1. Announcement r Project 2 due next week! r Homework 3 available soon, will put it online r Recitation tomorrow on Minet and project 2

2. Outline r Introduction and Network Service Models r Routing Principles m Link State Algorithm m Distance Vector Algorithm

3. Network layer functions r transport packet from sending to receiving hosts r network layer protocols in every host, router three important functions: r path determination: route taken by packets from source to dest. Routing algorithms r forwarding: move packets from router’s input to appropriate router output r call setup: some network architectures require router call setup along path before data flows network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical application transport network data link physical application transport network data link physical

4. Virtual circuits r call setup, teardown for each call before data can flow r each packet carries VC identifier (not destination host ID) r every router on source-dest path maintains “state” for each passing connection “source-to-dest path behaves much like telephone circuit” m performance-wise m network actions along source-to-dest path

5. Virtual circuits: signaling protocols r used to setup, maintain teardown VC r used in ATM, frame-relay, X.25 r not used in today’s Internet application transport network data link physical application transport network data link physical 1. Initiate call 2. incoming call 3. Accept call 4. Call connected 5. Data flow begins 6. Receive data

6. Datagram networks: the Internet model r no call setup at network layer r routers: no state about end-to-end connections m no network-level concept of “connection” r packets forwarded using destination host address m packets between same source-dest pair may take different paths application transport network data link physical application transport network data link physical 1. Send data 2. Receive data

7. Datagram or VC network: why? Internet r data exchange among computers m “elastic” service, no strict timing req. r “smart” end systems (computers) m can adapt, perform control, error recovery m simple inside network, complexity at “edge” r many link types m different characteristics m uniform service difficult ATM r evolved from telephony r human conversation: m strict timing, reliability requirements r “dumb” end systems m telephones m complexity inside network

8. Outline r Introduction and Network Service Models r Routing Principles m Link State Algorithm m Distance Vector Algorithm

9. Router Architecture Overview Two key router functions: r run routing algorithms/protocol (RIP, OSPF, BGP) r forwarding datagrams from incoming to outgoing link

10. u y x wv z 2 2 1 3 1 1 2 5 3 5 Graph: G = (N,E) N = set of routers = { u, v, w, x, y, z } E = set of links ={ (u,v), (u,x), (v,x), (v,w), (x,w), (x,y), (w,y), (w,z), (y,z) } Graph abstraction Remark: Graph abstraction is useful in other network contexts Example: P2P, where N is set of peers and E is set of TCP connections

11. Graph abstraction: costs u y x wv z 2 2 1 3 1 1 2 5 3 5 c(x,x’) = cost of link (x,x’) - e.g., c(w,z) = 5 cost could always be 1, or inversely related to bandwidth, or inversely related to congestion Cost of path (x 1, x 2, x 3,…, x p ) = c(x 1,x 2 ) + c(x 2,x 3 ) + … + c(x p-1,x p ) Question: What’s the least-cost path between u and z ? Routing algorithm: algorithm that finds least-cost path

12. Routing Algorithm classification Global or decentralized information? Global: r all routers have complete topology, link cost info r “link state” algorithms Decentralized: r router knows physically- connected neighbors, link costs to neighbors r iterative process of computation, exchange of info with neighbors r “distance vector” algorithms Static or dynamic? Static: r routes change slowly over time Dynamic: r routes change more quickly m periodic update m in response to link cost changes

13. A Link-State Routing Algorithm Dijkstra’s algorithm r net topology, link costs known to all nodes m accomplished via “link state broadcast” m all nodes have same info r computes least cost paths from one node (‘source”) to all other nodes m gives routing table for that node r iterative: after k iterations, know least cost path to k dest.’s Notation:  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 dest. V  p(v): predecessor node along path from source to v, that is next v  N: set of nodes whose least cost path definitively known

14. Dijsktra’s Algorithm 1 Initialization: 2 N' = {u} 3 for all nodes v 4 if v adjacent to u 5 then D(v) = c(u,v) 6 else D(v) = ∞ 7 8 Loop 9 find w not in N' such that D(w) is a minimum 10 add w to N' 11 update D(v) for all v adjacent to w and not in N' : 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 N'

15. Dijkstra’s algorithm: example Step 0 1 2 3 4 5 N' u ux uxy uxyv uxyvw uxyvwz D(v),p(v) 2,u D(w),p(w) 5,u 4,x 3,y D(x),p(x) 1,u D(y),p(y) ∞ 2,x D(z),p(z) ∞ 4,y u y x wv z 2 2 1 3 1 1 2 5 3 5

16. Dijkstra’s algorithm: example (2) u y x wv z Resulting shortest-path tree from u: v x y w z (u,v) (u,x) destination link Resulting forwarding table in u:

17. Dijkstra’s algorithm, discussion Algorithm complexity: n nodes r each iteration: need to check all nodes, w, not in N r n*(n+1)/2 comparisons: O(n^2) r more efficient implementations possible: O(nlogn) Oscillations possible: r e.g., link cost = amount of carried traffic A D C B 1 1+e e 0 e 1 1 0 0 initially A D C B 2+e 0 0 0 1+e 1 … recompute routing A D C B 0 2+e 1+e 1 0 0 … recompute A D C B 2+e 0 e 0 1+e 1 … recompute

18. Distance Vector Algorithm Bellman-Ford Equation (dynamic programming) Define d x (y) := cost of least-cost path from x to y Then d x (y) = min {c(x,v) + d v (y) } where min is taken over all neighbors v of x v

19. Bellman-Ford example u y x wv z 2 2 1 3 1 1 2 5 3 5 Clearly, d v (z) = 5, d x (z) = 3, d w (z) = 3 d u (z) = min { c(u,v) + d v (z), c(u,x) + d x (z), c(u,w) + d w (z) } = min {2 + 5, 1 + 3, 5 + 3} = 4 Node that achieves minimum is next hop in shortest path ➜ forwarding table B-F equation says:

20. Distance Vector Algorithm r D x (y) = estimate of least cost from x to y r Distance vector: D x = [D x (y): y є N ] r Node x knows cost to each neighbor v: c(x,v) r Node x maintains D x = [D x (y): y є N ] r Node x also maintains its neighbors’ distance vectors m For each neighbor v, x maintains D v = [D v (y): y є N ]

21. Distance vector algorithm Basic idea: r Each node periodically sends its own distance vector estimate to neighbors r When a node x receives new DV estimate from neighbor, it updates its own DV using B-F equation: D x (y) ← min v {c(x,v) + D v (y)} for each node y ∊ N  Under minor, natural conditions, the estimate D x (y) converge to the actual least cost d x (y)

22. Distance Vector Algorithm Iterative, asynchronous: each local iteration caused by: r local link cost change r DV update message from neighbor Distributed: r each node notifies neighbors only when its DV changes m neighbors then notify their neighbors if necessary wait for (change in local link cost of msg from neighbor) recompute estimates if DV to any dest has changed, notify neighbors Each node:

23. x y z x y z 0 2 7 ∞∞∞ ∞∞∞ from cost to from x y z x y z ∞∞ ∞∞∞ cost to x y z x y z ∞∞∞ 710 cost to ∞ 2 0 1 ∞ ∞ ∞ x y z x y z 0 2 3 from cost to x y z x y z 0 2 3 from cost to x y z x y z 0 2 3 from cost to 2 0 1 3 1 0 2 0 1 3 1 0 2 0 1 3 1 0 time x z 1 2 7 y node x table node y table node z table D x (y) = min{c(x,y) + D y (y), c(x,z) + D z (y)} = min{2+0, 7+1} = 2 x y z x y z 0 2 3 from cost to x y z x y z 0 2 7 from cost to x y z x y z 0 2 7 from cost to 2 0 1 7 1 0 2 0 1 7 1 0 2 0 1 3 1 0 D x (z) = min{c(x,y) + D y (z), c(x,z) + D z (z)} = min{2+1, 7+0} = 3

24. Distance Vector: link cost changes Link cost changes: r node detects local link cost change r updates distance table (line 15) r if cost change in least cost path, notify neighbors (lines 23,24) X Z 1 4 50 Y 1 algorithm terminates “good news travels fast”

25. Distance Vector: link cost changes Link cost changes: r good news travels fast r bad news travels slow - “count to infinity” problem! X Z 1 4 50 Y 60 algorithm continues on!

26. Distance Vector: poisoned reverse If Z routes through Y to get to X : r Z tells Y its (Z’s) distance to X is infinite (so Y won’t route to X via Z) r will this completely solve count to infinity problem? X Z 1 4 50 Y 60 algorithm terminates

27. Comparison of LS and DV algorithms Message complexity r LS: with n nodes, E links, O(nE) msgs sent each r DV: exchange between neighbors only m convergence time varies Speed of Convergence r LS: O(n 2 ) algorithm requires O(nE) msgs m may have oscillations r DV: convergence time varies m may be routing loops m count-to-infinity problem Robustness: what happens if router malfunctions? LS: m node can advertise incorrect link cost m each node computes only its own table DV: m DV node can advertise incorrect path cost m each node’s table used by others error propagate thru network

28. Backup Slides

29. Distance Table: example A E D CB 7 8 1 2 1 2 D () A B C D A1764A1764 B 14 8 9 11 D5542D5542 E cost to destination via destination D (C,D) E c(E,D) + min {D (C,w)} D w = = 2+2 = 4 D (A,D) E c(E,D) + min {D (A,w)} D w = = 2+3 = 5 D (A,B) E c(E,B) + min {D (A,w)} B w = = 8+6 = 14 loop!

30. Distance table gives routing table D () A B C D A1764A1764 B 14 8 9 11 D5542D5542 E cost to destination via destination ABCD ABCD A,1 D,5 D,4 D,2 Outgoing link to use, cost destination Distance table Routing table

31. Distance Vector Algorithm: 1 Initialization: 2 for all adjacent nodes v: 3 D (*,v) = infinity /* 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 At all nodes, X:

32. Distance Vector Algorithm (cont.): 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 DV(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 w X X X X X w w