1. Network Layer4-1 Chapter 4 Network Layer Part 3: Routing Computer Networking: A Top Down Approach 6 th edition Jim Kurose, Keith Ross Addison-Wesley March 2012

2. Network Layer4-2 Chapter 4: Network Layer r 4. 1 Introduction r 4.2 Virtual circuit and datagram networks r 4.3 What’s inside a router r 4.4 IP: Internet Protocol m Datagram format m IPv4 addressing m ICMP m IPv6 r 4.5 Routing algorithms m Link state m Distance Vector m Hierarchical routing r 4.6 Routing in the Internet m RIP m OSPF m BGP r 4.7 Broadcast and multicast routing

3. Routing Algorithms r Need to compute the forwarding tables r Typically, a host is connected to one router (the default router or first-hop router) r We call this the source router r The default router of the destination is called the destination router r Goal: m Set of routers (nodes) m Links between routers with weights Network Layer4-3

4. Routing Algorithms r Method: graph algorithm (undirected) r Graph G = (N, E) m N is set of nodes (routers) m E is collection of edges (physical links) Represent by endpoints: (x,y) m Edges have a value representing its cost Could be physical length Link speed Monetary cost We’ll ignore what the cost represents c(x,y) is the cost on an edge If edge does not exist, c(x,y) = ∞ Network Layer4-4

5. Routing Algorithms r Terminology m Path: a sequence of nodes (x 1, x 2,..x p ) such that each of the pairs (x 1,x 2 ), (x 2,x 3 ),…(x p-1,x p ) are edges in E m Cost: sum of all edge costs along the path m Least-cost path: path between x 1 and x p that has the least cost m In image, least-cost Path from u to w is (u, x, y, w) Network Layer4-5 u y x wv z 2 2 1 3 1 1 2 5 3 5

6. Routing Algorithms r Global routing algorithm m Computes the least-cost path using complete global knowledge about the network m Called link-state (LS) algorithms since it knows the ost of each link in network Network Layer4-6

7. Routing Algorithms r Decentralized routing algorithm m Calculation carried out in an iterative distributed manner m No node has complete information about the costs of all network links m Each node begins with only the knowledge of the costs of its own directly attached links m Iterative process used where nodes calculate and exchange info with neighbors m Distance-vector (DV) algorithm each node maintains a vector of estimates of the costs to all other nodes in the network Network Layer4-7

8. Network Layer4-8 Chapter 4: Network Layer r 4. 1 Introduction r 4.2 Virtual circuit and datagram networks r 4.3 What’s inside a router r 4.4 IP: Internet Protocol m Datagram format m IPv4 addressing m ICMP m IPv6 r 4.5 Routing algorithms m Link state m Distance Vector m Hierarchical routing r 4.6 Routing in the Internet m RIP m OSPF m BGP r 4.7 Broadcast and multicast routing

9. Network Layer4-9 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 forwarding table for that node r iterative: after k iterations, know least cost path to k dest.’s Notation:  c(x,y): link cost from node x to y; = ∞ 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  N': set of nodes whose least cost path definitively known

10. Network Layer4-10 Dijsktra’s Algorithm 1 Initialization: (our node is u) 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'

11. Network Layer4-11 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

12. Network Layer4-12 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:

13. Network Layer4-13 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 A D C B 2+e 0 0 0 1+e 1 A D C B 0 2+e 1+e 1 0 0 A D C B 2+e 0 e 0 1+e 1 initially … recompute routing … recompute

14. Network Layer4-14 Chapter 4: Network Layer r 4. 1 Introduction r 4.2 Virtual circuit and datagram networks r 4.3 What’s inside a router r 4.4 IP: Internet Protocol m Datagram format m IPv4 addressing m ICMP m IPv6 r 4.5 Routing algorithms m Link state m Distance Vector m Hierarchical routing r 4.6 Routing in the Internet m RIP m OSPF m BGP r 4.7 Broadcast and multicast routing

15. Network Layer4-15 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

16. Network Layer4-16 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:

17. Network Layer4-17 Distance Vector Algorithm r D x (y) = estimate of least cost from x to y r Node x knows cost to each neighbor v: c(x,v) r Node x maintains distance vector 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 ]

18. Network Layer4-18 Distance vector algorithm (4) Basic idea: r From time-to-time, each node sends its own distance vector estimate to neighbors r Asynchronous 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)

19. Network Layer4-19 Distance Vector Algorithm (5) 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 or msg from neighbor) recompute estimates if DV to any dest has changed, notify neighbors Each node:

20. Network Layer4-20 x y z x y z 0 2 7 ∞∞∞ ∞∞∞ from cost to from x y z x y z 0 from cost to x y z x y z ∞∞ ∞∞∞ cost to x y z x y z ∞∞∞ 710 cost to ∞ 2 0 1 ∞ ∞ ∞ 2 0 1 7 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 D x (z) = min{c(x,y) + D y (z), c(x,z) + D z (z)} = min{2+1, 7+0} = 3 32

21. Network Layer4-21 x y z x y z 0 2 7 ∞∞∞ ∞∞∞ from cost to from 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 ∞∞ ∞∞∞ cost to x y z x y z 0 2 7 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 x y z x y z 0 2 7 from cost to x y z x y z ∞∞∞ 710 cost to ∞ 2 0 1 ∞ ∞ ∞ 2 0 1 7 1 0 2 0 1 7 1 0 2 0 1 3 1 0 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 D x (z) = min{c(x,y) + D y (z), c(x,z) + D z (z)} = min{2+1, 7+0} = 3

22. Network Layer4-22 Distance Vector: link cost changes Link cost changes: r node detects local link cost change r updates routing info, recalculates distance vector r if DV changes, notify neighbors “good news travels fast” x z 1 4 50 y 1 At time t 0, y detects the link-cost change, updates its DV, and informs its neighbors. At time t 1, z receives the update from y and updates its table. It computes a new least cost to x and sends its neighbors its DV. At time t 2, y receives z’s update and updates its distance table. y’s least costs do not change and hence y does not send any message to z.

23. Network Layer4-23 Distance Vector: link cost changes Link cost changes: r good news travels fast r bad news travels slow - “count to infinity” problem! r 44 iterations before algorithm stabilizes: see text Poisoned reverse: r If Z routes through Y to get to X : m 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

24. Network Layer4-24 Comparison of LS and DV algorithms Message complexity r LS: with n nodes, E links, O(nE) msgs sent 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

25. Network Layer4-25 Chapter 4: Network Layer r 4. 1 Introduction r 4.2 Virtual circuit and datagram networks r 4.3 What’s inside a router r 4.4 IP: Internet Protocol m Datagram format m IPv4 addressing m ICMP m IPv6 r 4.5 Routing algorithms m Link state m Distance Vector m Hierarchical routing r 4.6 Routing in the Internet m RIP m OSPF m BGP r 4.7 Broadcast and multicast routing

26. Network Layer4-26 Hierarchical Routing scale: with 200 million destinations: r can’t store all dest’s in routing tables! r routing table exchange would swamp links! administrative autonomy r internet = network of networks r each network admin may want to control routing in its own network Our routing study thus far - idealization r all routers identical r network “flat” … not true in practice

27. Network Layer4-27 Hierarchical Routing r aggregate routers into regions, “autonomous systems” (AS) r routers in same AS run same routing protocol m “intra-AS” routing protocol m routers in different AS can run different intra- AS routing protocol Gateway router r Direct link to router in another AS

28. Network Layer4-28 3b 1d 3a 1c 2a AS3 AS1 AS2 1a 2c 2b 1b Intra-AS Routing algorithm Inter-AS Routing algorithm Forwarding table 3c Interconnected ASes r forwarding table configured by both intra- and inter-AS routing algorithm m intra-AS sets entries for internal dests m inter-AS & intra-As sets entries for external dests

29. Network Layer4-29 3b 1d 3a 1c 2a AS3 AS1 AS2 1a 2c 2b 1b 3c Inter-AS tasks r suppose router in AS1 receives datagram destined outside of AS1: m router should forward packet to gateway router, but which one? AS1 must: 1. learn which dests are reachable through AS2, which through AS3 2. propagate this reachability info to all routers in AS1 Job of inter-AS routing!

30. Network Layer4-30 Example: Setting forwarding table in router 1d r suppose AS1 learns (via inter-AS protocol) that subnet x reachable via AS3 (gateway 1c) but not via AS2. r inter-AS protocol propagates reachability info to all internal routers. r router 1d determines from intra-AS routing info that its interface I is on the least cost path to 1c. m installs forwarding table entry (x,I) 3b 1d 3a 1c 2a AS3 AS1 AS2 1a 2c 2b 1b 3c x …

31. Network Layer4-31 Example: Choosing among multiple ASes r now suppose AS1 learns from inter-AS protocol that subnet x is reachable from AS3 and from AS2. r to configure forwarding table, router 1d must determine towards which gateway it should forward packets for dest x. m this is also job of inter-AS routing protocol! 3b 1d 3a 1c 2a AS3 AS1 AS2 1a 2c 2b 1b 3c x … …

32. Network Layer4-32 Learn from inter-AS protocol that subnet x is reachable via multiple gateways Use routing info from intra-AS protocol to determine costs of least-cost paths to each of the gateways Hot potato routing: Choose the gateway that has the smallest least cost Determine from forwarding table the interface I that leads to least-cost gateway. Enter (x,I) in forwarding table Example: Choosing among multiple ASes r now suppose AS1 learns from inter-AS protocol that subnet x is reachable from AS3 and from AS2. r to configure forwarding table, router 1d must determine towards which gateway it should forward packets for dest x. m this is also job of inter-AS routing protocol! r hot potato routing: send packet towards closest of two routers.

33. Network Layer4-33 Chapter 4: Network Layer r 4. 1 Introduction r 4.2 Virtual circuit and datagram networks r 4.3 What’s inside a router r 4.4 IP: Internet Protocol m Datagram format m IPv4 addressing m ICMP m IPv6 r 4.5 Routing algorithms m Link state m Distance Vector m Hierarchical routing r 4.6 Routing in the Internet m RIP m OSPF m BGP r 4.7 Broadcast and multicast routing

34. Network Layer4-34 Intra-AS Routing r also known as Interior Gateway Protocols (IGP) r most common Intra-AS routing protocols: m RIP: Routing Information Protocol m OSPF: Open Shortest Path First m IGRP: Interior Gateway Routing Protocol (Cisco proprietary)

35. Network Layer4-35 Chapter 4: Network Layer r 4. 1 Introduction r 4.2 Virtual circuit and datagram networks r 4.3 What’s inside a router r 4.4 IP: Internet Protocol m Datagram format m IPv4 addressing m ICMP m IPv6 r 4.5 Routing algorithms m Link state m Distance Vector m Hierarchical routing r 4.6 Routing in the Internet m RIP m OSPF m BGP r 4.7 Broadcast and multicast routing

36. Network Layer4-36 RIP ( Routing Information Protocol) r distance vector algorithm r included in BSD-UNIX Distribution in 1982 r distance metric: # of hops (max = 15 hops) D C BA u v w x y z destination hops u 1 v 2 w 2 x 3 y 3 z 2 From router A to subnets:

37. Network Layer4-37 RIP advertisements r distance vectors: exchanged among neighbors every 30 sec via Response Message (also called advertisement) r each advertisement: list of up to 25 destination subnets within AS

38. Network Layer4-38 RIP: Example Destination Network Next Router Num. of hops to dest. wA2 yB2 zB7 x--1 ….…..... w xy z A C D B Routing/Forwarding table in D

39. Network Layer4-39 RIP: Example Destination Network Next Router Num. of hops to dest. wA2 yB2 zB A7 5 x--1 ….…..... Routing/Forwarding table in D w xy z A C D B Dest Next hops w - 1 x - 1 z C 4 …. …... Advertisement from A to D

40. Network Layer4-40 RIP: Link Failure and Recovery If no advertisement heard after 180 sec --> neighbor/link declared dead m routes via neighbor invalidated m new advertisements sent to neighbors m neighbors in turn send out new advertisements (if tables changed) m link failure info quickly (?) propagates to entire net m poison reverse used to prevent ping-pong loops (infinite distance = 16 hops)

41. Network Layer4-41 RIP Table processing r RIP routing tables managed by application-level process called route-d (daemon) r advertisements sent in UDP packets, periodically repeated physical link network forwarding (IP) table Transprt (UDP) routed physical link network (IP) Transprt (UDP) routed forwarding table