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EE 122: Intra-domain routing

EE 122: Intra-domain routing. Ion Stoica September 30, 2002. (* this presentation is based on the on-line slides of J. Kurose & K. Rose). Internet Routing. Internet organized as a two level hierarchy First level – autonomous systems (AS’s)

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EE 122: Intra-domain routing

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  1. EE 122: Intra-domain routing Ion Stoica September 30, 2002 (* this presentation is based on the on-line slides of J. Kurose & K. Rose)

  2. 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., RIP • Link State, e.g., OSPF • Between AS’s runs inter-domain routing protocols, e.g., Border Gateway Routing (BGP) • De facto standard today, BGP-4 istoica@cs.berkeley.edu

  3. Example Interior router BGP router AS-1 AS-3 AS-2 istoica@cs.berkeley.edu

  4. Intra-domain Routing Protocols • Based on unreliable datagram delivery • Distance vector • Routing Information Protocol (RIP), based on Bellman-Ford • Each neighbor periodically exchange reachability information to its neighbors • Minimal communication overhead, but it takes long to converge, i.e., in proportion to the maximum path length • Link state • Open Shortest Path First Protocol (OSPF), based on Dijkstra • Each network periodically floods immediate reachability information to other routers • Fast convergence, but high communication and computation overhead istoica@cs.berkeley.edu

  5. 5 3 5 2 2 1 3 1 2 1 C D E B A F Routing • Goal: determine a “good” path through the network from source to destination • Good means usually the shortest path • Network modeled as a graph • Routers  nodes • Link edges • Edge cost: delay, congestion level,… istoica@cs.berkeley.edu

  6. Dijkstra’s algorithm Net topology, link costs known to all nodes Accomplished via “link state broadcast” All nodes have same info Compute least cost paths from one node (‘source”) to all other nodes Iterative: after k iterations, know least cost path to k closest destinations Notations c(i,j): link cost from node i to j; cost infinite if not direct neighbors 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 Link State Routing Algorithm istoica@cs.berkeley.edu

  7. Dijsktra’s Algorithm 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 D(v) = min( D(v), D(w) + c(w,v) ); 13 // new cost to v is either old cost to v or known 14 // shortest path cost to w plus cost from w to v 15 until all nodes in S; istoica@cs.berkeley.edu

  8. C D A E 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 D(F),p(F) 5 3 5 2 2 1 3 1 2 1 istoica@cs.berkeley.edu

  9. C D A E 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 istoica@cs.berkeley.edu

  10. C D A E 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 istoica@cs.berkeley.edu

  11. C D A E 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 istoica@cs.berkeley.edu

  12. C D A E 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 istoica@cs.berkeley.edu

  13. C D A E 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 ADEBCF D(F),p(F) 4,E 5 3 5 2 2 1 3 1 2 1 istoica@cs.berkeley.edu

  14. C C C C D D D D B B A B A B A 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 Dijkstra’s Algorithm: Discussion • Algorithm complexity: n nodes • Each iteration: need to check all nodes, w, not in S • n*(n+1)/2 comparisons: O(n**2) • More efficient implementations possible: O(n*log(n)) • Oscillation possible • E.g., link cost = amount of carried traffic 1 1+e 0 0 e 0 1 1 e initially istoica@cs.berkeley.edu

  15. Distance Vector Routing Algorithm • Iterative: continues until no nodes exchange info • Asynchronous: nodes need not exchange info/iterate in lock step! • Distributed: each node communicates only with directly-attached neighbors • Routing (distance) table data structure – each router maintains • Row for each possible destination • Column for each directly-attached neighbor to node • Entry in row Y and column Z of node X  distance from X to Y, via Z as next hop istoica@cs.berkeley.edu

  16. cost to destination via E D () A B C D A 1 7 6 4 B 14 8 9 11 D 5 5 4 2 destination C D B A E E E D (C,D) D (A,D) D (A,B) D D B c(E,D) + min {D (A,w)} c(E,D) + min {D (C,w)} c(E,B) + min {D (A,w)} = = = w w w = = = 2+2 = 4 8+6 = 14 2+3 = 5 Example: Distance (Routing) Table 1 6 2 8 1 E 2 loop! loop! istoica@cs.berkeley.edu

  17. cost to destination via E D () A B C D A 1 7 6 4 B 14 8 9 11 D 5 5 4 2 destination Routing Table  Forwarding Table Outgoing link to use, cost A B C D A,1 D,5 D,4 D,2 destination Forwarding table Distance (routing) table istoica@cs.berkeley.edu

  18. wait for (change in local link cost of msg from neighbor) recompute distance table if least cost path to any dest has changed, notify neighbors Distance Vector Routing: Overview Each node: • Each local iteration caused by: • Local link cost change • Message from neighbor: its least cost path change from neighbor • Each node notifies neighbors only when its least cost path to any destination changes • Neighbors then notify their neighbors if necessary istoica@cs.berkeley.edu

  19. Distance Vector Algorithm At all nodes, X: 1 Initialization: 2 for all adjacent nodes v: 3 D (*,v) = /* the * operator means "for all rows" */ 4 D (v,v) = c(X,v) 5 for all destinations, y 6 send min D (y,w) to each neighbor /* w over all X's neighbors */ X X X w istoica@cs.berkeley.edu

  20. Distance Vector Algorithm (cont’d) 8 loop 9 wait (until I see a link cost change to neighbor V 10 or until I receive update from neighbor V) 11 12 if (c(X,V) changes by d) 13 /* change cost to all dest's via neighbor v by d */ 14 /* note: d could be positive or negative */ 15 for all destinations y: D (y,V) = D (y,V) + d 16 17 else if (update received from V wrt destination Y) 18 /* shortest path from V to some Y has changed */ 19 /* V has sent a new value for its min D (Y,w) */ 20 /* call this received new value is "newval" */ 21 for the single destination y: D (Y,V) = c(X,V) + newval 22 23 if we have a new min D (Y,w) for any destination Y 24 send new value of min D (Y,w) to all neighbors 25 26 forever X X V w X X w X w istoica@cs.berkeley.edu

  21. 2 1 7 X Y Z Example: Distance Vector Algorithm istoica@cs.berkeley.edu

  22. 2 1 7 Y Z X X c(X,Y) + min {D (Z,w)} c(X,Z) + min {D (Y,w)} D (Y,Z) D (Z,Y) = = w w = = 2+1 = 3 7+1 = 8 X Y Z Example: Distance Vector Algorithm istoica@cs.berkeley.edu

  23. 2 1 7 X Y Z Example: Distance Vector Algorithm istoica@cs.berkeley.edu

  24. 2 1 7 X Y Z Example: Distance Vector Algorithm istoica@cs.berkeley.edu

  25. 1 4 1 50 X Y Z Distance Vector: Link Cost Changes • Link cost changes: • Node detects local link cost change • Updates distance table (line 15) • If cost change in least cost path, notify neighbors (lines 23,24) algorithm terminates “good news travels fast” istoica@cs.berkeley.edu

  26. 60 4 1 50 X Y Z Distance Vector: Link Cost Changes • Link cost changes • Good news travels fast • Bad news travels slow - “count to infinity” problem! algorithm continues on! istoica@cs.berkeley.edu

  27. 60 4 1 50 X Y Z Distance Vector: Poisoned Reverse • If Z routes through Y to get to X: • Z tells Y its (Z’s) distance to X is infinite (so Y won’t route to X via Z) • Will this completely solve count to infinity problem? algorithm terminates istoica@cs.berkeley.edu

  28. Per node message complexity LS: O(n*e) messages; n – number of nodes; e – number of edges DV: O(d) messages; where d is node’s degree Complexity LS: O(n**2) with O(n*e) messages DV: convergence time varies may be routing loops 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: DV node can advertise incorrect path cost each node’s table used by others; error propagate through network Link State vs. Distance Vector istoica@cs.berkeley.edu

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