EE122: Discussion #4

EE122: Discussion #4

Link-State RoutingDistance Vector Routing

Routing: What to keep in mind

• Many ways to route: flooding, link-state, distance-vector, path-vector…

• Main considerations for a routing algorithm– Scale– Message complexity – How many messages sent in…

– Speed of Convergence– Robustness – What happens if a router…

• initialization? • link dies?

• link updates? • link comes up?

• fails? • is sabotaged?

• misbehaves?

Link-State (LS) Algorithm

• Broadcast link-state packets• All routers know entire graph• Run Dijkstra’s Algorithm (this is in the textbook!)

Distance Vector (DV) Routing

Each node maintains 2 things

• Routing table– Cost of going to every destination,

through every neighbor

• Forwarding information– Next hop neighbor for every

destination

Node D

B C

A 8 4

B 6 2

C 7 1

B

A C

D

11

5

2

6

4

2

1Destinations

Neighbors

Distance Vector Routing

• Three “functions”– Initialization– Neighbor update message– Link update

Distance Vector RoutingInitialization

• For all neighbor nodes,– Set routing table entry to cost of link

with neighbor

• For all other nodes in network,– Set routing table entry to infinity (or

“?”)

• Notify neighbors

Node D

B C

A ? ?

B 6 ?

C ? 1

B

A C

D

11

5

2

6B

C

D

1

6

Distance Vector RoutingNeighbor Update Msg

• Whenever a node gets forwarding information from neighbor (say X)– Update cost to every destination

through neighbor X– Update forwarding information

Node D

B C

A ? ?

B 6 ?

C ? 1C->D: {(A, 5), (B, 1), (D, 1)}

B

C

D

1

6


• Whenever I get a message from neighbor (say X) about their forwarding information– Update cost to every destination


Node D

B C

A ? ?

B 6 ?

C ? 1C->D: {(A, 5), (B, 1), (D, 1)}

D’s cost of reaching A thru C =

D’s cost of reaching C +

C’s cost of reaching A

B

C

D

1

6

A 5

1




Node D

B C

A ? ? 6

B 6 ? 2

C ? 1C->D: {(A, 5), (B, 1), (D, 1)}

B

C

D

1

6

A 5

1

Node D

B C

A ? ? 6

B 6 ? 2

C ? 1




• If forwarding information changed, send it to all neighbors

Node D

B C

A ? ? 6

B 6 ? 2

C ? 1

D->BC: {(A, 6), (B, 2), (C, 1)}

B

C

D

1

6

A 5

1

B

C

D

1

6

A 5

1

Node D

B C

A ? ? 6

B 6 ? 2

C ? 1

Distance Vector RoutingLink Update

• Whenever a link updates– Update cost in table– Update forwarding information


Node D

B C

A ? ? 6

B 6 1 ? 2

C ? 1

1

B

C

D

1

6

A 5

1

Node D

B C

A ? ? 6

B 6 ? 2

C ? 1

Distance Vector RoutingLink Update

• Whenever a link updates– Update cost in table– Update forwarding information


Node D

B C

A ? ? 6

B 6 1 ? 2

C ? 1

1

D->BC: {(A, 6), (B, 1), (C, 1)}

Distance Vector (DV) Routing/* Distance to node u through neighbor n. Initialized all to infinity. */d[n][u] = infinity;/* Distance to neighbor n. Know from beginning. */c[n] = {…};/* Best distances, initialize all as infinity. */b[u] = infinity;

initialize() {/* Set all values can from

known neighbor distances. */foreach n in Neighbord[n][n] = c[n];b[n] = c[n];send_to_neighbors(b);

}

link_update(l, n) {// Diff between old and newa = c[n] – l;c[n] = l;change = false;foreach u in Graph// Update distance to u through nd[n][u] += a;// If new min distance, updateif b[u] != min(d[*][u])b[u] = min(d[*][u]);change = true;if changesend_to_neighbors(b);

}

recv_update(v, n) {change = false;foreach u in Graph// Update distance to u through nd[n][u] = c[n] + v[u];// If new min distance, updateif b[u] != min(d[*][u])b[u] = min(d[*][u]);change = true;if changesend_to_neighbors(b);

}

Group Work: DV Routing “Game”• Groups of 5-10

– Pair up so there are 5 nodes• Worksheet

– Node name– Link state: (neighbor, cost)

• Rules– No talking

• You can tell your group what node you are• Can ask questions

– Communicate via pieces of paper• Write and hand messages only to neighbors• Message format: (A - __ B - __ C - __ D - __ E - __)

– After converge route a piece of paper from A to B• Write your node on the paper before forwarding, to show the path• Node B bring paper to me• First group to finish get a prize!




}


}


}

• After converge route a piece of paper from A to B• Write your node on the paper before

forwarding, to show the path• Node B bring paper to me• First group to finish get a prize!

DV Routing: Scenario 1

D E

A C B

11

1

1

4

6

8

Node A

C D

B 7 4

C 6 3

D 8 1

E 7 2

Node B

C E

A 4 10

C 1 9

D 3 9

E 2 8

Node C

A B D E

A 6 5 5 3

B 9 1 7 3

D 7 4 4 2

E 8 3 5 1

Node D

A C E

A 1 7 3

B 4 5 3

C 4 4 2

E 3 5 1

Node E

B C D

A 12 4 2

B 8 2 4

C 9 1 3

D 11 3 1

A->B path = A –> D –> E –> C –> B

DV: initialize()B

Node AB C

B 2 ?C ? 5D ? ?

A C

D

11

5

2

6

initialize() {foreach u in Graph

b[u] = nil;foreach n in Neighbor

foreach u in Graphd[n][u] = infinity;

d[n][n] = c[n];send_vector_to_neighbors();

}

un

Node B

A C D

A 2 ? ?

C ? 1 ?

D ? ? 6

un

Node C

A B D

A 5 ? ?

B ? 1 ?

D ? ? 1

un

Node D

B C

A ? ?

B 6 ?

C ? 1

un

B->ACD: {(A, 2), (C, 1), (D, 6)}

DV: Message 1B

Node AB C

B 2 ?C ? 3 5D ? 8 ?

A C

D

11

5

2

6

recv_update(v, n) {change = false;foreach u in Graph

d[n][u] = c[n] + v[u];if d[b[u]][u] > d[n][u]

b[u] = n;change = true;

if changesend_vector_to_neighbors();

}

un

Node B

A C D

A 2 ? ?

C ? 1 ?

D ? ? 6

un

Node C

A B D

A 5 ? 3 ?

B ? 1 ?

D ? ? 7 1

un

Node D

B C

A ? 8 ?

B 6 ?

C ? 7 1

un

1. B->ACD: {(A, 2), (C, 1), (D, 6)}

C->ABD: {(A, 3), (B, 1), (D, 1)}

DV: Message 2B

Node AB C

B 2 ? 6C ? 3 5D ? 8 ? 6

A C

D

11

5

2

6





}

un

Node B

A C D

A 2 ? 4 ?

C ? 1 ?

D ? ? 2 6

un

Node C

A B D

A 5 ? 3 ?

B ? 1 ?

D ? ? 7 1

un

Node D

B C

A ? 8 ? 4

B 6 ? 2

C ? 7 1

un

1. B->ACD: {(A, 2), (C, 1), (D, 6)}2. C->ABD: {(A, 3), (B, 1), (D, 1)}

A->BC: {(B, 2), (C, 3), (D, 6)}

DV: Message 3B

Node AB C

B 2 ? 6C ? 3 5D ? 8 ? 6

A C

D

11

5

2

6





}

un

Node B

A C D

A 2 ? 4 ?

C ? 5 1 ?

D ? 8 ? 2 6

un

Node C

A B D

A 5 ? 3 ?

B ? 7 1 ?

D ? 11 ? 7 1

un

Node D

B C

A ? 8 ? 4

B 6 ? 2

C ? 7 1

un

1. B->ACD: {(A, 2), (C, 1), (D, 6)}2. C->ABD: {(A, 3), (B, 1), (D, 1)}3. A->BC: {(B, 2), (C, 3), (D, 6)}

No change

D->BC: {(A, 4), (B, 2), (C, 1)}

DV: Message 4B

Node AB C

B 2 ? 6C ? 3 5D ? 8 ? 6

A C

D

11

5

2

6





}

un

Node B

A C D

A 2 ? 4 ? 10

C ? 5 1 ? 7

D ? 8 ? 2 6

un

Node C

A B D

A 5 ? 3 ? 5

B ? 7 1 ? 3

D ? 11 ? 7 1

un

Node D

B C

A ? 8 ? 4

B 6 ? 2

C ? 7 1

un

1. B->ACD: {(A, 2), (C, 1), (D, 6)}2. C->ABD: {(A, 3), (B, 1), (D, 1)}3. A->BC: {(B, 2), (C, 3), (D, 6)}4. D->BC: {(A, 4), (B, 2), (C, 1)}

No change

B->ACD: {(A, 2), (C, 1), (D, 2)}

DV: Message 5B

Node AB C

B 2 ? 6C ? 3 5D ? 8 4 ? 6

A C

D

11

5

2

6





}

un

Node B

A C D

A 2 ? 4 ? 10

C ? 5 1 ? 7

D ? 8 ? 2 6

un

Node C

A B D

A 5 ? 3 ? 5

B ? 7 1 ? 3

D ? 11 ? 7 3 1

un

Node D

B C

A ? 8 ? 4

B 6 ? 2

C ? 7 1

un

1. B->ACD: {(A, 2), (C, 1), (D, 6)}2. C->ABD: {(A, 3), (B, 1), (D, 1)}3. A->BC: {(B, 2), (C, 3), (D, 6)}4. D->BC: {(A, 4), (B, 2), (C, 1)}5. B->ACD: {(A, 2), (C, 1), (D, 2)}

A->BC: {(B, 2), (C, 3), (D, 4)}

DV: Message 6B

Node AB C

B 2 ? 6C ? 3 5D ? 8 4 ? 6

A C

D

11

5

2

6





}

un

Node B

A C D

A 2 ? 4 ? 10

C ? 5 1 ? 7

D ? 8 6 ? 2 6

un

Node C

A B D

A 5 ? 3 ? 5

B ? 7 1 ? 3

D ? 11 9 ? 7 3 1

un

Node D

B C

A ? 8 ? 4

B 6 ? 2

C ? 7 1

un

1. B->ACD: {(A, 2), (C, 1), (D, 6)}2. C->ABD: {(A, 3), (B, 1), (D, 1)}3. A->BC: {(B, 2), (C, 3), (D, 6)}4. D->BC: {(A, 4), (B, 2), (C, 1)}5. B->ACD: {(A, 2), (C, 1), (D, 2)}6. A->BC: {(B, 2), (C, 3), (D, 4)}

Converged!

DV Routing: Scenario 2• Flip paper to other side

– Same node– But new forwarding table!

• Something happens to your network!• Same Rules

– No talking• You can tell your group what node you are (but that’s it!)• Can ask me questions

– Communicate via pieces of paper• Write and hand messages only to neighbors

• Go!




}


}


}


A

D

E

C

B

2

2

2

2

2

Node A

C D

B 4 4

C 2 6

D 6 2

E 4 8 12 16 20 21

8 12 16 20 24 25

Node B

C D

A 4 4

C 2 6

D 6 2

E 4 8 12 16 20 21

8 12 16 20 24 25

Node C

A B E

A 2 6 6

B 6 2 6

D 4 4 4

E 6 10 14 18 22

6 10 14 18 22

2 19

Node D

A B

A 2 6

B 6 2

C 4 4

E 6 10 14 18 22

6 10 14 18 22

Node E

C

A 4 21

B 4 21

C 2 19

D 6 23

19

1. C->ABE: (E, 6)2. A->CD: (E, 8)3. B->CD: (E, 8)4. D->AB: (E, 10)5. C->ABE: (E, 10)6. A->CD: (E, 12)7. B->CD: (E, 12)8. D->AB: (E, 14)9. C->ABE: (E, 14)10. A->CD: (E, 16)11. B->CD: (E, 16)12. D->AB: (E, 18)

13. C->ABE: (E, 18)14. A->CD: (E, 20)15. B->CD: (E, 20)16. D->AB: (E, 22)17. C->ABE: (E, 19)18. A->CD: (E, 21)19. B->CD: (E, 21)20. D->AB: (E, 23)

Count to Infinity!

27

Count to infinity [1]

A

B

C

1

1

Node B

A C

A 1 3

B …

C …

Node C

B

A 2

B …

C …

28


A

B

C

∞

1

Node B

A C

A ∞ 3

B …

C …

Node C

B

A 2

B …

C …

Node B

A C

A ∞ 3

B …

C …

29


A

B

C

1

∞

Node C

B

A 2

B …

C …

Node B

A C

A ∞ 3

B …

C …B->C: { (A, 3), … }

Node C

B

A 4

B …

C …


A

B

C

1

∞

Node C

B

A 2

B …

C …

Node B

A C

A ∞ 5

B …

C …

Node C

B

A 4

B …

C …C->B: { (A, 4), … }

31


A

B

C

1

…and they counted happily ever after to infinity!

∞Node B

A C

A ∞ 5

B …

C …B->C: { (A, 5), … }

Node C

B

A 6

B …

C …

32

Why does this occur?

• Routers B and C don’t know that their paths to A are through each other!

• Poison Reverse: To the neighbor who is providing me my best path, I advertise a cost of infinity

DV Routing: Poison Reversesend_to_neighbors (b) {

foreach n in Neighborssend(b);

}

send_to_neighbors_poison_reverse(b) {foreach n in Neighbors

c = copy(b);foreach u in Graph

// If use neighbor to get u, say cost is infinityif n == min_neighbor(d[*][u]) // Tie-breaker: alphabetic

c[u] = infinity;send(c);

}

34


A

B

C

1

1

Node B

A C

A 1 ∞

B …

C …

Node C

B

A 2

B …

C …


A

D

E

C

B

2

2

2

2

2

Node A

C D

B 4 4

C 2 ?

D ? 2

E 4 ?

Node B

C D

A 4 4

C 2 6

D 6 2

E 4 8

Node C

A B E

A 2 ? ?

B ? 2 ?

D 4 4 ?

E ? ? 2

Node D

A B

A 2 6

B 6 2

C 4 4

E 6 6

Node E

C

A 4

B 4

C 2

D 6

19

Before link change with Poison Reverse


A

D

E

C

B

2

2

2

2

2

Node A

C D

B 4 4

C 2 ?

D ? 2

E 4 21 12 21

? 23 ?

Node B

C D

A 4 4

C 2 6

D 6 2

E 4 21 ? 21

8 ? 1825

Node C

A B E

A 2 ? ?

B ? 2 ?

D 4 4 ?

E ? ? 10 ? 2 19

Node D

A B

A 2 6

B 6 2

C 4 4

E 6 23 14 23

6 ? 23

Node E

C

A 4 21

B 4 21

C 2 19

D 6 23

19

1. C-> A: (E, 19) B: (E, 19) E: (E, ?)

2. A-> C: (E, ?) D: (E, 21)3. B-> C: (E, 8) D: (E, ?)4. D-> A: (E, 23) B: (E, ?)5. C-> A: (E, 10) B: (E, ?) E: (E,

10)6. A-> C: (E, ?) D: (E, 12)7. B-> C: (E, ?) D: (E, ?)8. D-> A: (E, ?) B: (E, 16)9. C-> A: (E, 19) B: (E, 19) E:

(E, ?)10. A-> C: (E, ?) D: (E, 21)11. D-> A: (E, ?) B: (E, 23)12. B-> C: (E, ?) D: (E, 21)

Link-State vs. Distance Vector

Link-State• Message complexity

– O(|N||E|) messages sent– Link cost change -> everyone

notified

• Speed of convergence– O(|N|2) with O(|N||E|) messages

• Robustness– Table calculation semi-separated

between nodes

Distance Vector• Message complexity

– Messages only between neighbors

– Link cost change -> notify only if changes the cost of the min path

• Speed of convergence– Can be slow– Potential of loops– Count-to-infinity

• Robustness– Node’s table dependent on other

nodes’ calculations

EE122: Discussion #4

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