1 / 46

EE 122 : Shortest Path Routing

EE 122 : Shortest Path Routing. Ion Stoica TAs: Junda Liu, DK Moon, David Zats http://inst.eecs.berkeley.edu/~ee122/fa09 (Materials with thanks to Vern Paxson , Jennifer Rexford, and colleagues at UC Berkeley). What is Routing?. Routing implements the core function of a network:

malini
Download Presentation

EE 122 : Shortest Path Routing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. EE 122: Shortest Path Routing Ion Stoica TAs: Junda Liu, DK Moon, David Zats http://inst.eecs.berkeley.edu/~ee122/fa09 (Materials with thanks to Vern Paxson, Jennifer Rexford,and colleagues at UC Berkeley)

  2. What is Routing? Routing implements the core function of a network: It ensures that information accepted for transfer at a source node is delivered to the correct set of destination nodes, at reasonable levels of performance.

  3. Internet Routing • Internet organized as a two level hierarchy • First level – autonomous systems (AS’s) • AS – region of network under a single administrative domain • AS’s run an intra-domain routing protocols • Distance Vector, e.g., Routing Information Protocol (RIP) • Link State, e.g., Open Shortest Path First (OSPF) • Between AS’s runs inter-domain routing protocols, e.g., Border Gateway Routing (BGP) • De facto standard today, BGP-4

  4. Example Interior router BGP router AS-1 AS-3 AS-2

  5. Forwarding vs. Routing • Forwarding: “data plane” • Directing a data packet to an outgoing link • Individual router using a forwarding table • Routing: “control plane” • Computing paths the packets will follow • Routers talking amongst themselves • Individual router creating a forwarding table

  6. Link State Routing E.g. Algorithm: Dijkstra E.g. Protocol: OSPF Distance Vector Routing E.g. Algorithm: Bellman-Ford E.g. Protocol: RIP Know Thy Network • Routing requires knowledge of the network structure • Centralized global state • Single entity knows the complete network structure • Can calculate all routes centrally • Problems with this approach? • Distributed global state • Every router knows the complete network structure • Independently calculates routes • Problems with this approach? • Distributed no-global state • Every router knows only about its neighboring routers • Independently calculates routes • Problems with this approach?

  7. 5 3 5 2 2 1 3 1 2 1 C D A B E F Modeling a Network • Modeled as a graph • Routers  nodes • Link  edges • Possible edge costs • delay • congestion level • Goal of Routing • Determine a “good” path through the network from source to destination • Good usually means the shortest path

  8. Host C Host D Host A N2 N1 N3 N5 Host B Host E N4 N6 N7 Link State: Control Traffic • Each node floods its local information to every other node in the network • Each node ends up knowing the entire network topology  use Dijkstra to compute the shortest path to every other node

  9. C C C C C C C A A A A A A A D D D D D D D Host C Host D Host A B B B B B B B E E E E E E E N2 N1 N3 N5 Host B Host E N4 N6 N7 Link State: Node State

  10. 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 D C A E B F 5 3 5 2 2 1 3 1 2 1 Notation Source

  11. Dijsktra’s Algorithm • 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 1 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) = ; 7 8 Loop 9 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;

  12. D C A E B F 5 3 5 2 2 1 3 1 2 1 Example: Dijkstra’s Algorithm D(B),p(B) 2,A D(D),p(D) 1,A D(C),p(C) 5,A D(E),p(E) Step 0 1 2 3 4 5 start S A D(F),p(F) 1 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) = ; …

  13. … • 8 Loop • 9 find w not in Ss.t. D(w) is a minimum; • 10 add w to S; • update D(v) for all v adjacent • to w and not in S: • If D(w) + c(w,v) < D(v) then • D(v) = D(w) + c(w,v); p(v) = w; • 14 until all nodes in S; D C A E B F 5 3 5 2 2 1 3 1 2 1 Example: Dijkstra’s Algorithm D(B),p(B) 2,A D(D),p(D) 1,A D(C),p(C) 5,A D(E),p(E) Step 0 1 2 3 4 5 start S A D(F),p(F)

  14. … • 8 Loop • 9 find w not in S s.t. D(w) is a minimum; • 10 add w to S; • update D(v) for all v adjacent • to w and not in S: • If D(w) + c(w,v) < D(v) then • D(v) = D(w) + c(w,v); p(v) = w; • 14 until all nodes in S; C D E A B F Example: Dijkstra’s Algorithm D(B),p(B) 2,A D(D),p(D) 1,A D(C),p(C) 5,A D(E),p(E) Step 0 1 2 3 4 5 start S A AD D(F),p(F) 5 3 5 2 2 1 3 1 2 1

  15. … • 8 Loop • 9 find w not in S s.t. D(w) is a minimum; • 10 add w to S; • update D(v) for all v adjacent • to w and not in S: • If D(w) + c(w,v) < D(v) then • D(v) = D(w) + c(w,v); p(v) = w; • 14 until all nodes in S; C D E A B F Example: Dijkstra’s Algorithm D(B),p(B) 2,A D(D),p(D) 1,A D(C),p(C) 5,A 4,D D(E),p(E) 2,D Step 0 1 2 3 4 5 start S A AD D(F),p(F) 5 3 5 2 2 1 3 1 2 1

  16. … • 8 Loop • 9 find w not in S s.t. D(w) is a minimum; • 10 add w to S; • update D(v) for all v adjacent • to w and not in S: • If D(w) + c(w,v) < D(v) then • D(v) = D(w) + c(w,v); p(v) = w; • 14 until all nodes in S; C D E A B F Example: Dijkstra’s Algorithm D(B),p(B) 2,A D(D),p(D) 1,A D(C),p(C) 5,A 4,D 3,E D(E),p(E) 2,D Step 0 1 2 3 4 5 start S A AD ADE D(F),p(F) 4,E 5 3 5 2 2 1 3 1 2 1

  17. … • 8 Loop • 9 find w not in S s.t. D(w) is a minimum; • 10 add w to S; • update D(v) for all v adjacent • to w and not in S: • If D(w) + c(w,v) < D(v) then • D(v) = D(w) + c(w,v); p(v) = w; • 14 until all nodes in S; C D E A B F Example: Dijkstra’s Algorithm D(B),p(B) 2,A D(D),p(D) 1,A D(C),p(C) 5,A 4,D 3,E D(E),p(E) 2,D Step 0 1 2 3 4 5 start S A AD ADE ADEB D(F),p(F) 4,E 5 3 5 2 2 1 3 1 2 1

  18. … • 8 Loop • 9 find w not in S s.t. D(w) is a minimum; • 10 add w to S; • update D(v) for all v adjacent • to w and not in S: • If D(w) + c(w,v) < D(v) then • D(v) = D(w) + c(w,v); p(v) = w; • 14 until all nodes in S; C D E A B F Example: Dijkstra’s Algorithm D(B),p(B) 2,A D(D),p(D) 1,A D(C),p(C) 5,A 4,D 3,E D(E),p(E) 2,D Step 0 1 2 3 4 5 start S A AD ADE ADEB ADEBC D(F),p(F) 4,E 5 3 5 2 2 1 3 1 2 1

  19. … • 8 Loop • 9 find w not in S s.t. D(w) is a minimum; • 10 add w to S; • update D(v) for all v adjacent • to w and not in S: • If D(w) + c(w,v) < D(v) then • D(v) = D(w) + c(w,v); p(v) = w; • 14 until all nodes in S; C D E A B F 5 3 5 2 2 1 3 1 2 1 Example: Dijkstra’s Algorithm D(B),p(B) 2,A D(D),p(D) 1,A D(C),p(C) 5,A 4,D 3,E D(E),p(E) 2,D Step 0 1 2 3 4 5 start S A AD ADE ADEB ADEBC ADEBCF D(F),p(F) 4,E

  20. D C A E B F 5 3 5 2 2 1 3 1 2 1 Example: Dijkstra’s Algorithm D(B),p(B) 2,A D(D),p(D) 1,A D(C),p(C) 5,A 4,D 3,E D(E),p(E) 2,D Step 0 1 2 3 4 5 start S A AD ADE ADEB ADEBC ADEBCF D(F),p(F) 4,E To determine path A  C (say), work backward from C via p(v)

  21. D C A E B F 5 3 5 2 2 1 3 1 2 1 The Forwarding Table • Running Dijkstra at node A gives the shortest path from A to all destinations • We then construct the forwarding table

  22. Complexity • How much processing does running the Dijkstra algorithm take? • Assume a network consisting of N nodes • Each iteration: need to check all nodes, w, not in S • N(N+1)/2 comparisons: O(N2) • More efficient implementations possible: O(N log(N))

  23. X A X A C B D C B D (a) (b) X A X A C B D C B D (c) (d) Obtaining Global State • Flooding • Each router sends link-state information out its links • The next node sends it out through all of its links • except the one where the information arrived • Note: need to remember previous msgs & suppress duplicates!

  24. Flooding the Link State • 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 • Time-to-live for each packet

  25. When to Initiate Flooding • Topology change • Link or node failure • Link or node recovery • Configuration change • Link cost change • See next slide for hazards of dynamic link costs based on current load • Periodically • Refresh the link-state information • Typically (say) 30 minutes • Corrects for possible corruption of the data

  26. e C C C C D D D D A A B A B B B A 0 2+e 2+e 2+e 0 0 0 0 1 1 1+e 1+e 1 1+e 0 e 0 0 … recompute … recompute routing … recompute Oscillations • Assume link cost = amount of carried traffic 1 1+e 0 0 e 0 1 1 initially • How can you avoid oscillations?

  27. 5 Minute Break Questions Before We Proceed?

  28. Distance Vector Routing • Each router knows the links to its immediate neighbors • Does not flood this information to the whole network • Each router has some idea about the shortest path to each destination • 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

  29. Host C Host D Host A N2 N1 N3 N5 Host B Host E N4 N6 N7 Information Flow in Distance Vector

  30. 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

  31. C D B A 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 = DZ(X,Y) Neighbor (next-hop) Node A 3 2 1 1 7 Destinations DC(A, D)

  32. C D B A 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 = DZ(X,Y) Node A 3 2 1 1 7 Smallest distance in row Y = shortest Distance of A to Y, D(A, Y)

  33. 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 Each node: 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 = 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

  34. Distance Vector Algorithm (cont’d) 1 Initialization: 2 for all neighbors V do 3 ifV adjacent to A 4 D(A, V) = c(A,V); else D(A, V) = ∞; 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 Vdo 12 DV(A,Y) = DV(A,Y) ± d 13 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 A’s best path to V

  35. C D B A Example:1st Iteration (C  A) Node A Node B 3 2 1 1 7 DC(A, B) = DC(A,C) + D(C, B) = 7 + 1 = 8 DC(A, D) = DC(A,C) + D(C, D) = 7 + 1 = 8 Node C Node D • loop: • … • 13 else if (update D(A, Y) fromC) • 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

  36. C D B A Example: 1st Iteration (B  A) Node A Node B 3 2 1 1 7 DB(A, C) = DB(A,B) + D(B, C) = 2 + 1 = 3 DB(A, D) = DB(A,B) + D(B, D) = 2 + 3 = 5 Node C Node D • loop: • … • 13 else if (update D(A, Y) fromB) • 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

  37. C D B A Example:End of 1st Iteration Node A Node B 3 2 1 1 7 Node C Node D End of 1st Iteration All nodes knows the best two-hop paths

  38. C D B A Example:2nd Iteration (A  B) Node A Node B 3 2 1 1 7 DA(B, C) = DA(B,A) + D(A, C) = 2 + 3 = 5 DA(B, D) = DA(B,A) + D(A, D) = 2 + 5 = 7 Node C Node D • loop: • … • 13 else if (update D(B, Y) fromA) • 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

  39. C D B A Example:End of 2nd Iteration Node A Node B 3 2 1 1 7 Node C Node D End of 2nd Iteration All nodes knows the best three-hop paths

  40. C D B A Example:End of 3rd Iteration Node A Node B 3 2 1 1 7 Node C Node D End of 2nd Iteration: Algorithm Converges!

  41. C A B Link cost changes here Algorithm terminates 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) / 10 if (c(A,V) changes by ±d) /* case 1 */ 11 for all destinations Y that go through Vdo 12 DV(A,Y) = DV(A,Y) ± d 13 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 1 4 1 50 Node B “good news travels fast” Node C time

  42. C A B Distance Vector: 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) / 10 if (c(A,V) changes by ±d) /*  case 1 */ 11 for all destinations Y that go through Vdo 12 DV(A,Y) = DV(A,Y) ± d 13 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 60 4 1 50 “bad news travels slowly” Node B Node C … time Link cost changes here

  43. 60 4 1 50 C A B Distance Vector: Poisoned Reverse • If B routes through C to get to A: • Btells 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? Node B Node C time Link cost changes here; C updates D(C, A) = 60 as Bhas advertised D(B, A) = ∞ Algorithm terminates

  44. Routing Information Protocol (RIP) • Simple distance-vector protocol • Nodes send distance vectors every 30 seconds • … or, when an update causes a change in routing • Link costs in RIP • All links have cost 1 • Valid distances of 1 through 15 • … with 16 representing infinity • Small “infinity”  smaller “counting to infinity” problem • RIP is limited to fairly small networks • E.g., campus

  45. Per-nodemessagecomplexity: LS: O(e) messages e: number of edges DV: O(d) messages, many times d is node’s degree Complexity/Convergence LS: O(N log N) computation Requires global flooding DV: convergence time varies Count-to-infinity problem Robustness: what happens if router malfunctions? LS: Node can advertise incorrect link cost Each node computes only its own table DV: Node can advertise incorrect path cost Each node’s table used by others; errors propagate through network Link State vs. Distance Vector

  46. Summary • Routing is a distributed algorithm • Different from forwarding • React to changes in the topology • Compute the shortest paths • Two main shortest-path algorithms • Dijkstra  link-state routing (e.g., OSPF, IS-IS) • Bellman-Ford  distance-vector routing (e.g., RIP) • Convergence process • Changing from one topology to another • Transient periods of inconsistency across routers • Next time: BGP • Reading: K&R 4.6.3

More Related