid:144) works with unidirectionallinks, there is much to improveover (cid:135)K(cid:138)(cid:139)(cid:135)K(cid:140) (cid:135)(cid:10)(cid:144) (cid:135)(cid:18)(cid:137)(cid:145)(cid:137) (cid:135)(cid:10)(cid:138)(cid:145)(cid:146) ULP.OnedrawbackofULPisthatthesearchingprocessofin- (cid:135)(cid:10)(cid:147) (cid:135)(cid:16)(cid:137)(cid:148) (cid:135)(cid:16)(cid:137)(cid:147) clusivecycleconsumesalotofnetworkresourcesbyinitializing thecyclesizeofalinkto˜ andfloodingthelinkstatethrough- outthenetwork. Thiscanbeimprovedbylimitingthedistance Fig.7. A20-NodeSampleNetworkTopology ofthelink-statepropagationinsearchfortheinclusivecycle. Fig. 8 shows simulation results of ULP and EOSPF on the REFERENCES 20-node network of Fig. 7. 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