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EE122: Discussion #4

EE122: Discussion #4. Link-State Routing Distance 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

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EE122: Discussion #4

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  1. EE122: Discussion #4 Link-State Routing Distance Vector Routing

  2. 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…

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

  4. Distance Vector (DV) Routing 6 D B Each node maintains 2 things • Routing table • Cost of going to every destination, through every neighbor • Forwarding information • Next hop neighbor for every destination 1 2 1 C A 5 Neighbors Destinations

  5. Distance Vector Routing • Three “functions” • Initialization • Neighbor update message • Link update

  6. Distance Vector Routing 6 6 D D B B Initialization • 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 1 2 1 1 C C A 5

  7. Distance Vector Routing 6 D B Neighbor Update Msg • Whenever a node gets forwarding information from neighbor (say X) • Update cost to every destination through neighbor X • Update forwarding information 1 C C->D: {(A, 5), (B, 1), (D, 1)}

  8. Distance Vector Routing 6 D B Neighbor Update Msg • Whenever I get a message from neighbor (say X) about their forwarding information • Update cost to every destination through neighbor X • Update forwarding information 1 C 1 D’s cost of reaching A thru C = D’s cost of reaching C + C’s cost of reaching A A 5 C->D: {(A, 5), (B, 1), (D, 1)}

  9. Distance Vector Routing 6 D B Neighbor Update Msg • Whenever a node gets forwarding information from neighbor (say X) • Update cost to every destination through neighbor X • Update forwarding information 1 C 1 A 5 C->D: {(A, 5), (B, 1), (D, 1)}

  10. Distance Vector Routing 6 D B Neighbor Update Msg • Whenever a node gets forwarding information from neighbor (say X) • Update cost to every destination through neighbor X • Update forwarding information • If forwarding information changed, send it to all neighbors 1 C 1 A 5 D->BC: {(A, 6), (B, 2), (C, 1)}

  11. Distance Vector Routing 6 D 1 B Link Update • Whenever a link updates • Update cost in table • Update forwarding information • If forwarding information changed, send it to all neighbors 1 C 1 A 5

  12. Distance Vector Routing 6 D 1 B Link Update • Whenever a link updates • Update cost in table • Update forwarding information • If forwarding information changed, send it to all neighbors 1 C 1 A 5 D->BC: {(A, 6), (B, 1), (C, 1)}

  13. 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. */ foreachn in Neighbor d[n][n] = c[n]; b[n] = c[n]; send_to_neighbors(b); } link_update(l, n) { // Diff between old and new a = c[n] – l; c[n] = l; change = false; foreachu in Graph // Update distance to u through n d[n][u] += a; // If new min distance, update if b[u] != min(d[*][u]) b[u] = min(d[*][u]); change = true; if change send_to_neighbors(b); } recv_update(v, n) { change = false; foreach u in Graph // Update distance to u through n d[n][u] = c[n] + v[u]; // If new min distance, update if b[u] != min(d[*][u]) b[u] = min(d[*][u]); change = true; if change send_to_neighbors(b); }

  14. 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!

  15. 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. */ foreachn in Neighbor d[n][n] = c[n]; b[n] = c[n]; send_to_neighbors(b); } link_update(l, n) { // Diff between old and new a = c[n] – l; c[n] = l; change = false; foreachu in Graph // Update distance to u through n d[n][u] += a; // If new min distance, update if b[u] != min(d[*][u]) b[u] = min(d[*][u]); change = true; if change send_to_neighbors(b); } recv_update(v, n) { change = false; foreach u in Graph // Update distance to u through n d[n][u] = c[n] + v[u]; // If new min distance, update if b[u] != min(d[*][u]) b[u] = min(d[*][u]); change = true; if change send_to_neighbors(b); } • 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!

  16. DV Routing: Scenario 1 1 D E 1 8 A->B path = A –> D –> E –> C –> B 1 4 A C B 6 1

  17. DV: initialize() 6 D B 1 2 1 C A 5 initialize() { foreach u in Graph b[u] = nil; foreach n in Neighbor foreachu in Graph d[n][u] = infinity; d[n][n] = c[n]; send_vector_to_neighbors(); } B->ACD: {(A, 2), (C, 1), (D, 6)} n n n n u u u u

  18. DV: Message 1 6 B->ACD: {(A, 2), (C, 1), (D, 6)} D B 1 2 1 C A 5 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 change send_vector_to_neighbors(); } C->ABD: {(A, 3), (B, 1), (D, 1)} n n n n u u u u

  19. DV: Message 2 6 B->ACD: {(A, 2), (C, 1), (D, 6)} C->ABD: {(A, 3), (B, 1), (D, 1)} D B 1 2 1 C A 5 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 change send_vector_to_neighbors(); } A->BC: {(B, 2), (C, 3), (D, 6)} n n n n u u u u

  20. DV: Message 3 6 B->ACD: {(A, 2), (C, 1), (D, 6)} C->ABD: {(A, 3), (B, 1), (D, 1)} A->BC: {(B, 2), (C, 3), (D, 6)} D B 1 2 1 C A 5 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 change send_vector_to_neighbors(); } No change D->BC: {(A, 4), (B, 2), (C, 1)} n n n n u u u u

  21. DV: Message 4 6 B->ACD: {(A, 2), (C, 1), (D, 6)} C->ABD: {(A, 3), (B, 1), (D, 1)} A->BC: {(B, 2), (C, 3), (D, 6)} D->BC: {(A, 4), (B, 2), (C, 1)} D B 1 2 1 C A 5 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 change send_vector_to_neighbors(); } No change B->ACD: {(A, 2), (C, 1), (D, 2)} n n n n u u u u

  22. DV: Message 5 6 B->ACD: {(A, 2), (C, 1), (D, 6)} C->ABD: {(A, 3), (B, 1), (D, 1)} A->BC: {(B, 2), (C, 3), (D, 6)} D->BC: {(A, 4), (B, 2), (C, 1)} B->ACD: {(A, 2), (C, 1), (D, 2)} D B 1 2 1 C A 5 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 change send_vector_to_neighbors(); } A->BC: {(B, 2), (C, 3), (D, 4)} n n n n u u u u

  23. DV: Message 6 6 B->ACD: {(A, 2), (C, 1), (D, 6)} C->ABD: {(A, 3), (B, 1), (D, 1)} A->BC: {(B, 2), (C, 3), (D, 6)} D->BC: {(A, 4), (B, 2), (C, 1)} B->ACD: {(A, 2), (C, 1), (D, 2)} A->BC: {(B, 2), (C, 3), (D, 4)} D B 1 2 1 C A 5 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 change send_vector_to_neighbors(); } Converged! n n n n u u u u

  24. 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!

  25. 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. */ foreachn in Neighbor d[n][n] = c[n]; b[n] = c[n]; send_to_neighbors(b); } link_update(l, n) { // Diff between old and new a = c[n] – l; c[n] = l; change = false; foreachu in Graph // Update distance to u through n d[n][u] += a; // If new min distance, update if b[u] != min(d[*][u]) b[u] = min(d[*][u]); change = true; if change send_to_neighbors(b); } recv_update(v, n) { change = false; foreach u in Graph // Update distance to u through n d[n][u] = c[n] + v[u]; // If new min distance, update if b[u] != min(d[*][u]) b[u] = min(d[*][u]); change = true; if change send_to_neighbors(b); }

  26. DV Routing: Scenario 2 2 C->ABE: (E, 6) A->CD: (E, 8) B->CD: (E, 8) D->AB: (E, 10) C->ABE: (E, 10) A->CD: (E, 12) B->CD: (E, 12) D->AB: (E, 14) C->ABE: (E, 14) A->CD: (E, 16) B->CD: (E, 16) D->AB: (E, 18) C->ABE: (E, 18) A->CD: (E, 20) B->CD: (E, 20) D->AB: (E, 22) C->ABE: (E, 19) A->CD: (E, 21) B->CD: (E, 21) D->AB: (E, 23) D B 2 2 A C 2 2 19 E Count to Infinity!

  27. Count to infinity [1] A 1 B 1 C

  28. Count to infinity [2] A ∞ B 1 C

  29. Count to infinity [2] A ∞ B 1 B->C: { (A, 3), … } C

  30. Count to infinity [3] A ∞ B 1 C C->B: { (A, 4), … }

  31. Count to infinity [4] A ∞ B 1 B->C: { (A, 5), … } C …and they counted happily ever after to infinity!

  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

  33. DV Routing: Poison Reverse send_to_neighbors(b) { foreachn in Neighbors send(b); } send_to_neighbors_poison_reverse(b) { foreachn in Neighbors c = copy(b); foreach u in Graph // If use neighbor to get u, say cost is infinity if n == min_neighbor(d[*][u]) // Tie-breaker: alphabetic c[u] = infinity; send(c); }

  34. Count to infinity [1] A 1 B 1 C

  35. DV Routing: Scenario 2 2 D B 2 2 A C 2 2 19 E Before link change with Poison Reverse

  36. DV Routing: Scenario 2 2 C-> A: (E, 19) B: (E, 19) E: (E, ?) A-> C: (E, ?) D: (E, 21) B-> C: (E, 8) D: (E, ?) D-> A: (E, 23) B: (E, ?) C-> A: (E, 10) B: (E, ?) E: (E, 10) A-> C: (E, ?) D: (E, 12) B-> C: (E, ?) D: (E, ?) D-> A: (E, ?) B: (E, 16) C-> A: (E, 19) B: (E, 19) E: (E, ?) A-> C: (E, ?) D: (E, 21) D-> A: (E, ?) B: (E, 23) B-> C: (E, ?) D: (E, 21) D B 2 2 A C 2 2 19 E

  37. Link-State vs. Distance Vector Link-State 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 • 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

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