15-441 Computer NetworkingSummaryGraph ModelRoutes from Node AWays to Compute Shortest PathsOutlineDistance-Vector MethodDistance-Vector UpdateAlgorithmStartIteration #1Iteration #2Distance Vector: Link Cost ChangesSlide 14Distance Vector: Split HorizonDistance Vector: Poison ReversePoison Reverse FailuresRouting Information Protocol (RIP)RIP UpdatesRIP Staleness / Oscillation ControlSlide 21Link State Protocol ConceptSending Link States by FloodingDijkstra’s AlgorithmDijkstra’s Algorithm: ConceptDijkstra’s Algorithm: InitiallySlide 27Slide 28Slide 29Slide 30Slide 31Link State CharacteristicsOSPF Routing ProtocolOSPF Reliable FloodingOSPF Flooding OperationFlooding IssuesAdoption of OSPFComparison of LS and DV AlgorithmsSlide 39Next Lecture: BGP15-441 Computer NetworkingLecture 10: Intra-Domain RoutingRIP (Routing Information Protocol) & OSPF (Open Shortest Path First)Lecture 10: 2-10-2005 2Summary•The Story So Far… •IP addresses are structure to reflect Internet structure•IP packet headers carry these addresses•When Packet Arrives at Router•Examine header to determine intended destination•Look up in table to determine next hop in path•Send packet out appropriate port•Today’s lecture•How to generate the forwarding tableRouterLecture 10: 2-10-2005 3Graph Model•Represent each router as node•Direct link between routers represented by edge•Symmetric links undirected graph•Edge “cost” c(x,y) denotes measure of difficulty of using link•delay, $ cost, or congestion level•Task•Determine least cost path from every node to every other node•Path cost d(x,y) = sum of link costsAEFCDB23641113Lecture 10: 2-10-2005 4Routes from Node A•Properties•Some set of shortest paths forms tree•Shortest path spanning tree•Solution not unique•E.g., A-E-F-C-D also has cost 7AEFCDB23641113Forwarding Table for ADest Cost Next HopA 0 AB 4 BC 6 ED 7 BE 2 EF 5 ELecture 10: 2-10-2005 5Ways to Compute Shortest Paths•Centralized•Collect graph structure in one place•Use standard graph algorithm•Disseminate routing tables•Link-state•Every node collects complete graph structure•Each computes shortest paths from it•Each generates own routing table•Distance-vector•No one has copy of graph•Nodes construct their own tables iteratively•Each sends information about its table to neighborsLecture 10: 2-10-2005 6Outline•Distance Vector•Link StateLecture 10: 2-10-2005 7Distance-Vector Method•Idea•At any time, have cost/next hop of best known path to destination•Use cost when no path known•Initially•Only have entries for directly connected nodesAEFCDB23641113Initial Table for ADest Cost Next HopA 0 AB 4 BC–D–E 2 EF 6 FLecture 10: 2-10-2005 8Distance-Vector Update•Update(x,y,z)d c(x,z) + d(z,y) # Cost of path from x to y with first hop zif d < d(x,y)# Found better pathreturn d,z # Updated cost / next hopelsereturn d(x,y), nexthop(x,y) # Existing cost / next hopxzyc(x,z)d(z,y)d(x,y)Lecture 10: 2-10-2005 9Algorithm•Bellman-Ford algorithm•RepeatFor every node xFor every neighbor zFor every destination yd(x,y) Update(x,y,z)•Until convergeLecture 10: 2-10-2005 10StartAEFCDB23641113Table for ADst Cst HopA 0 AB 4 BC–D–E 2 EF 6 FTable for BDst Cst HopA 4 AB 0 BC–D 3 DE–F 1 FTable for CDst Cst HopA–B–C 0 CD 1 DE–F 1 FTable for DDst Cst HopA–B 3 BC 1 CD 0 DE–F–Table for EDst Cst HopA 2 AB–C–D–E 0 EF 3 FTable for FDst Cst HopA 6 AB 1 BC 1 CD–E 3 EF 0 FOptimum 1-hop pathsLecture 10: 2-10-2005 11Iteration #1Table for ADst Cst HopA 0 AB 4 BC 7 FD 7 BE 2 EF 5 ETable for BDst Cst HopA 4 AB 0 BC 2 FD 3 DE 4 FF 1 FTable for CDst Cst HopA 7 FB 2 FC 0 CD 1 DE 4 FF 1 FTable for DDst Cst HopA 7 BB 3 BC 1 CD 0 DE–F 2 CTable for EDst Cst HopA 2 AB 4 FC 4 FD–E 0 EF 3 FTable for FDst Cst HopA 5 BB 1 BC 1 CD 2 CE 3 EF 0 FOptimum 2-hop pathsAEFCDB23641113Lecture 10: 2-10-2005 12Iteration #2Table for ADst Cst HopA 0 AB 4 BC 6 ED 7 BE 2 EF 5 ETable for BDst Cst HopA 4 AB 0 BC 2 FD 3 DE 4 FF 1 FTable for CDst Cst HopA 6 FB 2 FC 0 CD 1 DE 4 FF 1 FTable for DDst Cst HopA 7 BB 3 BC 1 CD 0 DE 5 CF 2 CTable for EDst Cst HopA 2 AB 4 FC 4 FD 5 FE 0 EF 3 FTable for FDst Cst HopA 5 BB 1 BC 1 CD 2 CE 3 EF 0 FOptimum 3-hop pathsAEFCDB23641113Lecture 10: 2-10-2005 13Distance Vector: Link Cost ChangesLink cost changes:•Node detects local link cost change •Updates distance table •If cost change in least cost path, notify neighborsXZ1450Y1algorithmterminates“goodnews travelsfast”Lecture 10: 2-10-2005 14Distance Vector: Link Cost ChangesLink cost changes:•Good news travels fast •Bad news travels slow - “count to infinity” problem!XZ1450Y60algorithmcontinueson!Lecture 10: 2-10-2005 15Distance Vector: Split HorizonIf Z routes through Y to get to X :•Z does not advertise its route to X back to YalgorithmterminatesXZ1450Y60? ? ?Lecture 10: 2-10-2005 16Distance Vector: Poison ReverseIf Z routes through Y to get to X :•Z tells Y its (Z’s) distance to X is infinite (so Y won’t route to X via Z)•Eliminates some possible timeouts with split horizon•Will this completely solve count to infinity problem? XZ1450Y60algorithmterminatesLecture 10: 2-10-2005 17Poison Reverse Failures•Iterations don’t converge•“Count to infinity”•Solution•Make “infinity” smaller•What is upper bound on maximum path length?Table for ADst Cst HopC 7 FTable for BDst Cst HopC 8 ATable for FDst Cst HopC 1 CTable for FDst Cst HopC–Table for ADst Cst HopC–ForcedUpdateTable for BDst Cst HopC 14 AForcedUpdateF C6111BDA4Table for DDst Cst HopC 9 BForcedUpdateTable for ADst Cst HopC 13 DBetterRouteTable for DDst Cst HopC 15 BTable for ADst Cst HopC 19 DForcedUpdate•••ForcedUpdateLecture 10: 2-10-2005 18Routing Information Protocol (RIP)•Earliest IP routing protocol (1982 BSD)•Current standard is version 2 (RFC 1723)•Features•Every link has cost 1•“Infinity” = 16•Limits to networks where everything reachable within 15 hops•Sending Updates•Every router listens for updates on UDP port 520•RIP message can contain entries for up to 25 table entriesLecture 10: 2-10-2005 19RIP Updates•Initial•When router first starts, asks for copy of table for every neighbor•Uses it to iteratively generate own table•Periodic•Every 30 seconds, router sends copy of its table to each neighbor•Neighbors use to iteratively update their
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