Basics of Routing and Link-State Routing

Transcription

1 Basics of Routing and Link-State Routing Antonio Carzaniga Faculty of Informatics Università della Svizzera italiana December 6, 206

2 Outline Routing problem Graph model Classes of routing algorithms Broadcast routing Link-state routing Dijkstra s algorithm

3 Routing Problem

4 Finding paths through a network Routing Problem

5 Routing Problem Finding paths through a network g h j d e f a b c

6 Routing Problem Finding paths through a network g 4 h j d e 9 f 2 a 3 4 b c Example:a j?

7 Graph Model Thenetworkismodeledasagraph G = (V,E)

8 Graph Model Thenetworkismodeledasagraph G = (V,E) Visasetofverticesrepresentingtherouters

9 Graph Model Thenetworkismodeledasagraph G = (V,E) Visasetofverticesrepresentingtherouters E V Visasetofedgesrepresentingcommunicationlinks e.g., (u,v) Eiffrouteruisonthesamesubnetasv

10 Graph Model Thenetworkismodeledasagraph G = (V,E) Visasetofverticesrepresentingtherouters E V Visasetofedgesrepresentingcommunicationlinks e.g., (u,v) Eiffrouteruisonthesamesubnetasv Gisassumedtobeanundirectedgraph,meaningthatlinksarebidirectional i.e., (u,v) E (v,u) Eforallu,v N

11 Graph Model Thenetworkismodeledasagraph G = (V,E) Visasetofverticesrepresentingtherouters E V Visasetofedgesrepresentingcommunicationlinks e.g., (u,v) Eiffrouteruisonthesamesubnetasv Gisassumedtobeanundirectedgraph,meaningthatlinksarebidirectional i.e., (u,v) E (v,u) Eforallu,v N Acostfunctionc :E costsarealwayspositive:c(e)>0foralle E linksaresymmetric:c(u,v) =c(v,u)forallu,v N

12 Routing in the Graph Model Foreveryrouteru V,foreveryotherrouterv V,computethepath P u v =u,x,x 2,...,x n,vsuchthat

13 Routing in the Graph Model Foreveryrouteru V,foreveryotherrouterv V,computethepath P u v =u,x,x 2,...,x n,vsuchthat P u v iscompletelycontainedinthenetworkgraphg.i.e., (u,x ) V,(x,x 2 ) V,...,(x n,v) V

14 Routing in the Graph Model Foreveryrouteru V,foreveryotherrouterv V,computethepath P u v =u,x,x 2,...,x n,vsuchthat P u v iscompletelycontainedinthenetworkgraphg.i.e., (u,x ) V,(x,x 2 ) V,...,(x n,v) V P u v isaleast-costpath,wherethecostofthepathis c(p u v ) =c(u,x )+c(x,x 2 )+...+c(x n,v)

15 Routing in the Graph Model Foreveryrouteru V,foreveryotherrouterv V,computethepath P u v =u,x,x 2,...,x n,vsuchthat P u v iscompletelycontainedinthenetworkgraphg.i.e., (u,x ) V,(x,x 2 ) V,...,(x n,v) V P u v isaleast-costpath,wherethecostofthepathis c(p u v ) =c(u,x )+c(x,x 2 )+...+c(x n,v) Compile u s forwarding table by adding the following entry: A(v) I u (x ) A(v)istheaddress(orsetofaddresses)ofrouterv I u (x )istheinterfacethatconnectsutothefirstnext-hoprouterx in P u v =u,x,x 2,...,x n,v

16 Back To The Example g 4 h j d e 9 f 2 a 3 4 b c Example:a j

17 Back To The Example g 4 h j d e 9 f 2 a 3 4 b c Example:a j least-costpathisp a j =a,e,b,f,j

18 Back To The Example g 4 h j d e 9 f a 3 4 b c Example:a j least-costpathisp a j =a,e,b,f,j a sforwardingtablewillcontainanentryj 2sinceI a (e) =2

19 There are two main strategies to implement a routing algorithm Two General Strategies

20 Two General Strategies There are two main strategies to implement a routing algorithm Link-state routing

21 Two General Strategies There are two main strategies to implement a routing algorithm Link-state routing globalviewofthenetwork local computation of least-cost paths

22 Two General Strategies There are two main strategies to implement a routing algorithm Link-state routing globalviewofthenetwork local computation of least-cost paths Distance-vector routing

23 Two General Strategies There are two main strategies to implement a routing algorithm Link-state routing globalviewofthenetwork local computation of least-cost paths Distance-vector routing localviewofthenetwork global computation of least-cost paths

24 Link-State Routing RouterumaintainsacompleteviewofthenetworkgraphG(includingalllinks and their costs)

25 Link-State Routing RouterumaintainsacompleteviewofthenetworkgraphG(includingalllinks and their costs) everyroutervadvertisesitsadjacentlinks(theircosts)toeveryotherrouterinthe network; this information is called link state link-state advertisements(lsas) are broadcast through the entire network

26 Link-State Routing RouterumaintainsacompleteviewofthenetworkgraphG(includingalllinks and their costs) everyroutervadvertisesitsadjacentlinks(theircosts)toeveryotherrouterinthe network; this information is called link state link-state advertisements(lsas) are broadcast through the entire network routers collect link-state advertisements from other routers, and they use them to compileandmaintainacompleteviewofg

27 Link-State Routing RouterumaintainsacompleteviewofthenetworkgraphG(includingalllinks and their costs) everyroutervadvertisesitsadjacentlinks(theircosts)toeveryotherrouterinthe network; this information is called link state link-state advertisements(lsas) are broadcast through the entire network routers collect link-state advertisements from other routers, and they use them to compileandmaintainacompleteviewofg Using its local representation of G, router u computes the least-cost paths from utoeveryotherrouterinthenetwork

28 Link-State Routing RouterumaintainsacompleteviewofthenetworkgraphG(includingalllinks and their costs) everyroutervadvertisesitsadjacentlinks(theircosts)toeveryotherrouterinthe network; this information is called link state link-state advertisements(lsas) are broadcast through the entire network routers collect link-state advertisements from other routers, and they use them to compileandmaintainacompleteviewofg Using its local representation of G, router u computes the least-cost paths from utoeveryotherrouterinthenetwork the computation is local

29 Link-State Advertisements g 4 h j d e 9 f 2 a 3 4 b c

30 Link-State Advertisements g 4 h j d e 9 f 2 a 3 4 b c LSA a = {(a,b,3),(a,e,),(a,d,)}

31 Link-State Advertisements g 4 h j d e 9 f b 3 a e d 2 a 3 4 b c LSA a = {(a,b,3),(a,e,),(a,d,)}

32 Link-State Advertisements g 4 h j d e 9 f b 3 a e d 2 a 3 4 b c LSA a = {(a,b,3),(a,e,),(a,d,)} LSA h = {(h,e,),(h,f,4),(h,j,4)}

33 Link-State Advertisements g 4 h j d e 9 f b 3 a e d h 2 a 3 4 b c f 4 4 j LSA a = {(a,b,3),(a,e,),(a,d,)} LSA h = {(h,e,),(h,f,4),(h,j,4)}

34 Link-State Advertisements g 4 h j d e 9 f b 3 a e d h 2 a 3 4 b c f 4 4 j LSA a = {(a,b,3),(a,e,),(a,d,)} LSA h = {(h,e,),(h,f,4),(h,j,4)} LSA d = {(d,a,),(d,g,),(d,e,3)}

35 Link-State Advertisements g 4 h j d e 9 f b 3 a e d 3 h g 2 a 3 4 b c f 4 4 j LSA a = {(a,b,3),(a,e,),(a,d,)} LSA h = {(h,e,),(h,f,4),(h,j,4)} LSA d = {(d,a,),(d,g,),(d,e,3)}

36 Link-State Advertisements g 4 h j d e 9 f b 3 a e d 3 h g 2 a 3 4 b c f 4 4 j LSA a = {(a,b,3),(a,e,),(a,d,)} LSA h = {(h,e,),(h,f,4),(h,j,4)} LSA d = {(d,a,),(d,g,),(d,e,3)} LSA f = {(f,c,),(f,b,),(f,e,3),(f,h,4),(f,j,2)}

37 Link-State Advertisements g 4 h j d e 9 f 2 a 3 4 b c b c 2 3 a e 9 f d 3 h j g LSA a = {(a,b,3),(a,e,),(a,d,)} LSA h = {(h,e,),(h,f,4),(h,j,4)} LSA d = {(d,a,),(d,g,),(d,e,3)} LSA f = {(f,c,),(f,b,),(f,e,3),(f,h,4),(f,j,2)}

38 Link-State Advertisements g 4 h j d e 9 f 2 a 3 4 b c b c 2 3 a e 9 f d 3 h j g LSA a = {(a,b,3),(a,e,),(a,d,)} LSA h = {(h,e,),(h,f,4),(h,j,4)} LSA d = {(d,a,),(d,g,),(d,e,3)} LSA f = {(f,c,),(f,b,),(f,e,3),(f,h,4),(f,j,2)}...

39 What do we need to implement link-state routing? Link-State Routing Ingredients

40 Link-State Routing Ingredients What do we need to implement link-state routing? EveryroutersendsitsLSAtoeveryotherrouterinthenetwork,soweneeda broadcast routing scheme

41 Link-State Routing Ingredients What do we need to implement link-state routing? EveryroutersendsitsLSAtoeveryotherrouterinthenetwork,soweneeda broadcast routing scheme OncewehavealltheLSAsfromeveryrouter,andthereforewecomplete knowledgeofg,weneedanalgorithmtocomputeleast-costpathsinagraph

42 Broadcast Routing

43 Broadcast Routing Flooding every router forwards a broadcast packet to every adjacent router, except the one that sent the packet

44 Broadcast Routing Flooding every router forwards a broadcast packet to every adjacent router, except the one that sent the packet Simple and elegant

45 Broadcast Routing Flooding every router forwards a broadcast packet to every adjacent router, except the one that sent the packet Simple and elegant Correct w.r.t. the broadcast requirement: a broadcast packet will eventually reach every router

46 Broadcast Routing Flooding every router forwards a broadcast packet to every adjacent router, except the one that sent the packet Simple and elegant Correct w.r.t. the broadcast requirement: a broadcast packet will eventually reach every router Any problem with this solution?

47 Broadcast Routing Flooding every router forwards a broadcast packet to every adjacent router, except the one that sent the packet Simple and elegant Correct w.r.t. the broadcast requirement: a broadcast packet will eventually reach every router Any problem with this solution? cycles in the network create packet storms

48 Broadcast Routing (2)

49 Broadcast Routing (2) Reverse-path broadcast every router forwards a broadcast packet to every adjacent router, except the one where it received the packet router arouteruacceptsabroadcastpacketporiginatingatroutersonlyifparriveson thelinkthatisonthedirect(unicast)pathfromutos

50 Broadcast Routing (2) Reverse-path broadcast every router forwards a broadcast packet to every adjacent router, except the one where it received the packet router arouteruacceptsabroadcastpacketporiginatingatroutersonlyifparriveson thelinkthatisonthedirect(unicast)pathfromutos Correct w.r.t. the broadcast requirement: a broadcast packet will eventually reach every router

51 Broadcast Routing (2) Reverse-path broadcast every router forwards a broadcast packet to every adjacent router, except the one where it received the packet router arouteruacceptsabroadcastpacketporiginatingatroutersonlyifparriveson thelinkthatisonthedirect(unicast)pathfromutos Correct w.r.t. the broadcast requirement: a broadcast packet will eventually reach every router NopacketstormseveninthepresenceofcyclesinG

52 Broadcast Routing (2) Reverse-path broadcast every router forwards a broadcast packet to every adjacent router, except the one where it received the packet router arouteruacceptsabroadcastpacketporiginatingatroutersonlyifparriveson thelinkthatisonthedirect(unicast)pathfromutos Correct w.r.t. the broadcast requirement: a broadcast packet will eventually reach every router NopacketstormseveninthepresenceofcyclesinG Any problem with this solution?

53 Broadcast Routing (2) Reverse-path broadcast every router forwards a broadcast packet to every adjacent router, except the one where it received the packet router arouteruacceptsabroadcastpacketporiginatingatroutersonlyifparriveson thelinkthatisonthedirect(unicast)pathfromutos Correct w.r.t. the broadcast requirement: a broadcast packet will eventually reach every router NopacketstormseveninthepresenceofcyclesinG Any problem with this solution? it requires(unicast) routing information so it is obviously useless to implement a routing algorithm

54 Sequence-number controlled flooding Broadcast Routing (3)

55 Broadcast Routing (3) Sequence-number controlled flooding theoriginatorsofabroadcastpacketmarksthepacketwithasequencenumbern s

56 Broadcast Routing (3) Sequence-number controlled flooding theoriginatorsofabroadcastpacketmarksthepacketwithasequencenumbern s everyrouterustoresthemostrecentsequencenumberseenfromeachsource router.let sassumethatuhasseensequencenumbersfromsupton s

57 Broadcast Routing (3) Sequence-number controlled flooding theoriginatorsofabroadcastpacketmarksthepacketwithasequencenumbern s everyrouterustoresthemostrecentsequencenumberseenfromeachsource router.let sassumethatuhasseensequencenumbersfromsupton s arouteracceptsabroadcastpacketporiginatingatsonlyifpcarriesasequence numberseq(p)thatishigherthanthemostrecentoneseenfroms:seq(p)>n s

58 Broadcast Routing (3) Sequence-number controlled flooding theoriginatorsofabroadcastpacketmarksthepacketwithasequencenumbern s everyrouterustoresthemostrecentsequencenumberseenfromeachsource router.let sassumethatuhasseensequencenumbersfromsupton s arouteracceptsabroadcastpacketporiginatingatsonlyifpcarriesasequence numberseq(p)thatishigherthanthemostrecentoneseenfroms:seq(p)>n s accepted packets are forwarded to every adjacent router, except the previous-hop router

59 Broadcast Routing (3) Sequence-number controlled flooding theoriginatorsofabroadcastpacketmarksthepacketwithasequencenumbern s everyrouterustoresthemostrecentsequencenumberseenfromeachsource router.let sassumethatuhasseensequencenumbersfromsupton s arouteracceptsabroadcastpacketporiginatingatsonlyifpcarriesasequence numberseq(p)thatishigherthanthemostrecentoneseenfroms:seq(p)>n s accepted packets are forwarded to every adjacent router, except the previous-hop router uupdatesitstableofsequencenumbersn s seq(p)

60 Executing locally at node u Dijkstra s Algorithm

61 Dijkstra s Algorithm Executing locally at node u Variables storing values known at each iteration

62 Dijkstra s Algorithm Executing locally at node u Variables storing values known at each iteration D[v],costoftheleast-costpathfromutov

63 Dijkstra s Algorithm Executing locally at node u Variables storing values known at each iteration D[v],costoftheleast-costpathfromutov p[v],nodeprecedingv(neighborofv)ontheleast-costpathfromutov

64 Dijkstra s Algorithm Executing locally at node u Variables storing values known at each iteration D[v],costoftheleast-costpathfromutov p[v],nodeprecedingv(neighborofv)ontheleast-costpathfromutov N,nodesofGwhoseleast-costpathfromuisdefinitelyknown

65 DIJKSTRA(G = (V,E),u) N {u} 2 forallv V 3 doifv neighbors(u) 4 thend[v] c(u,v) 5 p[v] u 6 elsed[v] 7 whilen V 8 dofindw NsuchthatD[w]isminimum 9 N N {w} 0 forallv neighbors(w)\n doifd[w]+c(w,v)<d[v] 2 thend[v] D[w]+c(w,v) 3 p[v] w Dijkstra s Algorithm

66 Example g 4 h j DIJKSTRA(G = (V,E),u) N {u} 2 forallv V 3 doifv neighbors(u) 4 thend[v] c(u,v) 5 p[v] u 6 else D[v] 7 whilen V 8 dofindw NsuchthatD[w]isminimum 9 N N {w} 0 forallv neighbors(w)\n doifd[w]+c(w,v)<d[v] 2 thend[v] D[w]+c(w,v) 3 p[v] w d e 9 f 2 a 3 4 b c