The Fundamentals of Routing

Transcription

1 The Fundamentals of Routing EE22 Fall 20 Scott Shenker Materials with thanks to Jennifer Rexford, Ion Stoica, Vern Paxson and other colleagues at Princeton and UC Berkeley

2 Announcements 94 is set up: 4 units: CCN: 2557 Everyone should be off wait list by now. Waiting for more accounts o Send me if you need one. Will set up bspace for 94 to hand in homework Open today with questions about project Hope you all handed in HW HW2 out on Wednesday Survey will be available after Wednesday s class 2

3 Questions about Project (for Shaddi) 3

4 Warning. This lecture contains detailed calculations Prolonged exposure may induce drowsiness Do not operate heavy machinery while listening 4

5 Where Are We? Motivated our basic design decisions Best-effort, packet-switching, blah, blah, blah Last lecture: how to build reliable transport on top This lecture: how to build the network itself Basic Task: deliver packets Need to route them, from anywhere to anywhere Today, we focus on routing 5

6 The Traditional Routing Curriculum Learning switches Link-state routing Dijkstra s Algorithm Distance-vector routing Bellman-Ford 6

7 I have some bad news.. Don t have anything interesting to say about routing Will follow standard curriculum Much of it covered in the text But will focus more on principles than details Will work through two algorithms, but details may wait until Wednesday..34 slides! Let s just see how timing goes If you don t want to be bored, ask questions! 7

8 Remember. Goal of the first portion of course is conceptual Ignore real networks Think about the basic concepts That s where we are. Later will deal with reality 8

9 Basics of Routing and Forwarding 9

10 Addressing (at a conceptual level) Assume all hosts have unique IDs No particular structure to those IDs Later in course will talk about real IP addressing 0

11 Packets (at a conceptual level) Assume packet headers contain: Source ID, Destination ID, and perhaps other information Destination Identifier Source Identifier Why include this? Payload

12 Switches/Routers Multiple ports (attached to other switches or hosts) incoming links Switch outgoing links Ports are typically duplex (incoming and outgoing) 2

13 Example of Network Graph Six ports, incoming/outgoing Four ports, incoming/outgoing 3

14 A Variety of Networks ISPs: carriers Backbone Edge Border (to other ISPs) Enterprises: companies, universities Core Edge Border (to outside) Datacenters: massive collections of machines Top-of-Rack Aggregation and Core Border (to outside) 4

15 UUNET s North American Network 5

16 Level3 s American Network 6

17 Enterprise Network 7

18 Partial Datacenter Network 8

19 Switches Enterprise/Edge: typically 24 to 48 ports Aggregation switches: 92 ports or more Backbone: typically fewer ports Border: typically very few ports 9

20 Forwarding Decisions When packet arrives, must choose outgoing port incoming links Switch outgoing links Consider packet header and routing table Decision is based on routing state (table) in switch 20

21 Forwarding Decisions When packet arrives.. Must decide which outgoing port to use In single transmission time Forwarding decisions must be simple Routing state dictates where to forward packets Assume decisions are deterministic Global routing state means collection of routing state in each of the routers Will focus on where this routing state comes from But first, a few preliminaries. 2

22 Forwarding vs Routing Forwarding: data plane Directing a data packet to an outgoing link Individual router using routing state Routing: control plane Computing paths the packets will follow Routers talking amongst themselves Jointly creating the routing state Two very different timescales. 22

23 Validity of Routing State 23

24 Valid Routing State Global routing state is valid if it produces forwarding decisions that always deliver packets to their destinations Valid is my terminology, not standard Goal of routing protocols: compute valid state But how can you tell if routing state if valid? 24

25 Necessary and Sufficient Condition Global routing state is valid if and only if: There are no dead ends (other than destination) There are no loops A dead end is when there is no outgoing port A packet arrives, but the forwarding decision does not yield any outgoing port A loop is when a packet cycles around the same set of nodes forever 25

26 Necessary: Obvious If you run into a deadend before hitting destination, you ll never reach the destination If you run into a loop, you ll never reach destination With deterministic forwarding, once you loop, you ll loop forever (assuming routing state is static) 26

27 Wandering Packets Packet reaches deadend and stops Packet falls into loop and never reaches destination 27

28 Sufficient: Easy Assume no deadends, no loops Packet must keep wandering, without repeating If ever enter same switch from same port, will loop Because forwarding decisions are deterministic Only a finite number of possible ports for it to visit It cannot keep wandering forever without looping Must eventually hit destination 28

29 The Secret of Routing Avoiding deadends is easy Avoiding loops is hard The key difference between routing protocols is how they avoid loops! Don t focus on details of mechanisms Just ask how are loops avoided? Will return to this later. 29

30 Making Forwarding Decisions Map PacketState+RoutingState into OutgoingPort At line rates.. Packet State: Destination ID Source ID Incoming Port (from switch, not packet) Other packet header information? Routing State: Stored in router 30

31 Forwarding Decision Dependencies Must depend on destination Could also depend on : Source: requires n 2 state Input port: not clear what this buys you Other header information: let s ignore for now We will focus only on destination-based routing But first consider the alternative 3

32 Source/Destination-Based Routing Paths from two different sources (to same destination) can be very different 32

33 Destination-Based Routing Paths from two different sources (to same destination) must coincide once they overlap 33

34 Destination-Based Routing Paths to same destination never cross Once paths to destination meet, they never split Set of paths to destination create a delivery tree Must cover every node exactly once Spanning Tree rooted at destination 34

35 A Delivery Tree for a Destination 35

36 Checking Validity of Routing State Focus only on a single destination Ignore all other routing state Mark outgoing port with arrow There can only be one at each node Eliminate all links with no arrows Look at what s left. 36

37 Example 37

38 Pick Destination 38

39 Put Arrows on Outgoing Ports 39

40 Remove Unused Links Leaves Spanning Tree: Valid 40

41 Second Example 4

42 Second Example Is this valid? 42

43 Lesson. Very easy to check validity of routing state for a particular destination Deadends are obvious Node without outgoing arrow Loops are obvious Disconnected from rest of graph 43

44 Computing Routing State 44

45 Forms of Route Computation Learn from observing. Not covered in your reading Centralized computation One node has the entire network map Pseudo-centralized computation All nodes have the entire network map Distributed computation No one has the entire network map 45

46 How Can You Avoid Loops? Restrict topology to spanning tree If the topology has no loops, packets can t loop! Central computation Can make sure no loops Minimizing metric in distributed computation Loops are never the solution to a minimization problem 46

47 Self-Learning on Spanning Tree 47

48 Easiest Way to Avoid Loops Use a topology where loops are impossible! Take arbitrary topology Build spanning tree (algorithm covered later) Ignore all other links (as before) Only one path to destinations on spanning trees Use learning switches to discover these paths No need to compute routes, just observe them 48

49 Consider previous graph 49

50 A Spanning Tree 50

51 Another Spanning Tree 5

52 Yet Another Spanning Tree 52

53 Flooding on a Spanning Tree If you want to send a packet that will reach all nodes, then switches can use the following rule: Ignoring all ports not on spanning tree! Originating switch sends flood packet out all ports When a flood packet arrives on one incoming port, send it out all other ports 53

54 Flooding on Spanning Tree 54

55 Flooding on Spanning Tree (Again) 55

56 Flooding on a Spanning Tree This works because the lack of loops prevents the flooding from cycling back on itself Eventually all nodes will be covered, exactly once 56

57 This Enables Learning! There is only one path from source to destination Each switch can learn how to reach a another node by remembering where its flooding packets came from! If flood packet from Node A entered switch from port 4, then to reach Node A, switch sends packets out port 4 57

58 Learning from Flood Packets Node A can be reached through this port Node A can be reached through this port Node A Once a node has sent a flood message, all other switches know how to reach it. 58

59 General Approach Flood first packet All switches learn where you are When destination responds, all switches learn where it is Done. 59

60 Self-Learning Switch When a packet arrives Inspect source ID, associate with incoming port Store mapping in the switch table Use time-to-live field to eventually forget mapping Packet tells switch how to reach A. B A C D 60

61 Self Learning: Handling Misses When packet arrives with unfamiliar destination Forward packet out all other ports Response will teach switch about that destination When in doubt, shout! B A C D 6

62 General Rule When switch receives a packet: index the switch table using destination ID if entry found for destination { } if dest on port from which packet arrived then drop packet else forward packet on port indicated else flood Why do this? forward on all but the interface on which the frame arrived 62

63 Summary of Learning Approach Avoids loop by restricting to spanning tree This makes flooding possible Flooding allows packet to reach destination And in the process switches learn how to reach source of flood No route computation 63

64 Weaknesses of This Approach? Requires loop-free topology (Spanning Tree) Slow to react to failures (entries time out) Very little control over paths Spanning Trees suck. 64

65 On to other routing techniques 65

66 A Little Test How many of you did the reading? 66

67 The Task Remove sheet of paper from beanbag, but do not look at sheet of paper until I say so You will have five minutes to complete this task Each sheet says: You are node X You are connected to nodes Y,Z Your job: find route from source (node ) to destination (node 40) in five minutes 67

68 Ground Rules You may not: Leave your seat (but you can stand) Pass your sheet of paper Let anyone copy your sheet of paper You may: Ask nearby friends for advice Shout to other participants (anything you want) Curse your instructor (sotto voce) You must: Try 68

69 Go! 69

70

71 5 Minute Break Questions Before We Proceed? 7

72 How Can You Avoid Loops? Restrict topology to spanning tree Central computation (can make sure no loops) Minimizing metric in distributed computation Any other techniques? 72

73 Organization for Rest of Lecture Link-state routing Distance-vector routing Goal of today: basic idea May review details on Wednesday Definitely go over details in section 73

74 Link-State Details in Section 74

75 Another Approach to Loop-Avoidance If one has a picture of the entire network, can compute routing state that does not produce loops This route computation can be done in many ways Here we will review Dijkstra s algorithm briefly But that s just because it is expected from such courses o Snore.. The real question is, how do you get picture of entire network? 75

76 Link-State Routing Is Conceptually Simple Each router keeps track of its incident links Each router broadcasts the link state To give every router a complete view of the graph Each router runs Dijkstra s algorithm Compute shortest paths, then construct forwarding table Example protocols Open Shortest Path First (OSPF) Intermediate System Intermediate System (IS-IS) Challenges: scaling, transient disruptions 76

77 Link State Routing Each node floods its local information Each node then knows entire network topology Host C Host A Host D N N2 N3 N5 Host B N4 Host E N6 N7 77

78 Link State: Each Node Has Global View Host A A B C D E Host C A B C D E A B C D Host D E N N2 A C D N3 A C D N5 B E A C D Host B N4 B E A C D B Host EE N6 B E N7 78

79 How to Compute Routes Each node should have same global view They each compute their own routing tables Using exactly the same algorithm Can use any algorithm that avoids loops Computing shortest paths is one such algorithm Associate a cost with each link Don t worry what it stands for. 79

80 Dijkstra s Shortest Path Algorithm INPUT: Network topology (graph), with link costs OUTPUT: Least cost paths from one node to all other nodes Produces tree of routes o Different from what we talked about before o Previous tree was rooted at destination o This is rooted at source o But shortest paths are reversible! 80

81 Least Cost Routes No sensible cost metric will be minimized by traversing a loop Least cost routes an easy way to avoid loops Least cost routes are also destination-based i.e., do not depend on the source Why is this? Therefore, least-cost paths form a spanning tree 8

82 Example 5 2 B 3 C 5 A F D E 82

83 Notation c(i,j): link cost from node i to j; cost infinite if not direct neighbors; 0 D(v): current value of cost of path from source to destination v p(v): predecessor node along path from source to v, that is next to v S: set of nodes whose least cost path definitively known 2 A Source 5 B 2 D 3 3 C E 5 2 F 83

84 Dijsktra s Algorithm Initialization: 2 S = {A}; 3 for all nodes v 4 if v adjacent to A 5 then D(v) = c(a,v); 6 else D(v) = ; c(i,j): link cost from node i to j D(v): current cost source v p(v): predecessor node along path from source to v, that is next to v S: set of nodes whose least cost path definitively known 7 8 Loop 9 find w not in S such that D(w) is a minimum; 0 add w to S; update D(v) for all v adjacent to w and not in S: 2 if D(w) + c(w,v) < D(v) then // w gives us a shorter path to v than we ve found so far 3 D(v) = D(w) + c(w,v); p(v) = w; 4 until all nodes in S; 84

85 Example: Dijkstra s Algorithm Step start S A D(B),p(B) 2,A D(C),p(C) 5,A D(D),p(D),A D(E),p(E) D(F),p(F) A 2 5 B D C E 5 2 F Initialization: 2 S = {A}; 3 for all nodes v 4 if v adjacent to A 5 then D(v) = c(a,v); 6 else D(v) = ; 85

86 Example: Dijkstra s Algorithm Step A 2 start S A 5 B D D(B),p(B) 2,A C E 5 2 F D(C),p(C) 5,A D(D),p(D),A D(E),p(E) D(F),p(F) 8 Loop 9 find w not in S s.t. D(w) is a minimum; 0 add w to S; update D(v) for all v adjacent to w and not in S: 2 If D(w) + c(w,v) < D(v) then 3 D(v) = D(w) + c(w,v); p(v) = w; 4 until all nodes in S; 86

87 Example: Dijkstra s Algorithm Step A 2 start S A AD 5 B D D(B),p(B) 2,A C E 5 2 D(C),p(C) 5,A F D(D),p(D),A D(E),p(E) D(F),p(F) 8 Loop 9 find w not in S s.t. D(w) is a minimum; 0 add w to S; update D(v) for all v adjacent to w and not in S: 2 If D(w) + c(w,v) < D(v) then 3 D(v) = D(w) + c(w,v); p(v) = w; 4 until all nodes in S; 87

88 Example: Dijkstra s Algorithm Step A 2 start S A AD 5 B D D(B),p(B) 2,A C E 5 2 D(C),p(C) 5,A 4,D F D(D),p(D),A D(E),p(E) 2,D D(F),p(F) 8 Loop 9 find w not in S s.t. D(w) is a minimum; 0 add w to S; update D(v) for all v adjacent to w and not in S: 2 If D(w) + c(w,v) < D(v) then 3 D(v) = D(w) + c(w,v); p(v) = w; 4 until all nodes in S; 88

89 Example: Dijkstra s Algorithm Step A 2 start S A AD ADE 5 B D D(B),p(B) 2,A C E 5 2 F D(C),p(C) 5,A 4,D 3,E D(D),p(D),A D(E),p(E) 2,D D(F),p(F) 4,E 8 Loop 9 find w not in S s.t. D(w) is a minimum; 0 add w to S; update D(v) for all v adjacent to w and not in S: 2 If D(w) + c(w,v) < D(v) then 3 D(v) = D(w) + c(w,v); p(v) = w; 4 until all nodes in S; 89

90 Example: Dijkstra s Algorithm Step A 2 start S A AD ADE ADEB 5 B D D(B),p(B) 2,A C E 5 2 F D(C),p(C) 5,A 4,D 3,E D(D),p(D),A D(E),p(E) 2,D D(F),p(F) 4,E 8 Loop 9 find w not in S s.t. D(w) is a minimum; 0 add w to S; update D(v) for all v adjacent to w and not in S: 2 If D(w) + c(w,v) < D(v) then 3 D(v) = D(w) + c(w,v); p(v) = w; 4 until all nodes in S; 90

91 Example: Dijkstra s Algorithm Step A 2 start S A AD ADE ADEB ADEBC 5 B D D(B),p(B) 2,A C E 5 2 F D(C),p(C) 5,A 4,D 3,E D(D),p(D),A D(E),p(E) 2,D D(F),p(F) 4,E 8 Loop 9 find w not in S s.t. D(w) is a minimum; 0 add w to S; update D(v) for all v adjacent to w and not in S: 2 If D(w) + c(w,v) < D(v) then 3 D(v) = D(w) + c(w,v); p(v) = w; 4 until all nodes in S; 9

92 Example: Dijkstra s Algorithm Step A start S A AD ADE ADEB ADEBC ADEBCF 2 5 B D D(B),p(B) 2,A C E 5 2 F D(C),p(C) 5,A 4,D 3,E D(D),p(D),A D(E),p(E) 2,D D(F),p(F) 4,E 8 Loop 9 find w not in S s.t. D(w) is a minimum; 0 add w to S; update D(v) for all v adjacent to w and not in S: 2 If D(w) + c(w,v) < D(v) then 3 D(v) = D(w) + c(w,v); p(v) = w; 4 until all nodes in S; 92

93 Example: Dijkstra s Algorithm Step start S A AD ADE ADEB ADEBC ADEBCF D(B),p(B) 2,A D(C),p(C) 5,A 4,D 3,E D(D),p(D),A D(E),p(E) 2,D D(F),p(F) 4,E A 2 5 B 2 D 3 3 C E 5 2 F To determine path A C (say), work backward from C via p(v) 93

94 The Forwarding Table Running Dijkstra at node A gives the shortest path from A to all destinations We then construct the forwarding table A 2 5 B 2 D 3 3 C E 5 2 F Destination B C D E Link (A,B) (A,D) (A,D) (A,D) F (A,D) 94

95 Complexity How much processing does running the Dijkstra algorithm take? Assume a network consisting of N nodes Each iteration: check all nodes w not in S N(N+)/2 comparisons: O(N 2 ) More efficient implementations: O(N log(n)) 95

96 Flooding the Topology Information Each router sends information out its ports The next node sends it out through all of its ports Except the one where the information arrived Need to remember previous msgs, suppress duplicates! X A X A C B D (a) C B D (b) X A X A C B D (c) C B D (d) 96

97 Making Flooding Reliable Reliable flooding Ensure all nodes receive link-state information Ensure all nodes use the latest version Challenges Packet loss Out-of-order arrival Solutions Acknowledgments and retransmissions Sequence numbers How can it still fail? 97

98 When to Initiate Flood? Topology change Link or node failure Link or node recovery Configuration change Link cost change Potential problems with making cost dynamic! Periodically Refresh the link-state information Typically (say) 30 minutes Corrects for possible corruption of the data 98

99 Convergence Getting consistent routing information to all nodes E.g., all nodes having the same link-state database Forwarding is consistent after convergence All nodes have the same link-state database All nodes forward packets on same paths 99

100 Convergence Delay Time elapsed before every router has a consistent picture of the network Sources of convergence delay Detection latency Flooding of link-state information Recomputation of forwarding tables Storing forwarding tables Performance during convergence period Lost packets due to blackholes and TTL expiry Looping packets consuming resources Out-of-order packets reaching the destination Very bad for VoIP, online gaming, and video 00

101 Transient Disruptions Inconsistent link-state database Some routers know about failure before others The shortest paths are no longer consistent Can cause transient forwarding loops B C B C A F A F D E Loop! D E A and D think that this is the path to C E thinks that this is the path to C 0

102 Reducing Convergence Delay Faster detection Smaller hello timers Link-layer technologies that can detect failures Faster flooding Flooding immediately Sending link-state packets with high-priority Faster computation Faster processors on the routers Incremental Dijkstra algorithm Faster forwarding-table update Data structures supporting incremental updates 02

103 Scaling Link-State Routing Overhead of link-state routing Flooding link-state packets throughout the network Running Dijkstra s shortest-path algorithm Becomes unscalable when 00s of routers Introducing hierarchy through areas Area Area 2 area border router Area 0 Area 3 Area 4 03

104 Distance-Vector Details in Section 04

105 Distributed Computation of Routes More scalable than Link-State No global flooding Each node computing the outgoing port based on: Local information (who it is connected to) Paths advertised by neighbors 05

106 Distributed Computation I am three hops away I am two hops away I am two hops away I am one hop away I am three hops away I am two hops away I am one hop away I am one hop away I am two hops away 06

107 Loops in a Distributed Computation If the nodes choose their paths according to different criterion, then loops can occur Example Node A is minimizing hop count Node B is minimizing latency Node C is maximizing capacity Node D is minimizing price Any of those goals are fine, if globally adopted Only a problem when nodes use different criteria Any criteria that results in destination-based routing is fine. 07

108 Distance Vector Routing Each router knows the links to its neighbors Does not flood this information to the whole network Each router has provisional shortest path E.g.: Router A: I can get to router B with cost via next hop router D Routers exchange this information with their neighboring routers Again, no flooding the whole network Routers update their idea of the best path using info from neighbors This iterative process converges with set of shortest paths 08

109 Information Flow in Distance Vector Host C Host A Host D N N2 N3 N5 Host B N4 Host E N6 N7 09

110 Information Flow in Distance Vector Host C Host A Host D N N2 N3 N5 Host B N4 Host E N6 N7 0

111 Information Flow in Distance Vector Host C Host A Host D N N2 N3 N5 Host B N4 Host E N6 N7

112 Why Is This Different From Flooding? 2

113 Bellman-Ford Algorithm INPUT: Link costs to each neighbor Not full topology OUTPUT: Next hop to each destination and the corresponding cost Does not give the complete path to the destination 3

114 Bellman-Ford - Overview Each router maintains a table Best known distance from X to Y, via Z as next hop = D Z (X,Y) Each local iteration caused by: Local link cost change Message from neighbor Notify neighbors only if least cost path to any destination changes Neighbors then notify their neighbors if necessary Each node: wait for (change in local link cost or msg from neighbor) recompute distance table if least cost path to any dest has changed, notify neighbors 4

115 Bellman-Ford - Overview Each router maintains a table Row for each possible destination Column for each directly-attached neighbor to node Entry in row Y and column Z of node X best known distance from X to Y, via Z as next hop = D Z (X,Y) Node A Neighbor (next-hop) A 2 B 7 3 C D B C B 2 8 C 3 7 D 4 8 Destinations D C (A, D)

116 Bellman-Ford - Overview Each router maintains a table Row for each possible destination Column for each directly-attached neighbor to node Entry in row Y and column Z of node X best known distance from X to Y, via Z as next hop = D Z (X,Y) Node A A 2 B 7 3 C D B C B 2 8 C 3 7 D 4 8 Smallest distance in row Y = shortest Distance of A to Y, D(A, Y)

117 Distance Vector Algorithm (cont d) Initialization: 2 for all neighbors V do c(i,j): link cost from node i to j 3 if V adjacent to A D 4 D(A, V) = c(a,v); Z (A,V): cost from A to V via Z 5 else 6 D(A, V) = ; 7 send D(A, Y) to all neighbors loop: 8 wait (until A sees a link cost change to neighbor V /* case */ 9 or until A receives update from neighbor V) /* case 2 */ 0 if (c(a,v) changes by ±d) /* case */ for all destinations Y that go through V do 2 D V (A,Y) = D V (A,Y) ± d 3 else if (update D(V, Y) received from V) /* case 2 */ /* shortest path from V to some Y has changed */ 4 D V (A,Y) = D V (A,V) + D(V, Y); /* may also change D(A,Y) */ 5 if (there is a new minimum for destination Y) 6 send D(A, Y) to all neighbors 7 forever D(A,V): cost of A s best path to V 7

118 Example: st Iteration (C A) A 2 B 7 7 loop: 3 else if (update D(A, Y) from C) 4 D C (A,Y) = D C (A,C) + D(C, Y); 5 if (new min. for destination Y) 6 send D(A, Y) to all neighbors 7 forever 3 C D Node A B C B 2 8 C 7 D 8 Node C A B D A 7 B D Node B A C D A 2 C D 3 D C (A, B) = D C (A,C) + D(C, B) = 7 + = 8 D C (A, D) = D C (A,C) + D(C, D) = 7 + = 8 Node D B C A B 3 C

119 Example: st Iteration (B A) A 2 B 7 7 loop: 3 else if (update D(A, Y) from B) 4 D B (A,Y) = D B (A,B) + D(B, Y); 5 if (new min. for destination Y) 6 send D(A, Y) to all neighbors 7 forever 3 C D Node A Node B B C A C D B 2 8 A 2 C 3 7 C D 5 8 D 3 D B (A, C) = D B (A,B) + D(B, C) = 2 + = 3 D B (A, D) = D B (A,B) + D(B, D) = = 5 Node C Node D A B D B C A 7 A B B 3 D C

120 Example: End of st Iteration Node A Node B B C A C D A 2 B 7 3 C D B 2 8 C 3 7 D 5 8 A 2 3 C 9 4 D 2 3 End of st Iteration All nodes knows the best two-hop paths Node C A B D A 7 3 B 9 4 D 4 Node D B C A 5 8 B 3 2 C 4

121 Example: 2 nd Iteration (A B) Node A Node B B C A C D A 2 B 7 3 C D B 2 8 C 3 7 D 5 8 A 2 3 C 5 4 D loop: 3 else if (update D(B, Y) from A) 4 D A (B,Y) = D A (B,A) + D(A, Y); 5 if (new min. for destination Y) 6 send D(B, Y) to all neighbors 7 forever D A (B, C) = D A (B,A) + D(A, C) = = 5 D A (B, D) = D A (B,A) + D(A, D) = = 7 Node C Node D A B D B C A 7 3 A 5 8 B 9 4 B 3 2 D 4 C 4

122 Example: End of 2 nd Iteration Node A Node B B C A C D A 2 B 7 3 C D B 2 8 C 3 7 D 4 8 A 2 3 C 5 4 D End of 2 nd Iteration All nodes knows the best three-hop paths Node C A B D A B 9 4 D 2 4 Node D B C A 5 4 B 3 2 C 4

123 Example: End of 3rd Iteration Node A Node B B C A C D A 2 B 7 3 C D B 2 8 C 3 7 D 4 8 A C 5 4 D End of 2 nd Iteration: Algorithm Converges! Node C A B D A B 9 4 D 4 Node D B C A 5 4 B 3 2 C 4

124 Intuition Initial state: best one-hop paths One round: best two-hop paths Two rounds: best three-hop paths Kth round: best (k+) hop paths This must eventually converge.but how does it respond to changes in cost? 24

125 Distance Vector: Link Cost Changes loop: 8 wait (until A sees a link cost change to neighbor V 9 or until A receives update from neighbor V) / 0 if (c(a,v) changes by ±d) /* case */ for all destinations Y that go through V do 2 D V (A,Y) = D V (A,Y) ± d 3 else if (update D(V, Y) received from V) /* case 2 */ 4 D V (A,Y) = D V (A,V) + D(V, Y); 5 if (there is a new minimum for destination Y) 6 send D(A, Y) to all neighbors 7 forever A 4 B 50 C Node B Node C A C A 4 6 C 9 A B A 50 5 A C A 6 C 9 A B A 50 5 A C A 6 C 9 A B A 50 2 A C A 3 C 3 A B A 50 2 good news travels fast B 54 B 54 B 5 B 5 Link cost changes here time Algorithm terminates 25

126 DV: Count to Infinity Problem loop: 8 wait (until A sees a link cost change to neighbor V 9 or until A receives update from neighbor V) / 0 if (c(a,v) changes by ±d) /* case */ for all destinations Y that go through V do 2 D V (A,Y) = D V (A,Y) ± d 3 else if (update D(V, Y) received from V) /* case 2 */ 4 D V (A,Y) = D V (A,V) + D(V, Y); 5 if (there is a new minimum for destination Y) 6 send D(A, Y) to all neighbors 7 forever 60 A 4 B 50 C Node B Node C A C A 4 6 C 9 A B A 50 5 A C A 60 6 C 9 A B A 50 5 A C A 60 6 C 9 A B A 50 7 A C A 60 8 C 9 A B A 50 7 bad news travels slowly B 54 B 54 B 0 B 0 Link cost changes here time 26

127 Distance Vector: Poisoned Reverse If B routes through C to get to A: - B tells C its (B s) distance to A is infinite (so C won t route to A via B) - Will this completely solve count to infinity problem? 60 A 4 B 50 C Node B A C A 4 6 C 9 A C A 60 6 C 9 A C A 60 6 C 9 A C A 60 5 C 9 A C A 60 5 C 9 Node C A B A 50 5 B A B A 50 5 B A B A 50 B A B A 50 B A B A 50 B Link cost changes here; C updates D(C, A) = 60 as B has advertised D(B, A) = time Algorithm terminates 27

128 Aside: Another Way to Avoid Loops? In Distributed Computation? Exchange entire paths, not just cost of paths Nodes can use arbitrary metrics to choose paths No need to agree on single metric No loops, but algorithm might not converge Will discuss later in semester 28

129 Routing: Just the Beginning Link state and distance-vector (and path vector) are the deployed routing paradigms But we know how to do much, much better Stay tuned for a later lecture where we: Reduce convergence time to zero Respond to failures instantly! 29

130 Next Lecture Review computations (if needed) What pieces are we missing? Naming Security Content retrieval??? 30