CS 43: Computer Networks. 23: Routing Algorithms November 14, 2018

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1 S 3: omputer Networks 3: Routing lgorithms November, 08

2 Last class NT: Network ddress Translators: NT is mostly bad, but in some cases, it s a necessary evil. IPv6: Simpler, faster, better Tunneling: IPv6 datagram carried as payload in IPv datagram among IPv routers IMP: Internet ontrol Message Protocol Slide

3 Today ontrol Plane: Routing: Link State Protocol istance Vector Protocol Slide 3

4 Interplay between routing, forwarding routing algorithm local forwarding table dest address output link address-range address-range address-range 3 address-range 3 routing algorithm determines end-end-path through network forwarding table determines local forwarding at this router IP destination address in arriving packet s header 3

5 Graph bstraction v w u z x y 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) }

6 Link ost u v x 3 3 w y z c(x,x ) = cost of link (x,x ) e.g., c(w,z) = ost of path (x, x, x 3,, x p ) = c(x,x ) + c(x,x 3 ) + + c(x p-,x p ) Key question: what is the least-cost path between u and z? Routing algorithm: algorithm that finds that least cost path

7 How should link costs be determined?. They should all be equal.. They should be a function of link capacity.. They should take current traffic characteristics into account (congestion, delay, etc.).. They should be manually determined by network administrators. E. They should be determined in some other way.

8 How should link costs be determined?. They should all be equal.. They should be a function of link capacity.. They should take current traffic characteristics into account (congestion, delay, etc.). Time-scales of these events are too short, for us to recompute routes every time.. They should be manually determined by network administrators. This is done when there are policy decisions to be made, that are unique to each administrative domain. E. They should be determined in some other way.

9 Link ost Typically simple: all links are equal Least-cost paths => shortest paths (hop count) Network operators add policy exceptions Lower operational costs Peering agreements Security concerns

10 Routing hallenges How to choose best path? efining best can be slippery How to scale to millions of users? Minimize control messages and routing table size How to adapt quickly to failures or changes? Node and link failures, plus message loss

11 How much information should a router know about the network?. The next hop and cost of forwarding to its neighbor(s). Less state.. The next hop and cost of forwarding to any destination.. The status and cost of every link in the network. etter decisions.. Some other amount of information.

12 Routing Table? t a minimum, the routing table at U needs to know the next hop for each possible destination. Probably want more info (e.g., path cost) u y x w v z 3 3 est Next Hop V V X X W X Y X Z X

13 Routing Table est Next Hop ost (Path) V V X X W X Y X Z X u v x 3 3 w y z t a minimum, the routing table at U needs to know the next hop for each possible destination. Probably want more info (e.g., path cost, maybe path itself) This is a key difference between routing & forwarding!

14 Routing lgorithm lasses Link State (Global) Routers maintain cost of each link in the network. onnectivity/cost changes flooded to all routers. onverges quickly (less inconsistency, looping, etc.). Limited network sizes. istance Vector (ecentralized) Routers maintain next hop & cost of each destination. onnectivity/cost changes iteratively propagate from neighbor to neighbor. Requires multiple rounds to converge. Scales to large networks.

15 Link-state Routing Two phases Reliable flooding Tell all routers what you know about your links Typically in response to event: link failure/recovery/cost Path calculation (ijkstra salgorithm) Each router computes best path over complete network Motivation Global information allows optimal routing Straightforward to implement and verify

16 looding LSs Routers transmit Link State dvertisement (LS) on links neighboring router forwards out all links except incoming Keep a copy locally; don t forward previously-seen LSs hallenges Packet loss Out-of-order arrival Solutions cknowledgments and retransmissions Sequence numbers Time-to-live for each packet

17 looding Example LS generated by X at T=0 T=0 X T= X T= X T=3 X

18 Initialization: N' = {u} 3 for all nodes v if v adjacent to u then (v) = c(u,v) 6 else (v) = 7 8 Loop ijkstra s lgorithm 9 find w not in N' such that (w) is a minimum 0 add w to N' update (v) for all v adjacent to w and not in N' : (v) = min( (v), (w) + c(w,v) ) 3 /* new cost to v is either old cost to v or known shortest path cost to w plus cost from w to v */ until all nodes in N' Nodes we ve determined lowest-cost path for already. est known cost for reaching node v.

19 ijkstra s lgorithm Initialization: N' = {u} Only know best route to self so far. 3 for all nodes v if v adjacent to u or every other router, set it s known distance to link cost if it s a neighbor. then (v) = c(u,v) Otherwise, set it to infinity. 6 else (v) = 7 8 Loop 9 find w not in N' such that (w) is a minimum 0 add w to N' update (v) for all v adjacent to w and not in N' : (v) = min( (v), (w) + c(w,v) ) 3 /* new cost to v is either old cost to v or known shortest path cost to w plus cost from w to v */ until all nodes in N'

20 ijkstra s lgorithm Initialization: N' = {u} 3 for all nodes v if v adjacent to u then (v) = c(u,v) 6 else (v) = 7 8 Loop 9 find w not in N' such that (w) is a minimum 0 add w to N' update (v) for all v adjacent to w and not in N' : (v) = min( (v), (w) + c(w,v) ) 3 /* new cost to v is either old cost to v or known shortest path cost to w plus cost from w to v */ until all nodes in N' Pick the node (w) that isn t already in N with the shortest distance (least cost path) and add it to N. heck all possible destinations from w. If going through w gives a lower cost to destination v, update (v).

21 ijkstra s lgorithm Example 0 E Goal: rom the perspective of node : etermine shortest path to every destination Other perspectives: Look up ijkstra s lgorithm on YouTube

22 ijkstra s lgorithm Step 0 0 E Previous Step est Path ost (v) E This Step est Path ost (v) 0? E??

23 ijkstra s lgorithm Step 0 E Previous Step est Path ost (v) 0? E?? Pick Min This Step est Path ost (v) 0 E

24 ijkstra s lgorithm Step 0 E an we find lower cost to any other node by going through? Previous Step est Path ost (v) 0? E?? This Step est Path ost (v) 0 E

25 ijkstra s lgorithm Step 0 E onsider path to : () or () + cost(, ) Previous Step est Path ost (v) 0? E?? This Step est Path ost (v) 0 E

26 ijkstra s lgorithm Step 0 E onsider path to : () = or () + cost(, ) + = 3 Previous Step est Path ost (v) 0? E?? This Step est Path ost (v) 0, 3 E

27 ijkstra s lgorithm Step 0 E onsider path to : () = or () + cost(, ) + = 6 Previous Step est Path ost (v) 0? E?? This Step est Path ost (v) 0, 3, 6 E

28 ijkstra s lgorithm Step 0 E Still no information about E or. Previous Step est Path ost (v) 0? E?? This Step est Path ost (v) 0, 3, 6 E??

29 ijkstra s lgorithm Step 0 E hoose. Previous Step est Path ost (v) 0, 3, 6 E?? Pick Min This Step est Path ost (v) 0, 3 E

30 ijkstra s lgorithm Step 0 E onsider path to : () = 6 or () + cost(, ) 3 + = Previous Step est Path ost (v) 0, 3, 6 E?? This Step est Path ost (v) 0, 3,, E

31 ijkstra s lgorithm Step 0 E onsider path to E: (E) = or () + cost(, E) = 3 Previous Step est Path ost (v) 0, 3, 6 E?? This Step est Path ost (v) 0, 3,, E,, E 3?

32 ijkstra s lgorithm Step 3 0 E hoose. Previous Step est Path ost (v) 0, 3,, E,, E 3? This Step est Path ost (v) 0, 3,, E

33 ijkstra s lgorithm Step 3 0 E No change for E. Previous Step est Path ost (v) 0, 3,, E,, E 3? This Step est Path ost (v) 0, 3,, E,, E 3

34 ijkstra s lgorithm Step 3 0 E onsider path to : () = or () + cost(, ) + = 0 Previous Step est Path ost (v) 0, 3,, E,, E 3? This Step est Path ost (v) 0, 3,, E,, E 3,,, 0

35 ijkstra s lgorithm Step 0 E hoose. Previous Step est Path ost (v) 0, 3,, E,, E 3,,, 0 This Step est Path ost (v) 0, 3,,,,, 0

36 ijkstra s lgorithm Step 0 E onsider path to E: (E) = 3 or () + cost(, E) 0 + = Previous Step est Path ost (v) 0, 3,, E,, E 3,,, 0 This Step est Path ost (v) 0, 3,, E,, E 3,,, 0

37 ijkstra s lgorithm Step 0 E hoose E. Previous Step est Path ost (v) 0, 3,, E,, E 3,,, 0 This Step est Path ost (v) 0, 3,, E,, E 3,,, 0

38 ijkstra s lgorithm one! Lot more state in routing table! est Path ost (v) inal nswer 0, 3,, E,, E 3,,, 0 0 E Populate orwarding Table orwarding Table est orward To E

39 ijkstra s lgorithm omplexity With N nodes and E edges s previously described it s O(N ) t each step, there are N nodes to choose next Total of N steps (each node must be chosen) astest known is O(N log N + E) Uses a min-heap

40 Link State - Summary + ast convergence (reacts to events quickly) + Small window of inconsistency Large number of messages sent on events Large routing tables as network size grows

41 Routing lgorithm lasses Link State (Global) Routers maintain cost of each link in the network. onnectivity/cost changes flooded to all routers. onverges quickly (less inconsistency, looping, etc.). Limited network sizes. istance Vector (ecentralized) Routers maintain next hop & cost of each destination. onnectivity/cost changes iteratively propagate from neighbor to neighbor. Requires multiple rounds to converge. Scales to large networks.

42 ellman-ord Equation let d x (y) := cost of least-cost path from x to y then d x (y) = min {c(x,v) + d v (y) } v cost from neighbor v to destination y cost to neighbor v min taken over all neighbors v of x

43 istance Vectors Let x (y) = vector of least cost from x to y Node x: Knows cost to each neighbor v: c(x,v) Maintains its neighbors distance vectors. or each neighbor v, x maintains: v = [ v (y): y є N ] s opposed to link state: Only keeps state for yourself and direct neighbors

44 istance Vector lgorithm Periodically, each node sends its own distance vector to neighbors Upon receiving new V from neighbor, update its local V using - equation: x (y) min v {c(x,v) + v (y)} for each node y N Under typical conditions, x (y) will converge to the least cost d x (y)

45 istance Vector lgorithm Iterative, asynchronous: Iteration when: Local link cost change V update from neighbor Periodic timer istributed: Each node knows only a portion of global link info each node: wait for (change in local link cost or msg from neighbor) recompute estimates if V to any dest has changed, notify neighbors

46 istance Vector Example Same network as ijkstra s example, without node E. What I ll show you next is routing table (of distance vectors) at each router.

47 istance Vector Round 0 Routers populate their forwarding table by taking the row minimum. Router Router Router Router Router

48 istance Vector Round 0 Router exchange their local vectors with direct neighbors. We ll assume they all exchange at once (synchronous). (Not realistic) Router Router Router Router Router

49 istance Vector Round Router will send to neighbors ( & ): I can get to in and in. Router Router Router Router 7 7

50 istance Vector Round Router 9 will send to neighbors (,,, ): I can get to in, in, in, and in. 6 Router Router Router Router

51 istance Vector Round Router 9 will send to neighbors (,, ): I can get to in, in, and in. 6 Router Router Router Router

52 istance Vector Round Router will send to neighbors (,, ): I can get to in, in, and in. 6 Router Router Router Router

53 istance Vector Round Router will send to neighbors (, ): I can get to in, in. 6 Router Router Router Router

54 t the end of round, how many routers need to update their forwarding tables?,, 3,, E Router Router Router Router Router

55 istance Vector Round Each router advertises the best cost it has to each destination. Nothing new to learn from or, so we ll skip their announcements. Router Router Router Router Router

56 istance Vector Round Router will send to neighbors (,,, ): I can get to in 3, in, in, and in 7. 6 Router Router Router Router 3 3? ?

57 istance Vector Round Router will send to neighbors (,, ): I can get to in, in, in 3, and in 9. 6 Router Router Router Router 3 3? ? ? 3?

58 istance Vector Round Router This process repeats for a while 6 Router Router Router Router 3 3? ? ? 3?

59 istance Vector onvergence Router Eventually, we reach a converged state. 6 Router Router Router Router

60 istance Vector onvergence Router inal forwarding tables: 6 Router Router Router Router

61 Of the links in red below, for how many would a failure cause a loop? 0,,, onsider the failures independently (not all at the same time). Router Router Router Router Router

62 Rewind: istance Vector Round Router will send to neighbors (,,, ): I can get to in 3, in, in, and in 7. 6 Router Router Router Router 3 3? ?

63 Rewind: istance Vector Round Poisoned reverse: on t advertise a lower value to a neighbor if you go through that neighbor to get there! No! Router Router Router Router Router 3 3? ?

64 Loop-prevention Route poisoning helps prevent loops, but doesn t guarantee loop free. Other mechanisms help too There will always be a window of vulnerability

65 Summary Link State + ast convergence (reacts to events quickly) + Small window of inconsistency istance Vector + + istributed (small tables) No flooding (fewer messages) Large number of messages sent on events Large routing tables as network size grows Slower convergence Larger window of inconsistency

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