The Fundamentals of Routingee122/fa11/notes/06-Routing.pdf · 1 The Fundamentals of Routing EE122...

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The Fundamentals of Routing

EE122 Fall 2011

Scott Shenker

http://inst.eecs.berkeley.edu/~ee122/

Materials with thanks to Jennifer Rexford, Ion Stoica, Vern Paxsonand 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 accountso 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 Wednesday’s 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– Dijkstra’s Algorithm

• Distance-vector routing– Bellman-Ford

6

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…..134 slides!– Let’s just see how timing goes

– If you don’t 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

• That’s where we are. Later will deal with reality…

8

9

Basics 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

Destination

Identifier

Source

Identifier

Payload

Why include

this?

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

UUNET’s North American Network

15

Level3’s 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 switch

20

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,

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

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!– Don’t 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: let’s 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 what’s 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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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 can’t loop!

• Central computation– Can make sure no loops

• Minimizing metric in distributed computation– Loops are never the solution to a minimization problem

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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 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

A

B

C

D

Packet tells switch how to reach A.

61

Self Learning: Handling Misses

When 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 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 arrivedthen drop packet

else 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 minutes67

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

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

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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 Dijkstra’s algorithm briefly

– But that’s just because it is expected from such courseso Snore…..

• The real question is, how do you get picture of

entire network?

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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

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

N1N2

N3

N4

N5

N7N6

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Link State: Each Node Has Global View

Host A

Host BHost E

Host D

Host C

N1N2

N3

N4

N5

N7N6

A

BE

D

C

A

BE

D

CA

BE

D

C

A

BE

D

C

A

BE

D

C

A

BE

D

C

A

BE

D

C

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

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 routeso 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

“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

5

3

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

2

13

1

1

2

5

3

5

Source

84

Dijsktra’’’’s Algorithm

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) = ;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 we’ve found so far

13 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: Dijkstra’’’’s Algorithm

Step012345

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

F

2

2

13

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


Step012345

start SA

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

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

…

8 Loop

9 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) then

13 D(v) = D(w) + c(w,v); p(v) = w;

14 until all nodes in S;

A

ED

CB

F

2

2

13

1

1

2

53

5

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

D(E),p(E) D(F),p(F)∞ ∞

87


Step012345

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

F

2

2

13

1

1

2

53

5

∞ ∞

…

8 Loop


10 add w to S;


to w and not in S:


13 D(v) = D(w) + c(w,v); p(v) = w;


88


Step012345

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

F

2

2

13

1

1

2

53

5

∞ ∞

…

8 Loop


10 add w to S;


to w and not in S:


13 D(v) = D(w) + c(w,v); p(v) = w;


89


Step012345

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

F

2

2

13

1

1

2

53

5…

8 Loop


10 add w to S;


to w and not in S:


13 D(v) = D(w) + c(w,v); p(v) = w;


90


Step012345

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

F

2

2

13

1

1

2

53

5…

8 Loop


10 add w to S;


to w and not in S:


13 D(v) = D(w) + c(w,v); p(v) = w;


91


Step012345

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

F

2

2

13

1

1

2

53

5…

8 Loop


10 add w to S;


to w and not in S:


13 D(v) = D(w) + c(w,v); p(v) = w;


92


Step012345

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

F

2

2

13

1

1

2

53

5…

8 Loop


10 add w to S;


to w and not in S:


13 D(v) = D(w) + c(w,v); p(v) = w;


93


Step012345

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

F

2

2

13

1

1

2

53

5

To 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

F

2

2

13

1

1

2

53

5Destination Link

B (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))

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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

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

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 Dijkstra’s shortest-path algorithm– Becomes unscalable when 100s of routers

• Introducing hierarchy through “areas”

Area 0

Area 1 Area 2

Area 3 Area 4

area

border

router

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:


• 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 = DZ(X,Y)

A C

12

7

B D3

1

B C

B 2 8

C 3 7

D 4 8

Node A

Neighbor (next-hop)

Destinations DC(A, D)


• 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 = DZ(X,Y)

A C

12

7

B D3

1

B C

B 2 8

C 3 7

D 4 8

Node A

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

117

Distance Vector Algorithm (cont’’’’d)

1 Initialization:2 for all neighbors V do3 if V adjacent to A

4 D(A, V) = c(A,V);

5 else6 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 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 do

12 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)


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 A’’’’s best path to V

Example:1st Iteration (C �� A)

A C

12

7

B D3

1

B C

B 2 8

C ∞ 7

D ∞ 8

Node A

A C D

A 2 ∞ ∞

C ∞ 1 ∞

D ∞ ∞ 3

Node B

Node C

A B D

A 7 ∞ ∞

B ∞ 1 ∞

D ∞ ∞ 1

B C

A ∞ ∞

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)


17 forever

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

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

Example: 1st Iteration (B �� A)

A C

12

7

B D3

1

B C

B 2 8

C 3 7

D 5 8

Node A

A C D

A 2 ∞ ∞

C ∞ 1 ∞

D ∞ ∞ 3

Node B

Node C

A B D

A 7 ∞ ∞

B ∞ 1

D ∞ ∞ 1

Node D7 loop:

…

13 else if (update D(A, Y) from B)

14 DB(A,Y) = DB(A,B) + D(B, Y);



17 forever

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

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

B C

A ∞ ∞

B 3 ∞

C ∞ 1

Example: End of 1st Iteration

A C

12

7

B D3

1

B C

B 2 8

C 3 7

D 5 8

Node A Node B

Node C

A B D

A 7 3 ∞

B 9 1 4

D ∞ 4 1

Node D

B C

A 5 8

B 3 2

C 4 1

End of 1st Iteration

All nodes knows the

best two-hop paths

A C D

A 2 3 ∞

C 9 1 4

D ∞ 2 3

Example: 2nd Iteration (A �� B)

A C

12

7

B D3

1

B C

B 2 8

C 3 7

D 5 8

Node A Node B

Node C

A B D

A 7 3 ∞

B 9 1 4

D ∞ 4 1

Node D

B C

A 5 8

B 3 2

C 4 1

A C D

A 2 3 ∞

C 5 1 4

D 7 2 3

7 loop:…

13 else if (update D(B, Y) from A)

14 DA(B,Y) = DA(B,A) + D(A, Y);


16 send D(B, Y) to all neighbors

17 forever

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

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

Example: End of 2nd Iteration

A C

12

7

B D3

1

B C

B 2 8

C 3 7

D 4 8

Node A

A C D

A 2 3 11

C 5 1 4

D 7 2 3

Node B

Node C

A B D

A 7 3 6

B 9 1 4

D 12 4 1

Node D

B C

A 5 4

B 3 2

C 4 1

End of 2nd Iteration

All nodes knows the

best three-hop paths

Example: End of 3rd Iteration

A C

12

7

B D3

1

B C

B 2 8

C 3 7

D 4 8

Node A

A C D

A 2 3 6

C 5 1 4

D 7 2 3

Node B

Node C

A B D

A 7 3 5

B 9 1 4

D 11 4 1

Node D

B C

A 5 4

B 3 2

C 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?

124

125

Distance Vector: Link Cost Changes

A C

14

50

B

1

“goodnews

travels

fast”

A C

A 4 6

C 9 1

Node B

A B

A 50 5

B 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) /


12 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 C

A 1 6

C 9 1

A B

A 50 5

B 54 1

A C

A 1 6

C 9 1

A B

A 50 2

B 51 1

A C

A 1 3

C 3 1

A B

A 50 2

B 51 1

126

DV: Count to Infinity Problem

A C

14

50

B

60

“badnews

travels

slowly”

Node B

Node C

Link cost changes heretime

…

loop:8 wait (until A sees a link cost change to neighbor V9 or until A receives update from neighbor V) /


12 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 C

A 4 6

C 9 1

A B

A 50 5

B 54 1

A C

A 60 6

C 9 1

A B

A 50 5

B 54 1

A C

A 60 6

C 9 1

A B

A 50 7

B 101 1

A C

A 60 8

C 9 1

A B

A 50 7

B 101 1

127

Distance Vector: Poisoned Reverse

A C

14

50

B

60• 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 infinityproblem?

Node B

Node C

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

B has advertised D(B, A) = ∞

time

Algorithm terminates

A C

A 4 6

C 9 1

A B

A 50 5

B ∞ 1

A C

A 60 6

C 9 1

A B

A 50 5

B ∞ 1

A C

A 60 6

C 9 1

A B

A 50 ∞

B ∞ 1

A C

A 60 51

C 9 1

A B

A 50 ∞

B ∞ 1

A C

A 60 51

C 9 1

A B

A 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 semester…128

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

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