06-Routing.pdf

1The Fundamentals of Routing

EE122 Fall 2011Scott Shenker

http://inst.eecs.berkeley.edu/~ee122/Materials with thanks to Jennifer Rexford, Ion Stoica, Vern Paxson

and other colleagues at Princeton and UC Berkeley

Announcements 194 is set up: 4 units: CCN: 25571

Everyone should be off wait list by now. Waiting for more accounts

o Send me email if you need one. Will set up bspace for 194 to hand in homework

Open today with questions about project 1

Hope you all handed in HW1 HW2 out on Wednesday

Survey will be available after Wednesdays class 2

Questions about Project 1 (for Shaddi)

3

Warning. This lecture contains detailed calculations

Prolonged exposure may induce drowsiness

Do not operate heavy machinery while listening

4

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

The Traditional Routing Curriculum Learning switches Link-state routing

Dijkstras Algorithm Distance-vector routing

Bellman-Ford

6

I have some bad news.. Dont 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..134 slides! Lets just see how timing goes If you dont want to be bored, ask questions!

7

Remember. Goal of the first portion of course is conceptual

Ignore real networks

Think about the basic concepts

Thats where we are. Later will deal with reality

8

9Basics of Routing and Forwarding

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

10

Packets (at a conceptual level) Assume packet headers contain:

Source ID, Destination ID, and perhaps other information

11

DestinationIdentifierSource

Identifier

Payload

Why includethis?

Switches/Routers Multiple ports (attached to other switches or hosts)

Ports are typically duplex (incoming and outgoing)12

incoming links outgoing linksSwitch

Example of Network Graph

13

Six ports, incoming/outgoing

Four ports, incoming/outgoing

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) 14

UUNETs North American Network

15

Level3s American Network

16

Enterprise Network

17

Partial Datacenter Network

18

Switches Enterprise/Edge: typically 24 to 48 ports Aggregation switches: 192 ports or more Backbone: typically fewer ports Border: typically very few ports

19

Forwarding Decisions When packet arrives, must choose outgoing port

Decision is based on routing state (table) in switch20

incoming links outgoing linksSwitch

Consider packet header

and routing table

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. 21

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.

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23

Validity of Routing State

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

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

Necessary: Obvious If you run into a deadend before hitting destination,

youll never reach the destination

If you run into a loop, youll never reach destination With deterministic forwarding, once you loop, youll loop

forever (assuming routing state is static)

26

Wandering Packets

27

Packet reaches deadend and stopsPacket falls into loop and never reaches destination

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

The Secret of Routing Avoiding deadends is easy Avoiding loops is hard The key difference between routing protocols is

how they avoid loops! Dont focus on details of mechanisms Just ask how are loops avoided?

Will return to this later.

29

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

Forwarding Decision Dependencies Must depend on destination

Could also depend on : Source: requires n2 state Input port: not clear what this buys you Other header information: lets ignore for now

We will focus only on destination-based routing But first consider the alternative

31

Source/Destination-Based Routing

32

Paths from two different sources (to same destination) can be very different

Destination-Based Routing

33

Paths from two different sources (to same destination) must coincide once they overlap

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

A Delivery Tree for a Destination

35

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 whats left.

36

Example 1

37

Pick Destination

38

Put Arrows on Outgoing Ports

39

Remove Unused Links

40

Leaves Spanning Tree: Valid

Second Example

41

Second Example

42

Is this valid?

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

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44

Computing Routing State

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

How Can You Avoid Loops? Restrict topology to spanning tree

If the topology has no loops, packets cant 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

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

Consider previous graph

49

A Spanning Tree

50

Another Spanning Tree

51

Yet Another Spanning Tree

52

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

Flooding on Spanning Tree

54

Flooding on Spanning Tree (Again)

55

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

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

Learning from Flood Packets

58

Node A

Node A can be reachedthrough this port

Node A can be reachedthrough this port

Once a node has sent a flood message, all other switches know how to reach it.

General Approach Flood first packet All switches learn where you are When destination responds, all switches learn

where it is

Done.

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60

Self-Learning SwitchWhen 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

A

B

C

D

Packet tells switch how to reach A.

61

Self Learning: Handling MissesWhen packet arrives with unfamiliar destination

Forward packet out all other ports

Response will teach switch about that destination

A

B

C

D

When in doubt, shout!

62

General RuleWhen switch receives a packet:index the switch table using destination IDif entry found for destination {

if dest on port from which packet arrivedthen drop packetelse forward packet on port indicated

}else flood

forward on all but the interface

on which the frame arrived

Why do this?

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

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

On to other routing techniques

65

66

A Little Test

How many of you did the reading?

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 1) to destination (node 40) in five minutes

67

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: Try68

Go!

69

1 16 36 7 25

10 19 5 34 38

29 33 15 39 23

14 9 2 35 11

22 32 26 21 37

3 28 12 30 4

27 20 31 18 24

40 8 17 6 13

71

5 Minute Break

Questions Before We Proceed?

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

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

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 Dijkstras algorithm briefly But thats just because it is expected from such courses

o Snore..

The real question is, how do you get picture of entire network?

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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 Dijkstras 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

77

Link State Routing Each node floods its local information Each node then knows entire network topology

Host A

Host BHost E

Host D

Host C

N1 N2

N3

N4

N5

N7N6

78

Link State: Each Node Has Global View

Host A

Host BHost E

Host D

Host C

N1 N2

N3

N4

N5

N7N6

A

BE

DC

A

BE

DC A

BE

DC

A

BE

DC

A

BE

DC

A

BE

DC

A

BE

DC

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 Dont worry what it stands for.

79

Dijkstras 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 beforeo Previous tree was rooted at destinationo This is rooted at sourceo But shortest paths are reversible!

80

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

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82

Example

A

ED

CB

F

2

2

13

1

1

2

53

5

83

Notation

c(i,j): link cost from node ito 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

A

ED

CB

F

2

21

3

1

1

2

53

5

Source

84

Dijsktras Algorithm1 Initialization:2 S = {A};3 for all nodes v4 if v adjacent to A5 then D(v) = c(A,v); 6 else D(v) = ;7 8 Loop9 find w not in S such that D(w) is a minimum; 10 add w to S; 11 update D(v) for all v adjacent to w and not in S: 12 if D(w) + c(w,v) < D(v) then

// w gives us a shorter path to v than weve found so far13 D(v) = D(w) + c(w,v); p(v) = w;14 until all nodes in S;

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

85

Example: Dijkstras AlgorithmStep

012345

start SA

D(B),p(B)2,A

D(C),p(C)5,A

D(D),p(D)1,A

D(E),p(E) D(F),p(F)

A

ED

CB

F2

21

3

1

1

2

53

5

1 Initialization:2 S = {A};3 for all nodes v4 if v adjacent to A5 then D(v) = c(A,v); 6 else D(v) = ;

86


012345

start SA

D(B),p(B)2,A

D(C),p(C)5,A

8 Loop9 find w not in S s.t. D(w) is a minimum; 10 add w to S; 11 update D(v) for all v adjacent

to w and not in S: 12 If D(w) + c(w,v) < D(v) then13 D(v) = D(w) + c(w,v); p(v) = w;14 until all nodes in S;

A

ED

CB

F2

21

3

1

1

2

53

5

D(D),p(D)1,A

D(E),p(E) D(F),p(F)

87


012345

start SA

AD

D(B),p(B)2,A

D(C),p(C)5,A

D(D),p(D)1,A

D(E),p(E) D(F),p(F)

A

ED

CB

F2

21

3

1

1

2

53

5



88


012345

start SA

AD

D(B),p(B)2,A

D(C),p(C)5,A4,D

D(D),p(D)1,A

D(E),p(E)

2,D

D(F),p(F)

A

ED

CB

F2

21

3

1

1

2

53

5



89


012345

start SA

ADADE

D(B),p(B)2,A

D(C),p(C)5,A4,D3,E

D(D),p(D)1,A

D(E),p(E)

2,D

D(F),p(F)

4,E

A

ED

CB

F2

21

3

1

1

2

53

5



90


012345

start SA

ADADE

ADEB

D(B),p(B)2,A

D(C),p(C)5,A4,D3,E

D(D),p(D)1,A

D(E),p(E)

2,D

D(F),p(F)

4,E

A

ED

CB

F2

21

3

1

1

2

53

5



91


012345

start SA

ADADE

ADEBADEBC

D(B),p(B)2,A

D(C),p(C)5,A4,D3,E

D(D),p(D)1,A

D(E),p(E)

2,D

D(F),p(F)

4,E

A

ED

CB

F2

21

3

1

1

2

53

5



92


012345

start SA

ADADE

ADEBADEBC

ADEBCF

D(B),p(B)2,A

D(C),p(C)5,A4,D3,E

D(D),p(D)1,A

D(E),p(E)

2,D

D(F),p(F)

4,E

A

ED

CB

F2

21

3

1

1

2

53

5



93


012345

start SA

ADADE

ADEBADEBC

ADEBCF

D(B),p(B)2,A

D(C),p(C)5,A4,D3,E

D(D),p(D)1,A

D(E),p(E)

2,D

D(F),p(F)

4,E

A

ED

CB

F2

21

3

1

1

2

53

5To determine path A C (say), work backward from C via p(v)

94

Running Dijkstra at node A gives the shortest path from A to all destinations

We then construct the forwarding table

The Forwarding Table

A

ED

CB

F2

21

3

1

1

2

53

5 Destination LinkB (A,B)C (A,D)D (A,D)E (A,D)F (A,D)

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+1)/2 comparisons: O(N2) 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

C B D(a)

X A

C B D(b)

X A

C B D(c)

X A

C B D(d)

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

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

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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

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

101

Inconsistent link-state database Some routers know about failure before others The shortest paths are no longer consistent Can cause transient forwarding loops

Transient Disruptions

A

ED

CB

F A

ED

CB

F

A and D think that thisis the path to C

E thinks that thisis the path to C

Loop!

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

103

Scaling Link-State Routing Overhead of link-state routing

Flooding link-state packets throughout the network Running Dijkstras shortest-path algorithm Becomes unscalable when 100s of routers

Introducing hierarchy through areas

Area 0

Area 1 Area 2

Area 3 Area 4

areaborderrouter

104

Distance-Vector

Details in Section

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

105

Distributed Computation

106

I am one hop away

I am one hop away

I am one hop away

I am two hops away

I am two hops away

I am two hops away

I am two hops away

I am three hops away

I am three hops away

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.

107

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 11 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

109

Information Flow in Distance Vector

Host A

Host BHost E

Host D

Host C

N1 N2

N3

N4

N5

N7N6

110


Host A

Host BHost E

Host D

Host C

N1 N2

N3

N4

N5

N7N6

111


Host A

Host BHost E

Host D

Host C

N1 N2

N3

N4

N5

N7N6

Why Is This Different From Flooding?

112

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

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Bellman-Ford - Overview Each router maintains a table

Best known distance from X to Y,via Z as next hop = DZ(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

wait for (change in local link cost or msg from neighbor)

recompute distance table

if least cost path to any dest has changed, notifyneighbors

Each node:


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 = DZ(X,Y)

A C12

7

B D3

1

B CB 2 8C 3 7D 4 8

Node A

Neighbor (next-hop)

Destinations DC(A, D)


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 = DZ(X,Y)

A C12

7

B D3

1

B CB 2 8C 3 7D 4 8

Node A

Smallest distance in row Y = shortestDistance of A to Y, D(A, Y)

117

Distance Vector Algorithm (contd)1 Initialization:2 for all neighbors V do3 if V adjacent to A4 D(A, V) = c(A,V);5 else6 D(A, V) = ;7 send D(A, Y) to all neighborsloop:

8 wait (until A sees a link cost change to neighbor V /* case 1 */9 or until A receives update from neighbor V) /* case 2 */10 if (c(A,V) changes by d) /* case 1 */11 for all destinations Y that go through V do12 DV(A,Y) = DV(A,Y) d13 else if (update D(V, Y) received from V) /* case 2 */

/* shortest path from V to some Y has changed */14 DV(A,Y) = DV(A,V) + D(V, Y); /* may also change D(A,Y) */15 if (there is a new minimum for destination Y)16 send D(A, Y) to all neighbors 17 forever

c(i,j): link cost from node i to j DZ(A,V): cost from A to V via Z D(A,V): cost of As best path to V

Example:1st Iteration (C A)

A C12

7

B D3

1

B CB 2 8C 7D 8

Node A

A C DA 2 C 1 D 3

Node B

Node C

A B DA 7 B 1 D 1

B CA B 3 C 1

Node D7 loop:

13 else if (update D(A, Y) from C) 14 DC(A,Y) = DC(A,C) + D(C, Y);15 if (new min. for destination Y)16 send D(A, Y) to all neighbors 17 forever

DC(A, B) = DC(A,C) + D(C, B) = 7 + 1 = 8DC(A, D) = DC(A,C) + D(C, D) = 7 + 1 = 8

Example: 1st Iteration (B A)

A C12

7

B D3

1

B CB 2 8C 3 7D 5 8

Node A

A C DA 2 C 1 D 3

Node B

Node C

A B DA 7 B 1D 1

Node D7 loop:

13 else if (update D(A, Y) from B) 14 DB(A,Y) = DB(A,B) + D(B, Y);15 if (new min. for destination Y)16 send D(A, Y) to all neighbors 17 forever

DB(A, C) = DB(A,B) + D(B, C) = 2 + 1 = 3DB(A, D) = DB(A,B) + D(B, D) = 2 + 3 = 5

B CA B 3 C 1

Example: End of 1st Iteration

A C12

7

B D3

1

B CB 2 8C 3 7D 5 8

Node A Node B

Node C

A B DA 7 3 B 9 1 4D 4 1

Node D

B CA 5 8B 3 2C 4 1

End of 1st Iteration All nodes knows the best two-hop paths

A C DA 2 3 C 9 1 4D 2 3

Example: 2nd Iteration (A B)

A C12

7

B D3

1

B CB 2 8C 3 7D 5 8

Node A Node B

Node C

A B DA 7 3 B 9 1 4D 4 1

Node D

B CA 5 8B 3 2C 4 1

A C DA 2 3 C 5 1 4D 7 2 3

7 loop:

13 else if (update D(B, Y) from A) 14 DA(B,Y) = DA(B,A) + D(A, Y);15 if (new min. for destination Y)16 send D(B, Y) to all neighbors 17 forever

DA(B, C) = DA(B,A) + D(A, C) = 2 + 3 = 5DA(B, D) = DA(B,A) + D(A, D) = 2 + 5 = 7

Example: End of 2nd Iteration

A C12

7

B D3

1

B CB 2 8C 3 7D 4 8

Node A

A C DA 2 3 11C 5 1 4D 7 2 3

Node B

Node C

A B DA 7 3 6B 9 1 4D 12 4 1

Node D

B CA 5 4B 3 2C 4 1

End of 2nd Iteration All nodes knows the best three-hop paths

Example: End of 3rd Iteration

A C12

7

B D3

1

B CB 2 8C 3 7D 4 8

Node A

A C DA 2 3 6C 5 1 4D 7 2 3

Node B

Node C

A B DA 7 3 5B 9 1 4D 11 4 1

Node D

B CA 5 4B 3 2C 4 1

End of 2nd Iteration: Algorithm

Converges!

Intuition Initial state: best one-hop paths One round: best two-hop paths Two rounds: best three-hop paths

Kth round: best (k+1) hop paths

This must eventually converge.but how does it respond to changes in cost?

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125

Distance Vector: Link Cost Changes

A C14

50

B1

goodnews travelsfast

A CA 4 6C 9 1

Node B

A BA 50 5B 54 1

Node C

Link cost changes heretime

Algorithm terminates

loop:8 wait (until A sees a link cost change to neighbor V9 or until A receives update from neighbor V) /10 if (c(A,V) changes by d) /* case 1 */11 for all destinations Y that go through V do12 DV(A,Y) = DV(A,Y) d13 else if (update D(V, Y) received from V) /* case 2 */14 DV(A,Y) = DV(A,V) + D(V, Y); 15 if (there is a new minimum for destination Y)16 send D(A, Y) to all neighbors 17 forever

A CA 1 6C 9 1

A BA 50 5B 54 1

A CA 1 6C 9 1

A BA 50 2B 51 1

A CA 1 3C 3 1

A BA 50 2B 51 1

126

DV: Count to Infinity Problem

A C14

50

B60

badnews travelsslowly

Node B

Node C

Link cost changes here time

loop:8 wait (until A sees a link cost change to neighbor V9 or until A receives update from neighbor V) /10 if (c(A,V) changes by d) /* case 1 */11 for all destinations Y that go through V do12 DV(A,Y) = DV(A,Y) d13 else if (update D(V, Y) received from V) /* case 2 */14 DV(A,Y) = DV(A,V) + D(V, Y); 15 if (there is a new minimum for destination Y)16 send D(A, Y) to all neighbors 17 forever

A CA 4 6C 9 1

A BA 50 5B 54 1

A CA 60 6C 9 1

A BA 50 5B 54 1

A CA 60 6C 9 1

A BA 50 7B 101 1

A CA 60 8C 9 1

A BA 50 7B 101 1

127

Distance Vector: Poisoned Reverse

A C14

50

B60 If B routes through C to get to A:

- B tells C its (Bs) distance to A is infinite (so C wont route to A via B)

- Will this completely solve count to infinityproblem?

Node B

Node C

Link cost changes here; C updates D(C, A) = 60 as B has advertised D(B, A) =

timeAlgorithm terminates

A CA 4 6C 9 1

A BA 50 5B 1

A CA 60 6C 9 1

A BA 50 5B 1

A CA 60 6C 9 1

A BA 50 B 1

A CA 60 51C 9 1

A BA 50 B 1

A CA 60 51C 9 1

A BA 50 B 1

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 semester128

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!

129

Next Lecture Review computations (if needed)

What pieces are we missing? Naming Security Content retrieval ???

130

Documents

06-Routing.pdf