Distance Vector Routing

Transcription

1 ÉOL POLYTHNIQU FÉÉRL LUSNN istance Vector Routing Jean Yves Le oudec 20

2 ontents. Routing in General 2. istance vector: theory 3. istance vector: practice (RIP) 4. Software efined Networking (SN) Textbook Section.., The control plane 2

3 . Introduction Why were routing protocols invented IP assumes routing tables are maintained at hosts and routers used by Packet Forwarding Routing = control method maintain routing tables automatically in routers Packet Forwarding for every packet done in real time Routing computation of routing tables or data structures for unicast and possibly multicast normally only between routers non real time: latency up to 2 minutes uses dedicated protocols (RIP, OSPF, IGRP (isco) for unicast and VMRP, M OSPF, PIM) Routing tables in hosts are normally derived from configuration info 3

4 What a routing protocol does find reachable destinations find best paths towards destinations best = distance to destination is minimal istance = computed using some metric Static metric does not depend on the network state; for example: number of hops link capacity and static delay dministrative cost ynamic metric depend on the network state link load current delay see end of section 4

5 How routing protocols work There are many different ways, which can be classified as istance Vector: very router knows only: its neighbours + distances to all destination (used inside domains interior routing) this module and lab 4 Link State: very router has a detailed map of entire network (used inside domains interior routing) module link state Path vector very router knows only: its neighbours + paths to all destination (used between domains exterior routing) module GP and lab 6 Source routing s an alternative to routing protocols it is also possible to configure routing tables using manual configuration (see lab )

6 6 Source Routing S RI data IS IS IS IS 4 3 source writes route into packet header (IP header extension) router reads next hop from packet header, moves pointer route discovered by the source, flooding with IP, this is called strict source routing : not used in the Internet but used in some ad hoc networks

7 2. istance Vector: Theory What it does: it computes shortest paths to all destinations ost of a path = sum of the cost of network links along the path ost of a link is setup by configuration Shortest path = path whose cost is minimal istance from node to node = cost of a shortest path from to How it works uses the istributed ellman Ford algorithm Fully distributed Using as only information the distances from self to all destinations 7

8 8 2. The entralized ellman Ford lgorithm lgorithm F input: a directed graph with links costs (, ); assume (, )>0 and when nodes iand j are not connected. output: vector s.t. ( )= cost of best path from node to node for for until return( ) do for

9 9 xample: shortest paths to node : run F for 0 F k= k= k= k= k= k= 6 2 2

10 Message Passing Interpretation of ellman Ford k= k=2 3 0 With F it is as if : at iteration, node receives from neighbors their previous costs and updates own cost by picking the best F can be interpreted as a synchronous message passing algorithm synchronous = nodes wait until iteration is finished before starting iteration 0

11 xample: shortest paths to node : run F, 0 F k= k= k= k= k= k= 6 2 2

12 2 t which does the algorithm stop? (i.e. what is the smallest such that?). k = 2. k = 2 3. k = 3 4. k = 4. k = 6. k 6 7. I don t know 60% 33% k= 0% 0% k=2 k=3 k=4 k= 4% 0% I don t know 2%

13 3 Solution: algorithm stops at 0 0 k= k= k= k= k= p()=4 p()= p()= p()=3 p()=3

14 4 orrectness of F Theorem. If the network is fully connected, F stops at the latest at (where number of nodes) and outputs the distance along shortest path from to, for all is the distance from to in at most hops 3. The next hop along a shortest path from to is found by nexthop(i) rgmin j i

15 omputation of shortest path tree When algorithm has converged, the next hop of node is obtained by looking for that minimizes 4 k=

16 2.2 ssume we start from other initial conditions. What will happen? replaced by values on graph k= %. The algorithm converges to the correct distances 2. The algorithm does not converge 3. The algorithm converges but not to the correct distances 4. I don t know The algorithmconverges to 27% The algorithmdoes not con 7% The algorithmconverges but I don t know 2% 6

17 7 Run F with bizarre initial conditions the value of is k= k= % 30%? 7. I don t know 2 3 2% 4 2% 2% I don t know 0%

18 8 Solution: Run F with bizarre initial conditions F k= k= k= k= k= On this example, algorithm F converges to the correct values in spite of abnormal initial conditions

19 ssume we break some links and start from these initial conditions. What will happen? replaced by values on graph 40% 4 49% The algorithm converges to the correct distances 2. The algorithm does not converge 3. The algorithm converges but not to the correct distances 4. I don t know The algorithm converges to... The algorithm does not con... The algorithm converges but... % I don t know 0% 9

20 20 Run F with disconnected network the value of is k= k= %? 7. I don t know 8% % 2 0% 0% 3 8% 6% 4 I don t know

21 2 Solution: F with disconnected network F 4 2 k= k= k= k= k=4 0 On this example, algorithm F converges to the correct values at and and counts to at and

22 22 orrectness of F with arbitrary initial condition and arbitrary network any nonnegative value Theorem 2. If there is a path from to, then for large enough where is the distance from to. It follows that if the network is fully connected, F with arbitrary initial conditions terminates and eventually computes the correct distances. However, in general, when is small is not the distance from to in hops. 2. If there is no path from to then lim. It follows that if the network is not fully connected, F does not terminate ( count to infinity ).

23 Proof We do the proof assuming all nodes are connected.. Let p k be the vector p k [i], i=2,. Let be the mapping that transforms an array x[i] i=2 into the array x defined for i by x[i]=min j i, j [(i,j) + x(j)] Let b be the array defined for i by b[i]= (i,) The algorithm can be rewritten in vector form as () p k = p k b where is the pointwise minimum 2. q () is a min plus linear equation and the operator satisfies (x y)= x y. Thus, q() can be solved using min plus algebra into (2) p k = k p 0 k b b b 3. efine the array e for i by e[i]=. Let p 0 =e. q (2) becomes (3) p k = k b b b. Now we have the ellman Ford algorithm with classical initial conditions, thus, by Theorem : (4) for k n : k b b b = q where q[i] is the distance from i to. 4. We can rewrite q(2) for k n as () p k = k p 0 q. k p 0 [i] can be written as [i,i ]+ [i,i 2 ]+ + [i k,i k ]+ p[i k ] thus (6) k p 0 [i] k a, where a is the minimum of all [i,j]. Thus k p 0 [i] tends to when k grows. Thus for k large enough, k p 0 is larger than q and can be ignored in q(). In other words, for k large enough : (6) p k = q 23

24 2.3 istributed ellman Ford F can be used to compute p(i) i.e. find the shortest path. However, this is not its main interest, because there is a better algorithm (ijkstra) that can be used in a centralized way. ut: it can be distributed as follows. istributed ellman Ford lgorithm, F prelim node maintains an estimate of the true distance to node ; node also keeps a record of latest values for all neighbors initial conditions are arbitrary but 0 at all steps; from time to time, i sends its value to all neighbours when receives an updated value from neighbor, node recomputes : eq () min i, j q j nexthop(i) is set to a value of j that achieves the min in eq() This is asynchronous message passing, i.e. nodes do not wait for complete rounds of iteration to be performed. 24

25 2 orrectness of F prelim Theorem: ssume at least one message is reliably sent to all neighbors by every node every time units and the network is fully connected. F prelim converges to the same result as the centralized version F (i.e. to the correct distances) in time units, where is the number of steps performed by F with same initial conditions. istributed ellman Ford lgorithm, F prelim node maintains an estimate of the true distance to node ; node also keeps a record of latest values for all neighbors initial conditions are arbitrary but 0 at all steps; from time to time, i sends its value to all neighbours when receives an updated value from neighbor, node recomputes : eq () min i, j q j nexthop(i) is set to a value of j that achieves the min in eq()

26 26 istributed ellman Ford F prelim possible run of algorithm F prelim. The table shows the successive values of q(i) 0 > 0 > 0 3 > > > > > > > onverged!

27 27 Super uper ellman Ford F prelim requires a node to remember all estimates q(j) received from all neighbors, even for not on the shortest path to destination; can we do better? possible modification would be to replace eq() by Super uper ellman Ford: when receives an updated value from neighbor, node recomputes : eq (s) min,, Node i now needs to store only its own estimate Q. does this work?

28 28 Is Super uper ellman Ford correct? 38% when receives an updated value from 3% neighbor, node recomputes : eq (s) min,,. Yes, regardless of initial condition 2. Only if initial conditions are and at time 0 3. It may fail, even with initial conditions as in I don t know Yes, regardless of initial con... Only if initial conditions are.. It may fail, even with initial... 22% % I don t know

29 29 Solution Super uper can only decrease. So if we start from initial conditions as in example «Impact of Initial onditions», the algorithm will not converge to the right value. It gets «stuck» with a low value. It is possible to show that it works if all initial conditions are above the final values, for example and initially. ut even then, it will not work if there is a topology change, since this is equivalent to starting from different initial conditions. Indeed, requiring that initial conditions are correct means that we are able to reset the entire network whenever there is a topology change (which is not feasible in practice).

30 30 istributed ellman Ford, the true version Requires only to remember distance from self to destination + the best neighbor (nexthop( )) and works for all initial conditions istributed ellman Ford lgorithm, F node maintains an estimate of the distance to node ; node remembers the best neighbor nexthop(i) initial conditions are arbitrary but 0 at all steps; from time to time, i sends its value to all neighbors when receives an updated value from, node recomputes : eq (2) if nexthop then, else min,, if eq(2) causes to be modified, nexthop

31 3 6 2 istributed ellman Ford F possible run of algorithm F. The table shows the successive values of and nexthop > > > > > >

32 32 istributed ellman Ford F, cont d nexthop 3 0 possible run of algorithm F. The table shows the successive values of > > > > > > > > > > > >

33 orrectness of F Theorem: ssume at least one message is reliably sent to all neighbors by every node every time units and the network is fully connected. F converges to the same result as the centralized version F (i.e. to the correct distances) in time units, where is the number of steps performed by F with same initial conditions. omment: The main difference with F prelim is that eq(2) replaces eq(). ssume we use F, and we start from a condition such that q(i) is indeed equal to the minimum given by eq () (which is what, intuitively, is true most of the time). When j is not equal to nexthop(i), both eq() and eq(2) have the same effect: the new value of q(i) is the same in both cases. In contrast, if j == nexthop(i), then eq (2) sets q(i) to the new value (i,j)+q(j), whereas eq() sets it to min jneighbor ((i,j)+q(j)). q(2) provides an upper bound on eq(), in this case. It turns out that the algorithm still works, by the same mechanism that makes the algorithm work even when the initial conditions are arbitrary. Indeed, node i will send its new value to all remaining neighbors, who will in turn do an update and eventually, node i will receive values of q(j) that will correct the problem. In other words, if the new value of q(i) is too high (compared to what would be obtained with eq ()), this is repaired in one round of exchanges with the neighbors. 33

34 Take Home Message ellman Ford, istributed (F ), allows a node to compute distances to one destination Stored information is: Next hop to destination istance to destination F works by message passing: every node informs its neighbors of its current distance F works even when initial conditions are not as expected (which occurs due to topology changes) If destination is unreachable (distance algorithms counts to infinity. ) then the 34

35 3. istance Vector routing in practice istance vector routing = based on F F is run in all routers for all possible destination prefixes Router i computes shortest path and next hop for all network prefixes n that it heard of. Initially: (i,n) = if i directly connected to n and implicitly (i,n) = + for any n that was never heard of. Node i receives from neighbour k latest values of (k,n) for all n (this is the distance vector). Node i computes the best estimates according to algorithm F c(i,) (,n) i c(i,k) k (k,n) n c(i,m) m (m,n) 3

36 Periodic Updates Updates are sent periodically (e.g. every 30 sec) If neighbour k is no longer present, node i will no longer receive hello messages, and after a timeout, this has the same effect as if node i would receive the message from k: for all n. Then algorithm F is run: It follows that if was the next hop to, then declares unreachable. c(i,) (,n) i c(i,k) k (k,n) n c(i,m) m (m,n) 36

37 37 ll link costs = xample net dist nxt n n, n4 n4, net dist nxt n n, n2 n2, n net dist nxt n4 m3 n3 n2 m m2 net dist nxt n3 n3, n4 n4, m3 m3, n2 n2, n3 n3, m m, m2 m2,

38 38 ll link costs = xample net dist nxt n n, n4 n4, from n n4 net dist nxt n n, n2 n2, n4 2 n, n net dist nxt n3 n3, n4 n4, m3 m3, n4 m3 n3 n2 m from n3 0 n4 0 m3 0 m2 net dist nxt n2 n2, n3 n3, m m, m2 m2, n4 2 n3, m3 2 n3,

39 39 ll link costs = xample net dist nxt net dist nxt n n, n4 n4, n n, n2 n2, n3 2 n2, n4 2 n, m 2 n2, m2 2 n2, m3 3 n2, net dist nxt n3 n3, n4 n4, m3 m3, n4 m3 n n3 n2 m from n2 n3 m m2 m2 n4 2 m3 2 net dist nxt n2 n2, n3 n3, m m, m2 m2, n4 2 n3, m3 2 n3,

40 40 xample Final net dist nxt n n, n2 2 n, n3 2 n4, n4 n4, m 3 n4, m2 3 n4, m3 2 n4, net dist nxt n n, n2 n2, n3 2 n2, n4 2 n, m 2 n2, m2 2 n2, m3 3 n2, n net dist nxt n 2 n4, n2 2 n3, n3 n3, n4 2 n4, m 2 n3, m2 2 n3, m3 m3, m3 n4 n3 n2 m m2 net dist nxt n 2 n2, n2 n2, n3 n3, m m, m2 m2, n4 2 n3, m3 2 n3,

41 4 ll link costs = xample Router Failure net dist nxt We show only the router in the next hop field n n2 n3 2 n4 2 m 2 m2 2 m3 3 n net dist nxt n 2 n2 2 n3 n4 m 2 m2 2 m3 n4 m3 n3 n2 m m2 net dist nxt n 2 n2 n3 m m2 n4 2 m3 2

42 42 ll link costs = xample Failure net dist nxt n n2 n3 2 n4 2 m 2 m2 2 m3 3 timeout n timeout net dist nxt n 2 n2 2 n3 n4 m 2 m2 2 m3 n4 m3 n3 n2 m m2 net dist nxt n 2 n2 n3 m m2 n4 2 m3 2

43 ll link costs = xample Failure net dist nxt n n2 n3 2 m 2 m2 2 m3 3 n net dist nxt n 3 n2 2 n3 n4 m 2 m2 2 m3 m3 n4 From : n 2 n2 n3 m m2 n4 2 m3 2 n3 n2 m m2 net dist nxt n 2 n2 n3 m m2 n4 2 m3 2 43

44 44 ll link costs = xample fter Failure net dist nxt n n2 n3 2 n4 3 m 2 m2 2 m3 3 n net dist nxt n 3 n2 2 n3 n4 m 2 m2 2 m3 n4 m3 n3 n2 m m2 net dist nxt n 2 n2 n3 m m2 n4 2 m3 2

45 xample : onclusion xample illustrates how ellman Ford is mapped to the network concepts how topology changes are taken into account most recent announcement replaces previous ones non refreshed announcements become obsolete how distance vector carries reachability information 4

46 ssume algorithm has converged a local b l 2 c l 3 d l3 2 e l3 3 ll link costs = a l3 2 b l3 3 c l6 3 d local e l6 2 l3 l4 a l 2 b local c l2 2 d l4 3 e l4 2 l2 l a l6 3 b l4 2 c l 2 d l6 2 e local xample 2 a l2 3 b l2 2 c local d l 3 e l 2 46

47 Links l and l6 fail simultaneously, detects failure a local b l 2 c l 3 d l3 2 e l3 3 ll link costs = a l3 2 b l3 3 c NR d local e NR l3 l4 a l 2 b local c l2 2 d l4 3 e l4 2 l2 l a l6 3 b l4 2 c l 2 d l6 2 e local xample 2 a l2 3 b l2 2 c local d l 3 e l 2 47

48 xample 2 : Zoom on and a local b l 2 c l 3 d l3 2 e l3 3 ll link costs = from : dest cost a b,d 2 c,e 3 a l3 2 b l3 3 c l3 4 d local e l3 4 l3 detects failure of a local b NR c NR d l3 2 e l3 3 a l3 2 b l3 3 c l3 4 d local e l3 4 l3 a local b l3 c l3 d l3 2 e l3 from : dest cost d a 2 b 3 c,e 4 a l3 2 b l3 3 c l3 d local e l3 l3 48

49 ll link costs = fter processing this update, a local b l3 c l3 d l3 2 e l3 from : dest cost a d 2 b 4 c,e a l3 2 b l3 3 c l3 d local e l3 l3 what is the distance at to e? I don t know 34% 2% 0% 0% % 6% 4% 6 I don t know 49

50 0 Solution a local b l3 c l3 d l3 2 e l3 from : dest cost a d 2 b 4 c,e a l3 2 b l3 3 c l3 d local e l3 l3 t : istributed ellman Ford (F ) update is received from next hop to e therefore new distance is accepted sets distance to e to

51 ount to Infinity ll link costs = a local b l3 c l3 d l3 2 e l3 a local b l3 6 c l3 7 d l3 2 e l3 7 a local b l3 6 c l3 7 d l3 2 e l3 7 from : dest cost a d 2 b 4 c,e l3 from : dest cost a d 2 b 4 c,e l3 from : dest cost a d 2 b 6 c,e 7 l3 a l3 2 b l3 c l3 6 d local e l3 6 a l3 2 b l3 c l3 6 d local e l3 6 a l3 2 b l3 7 c l3 8 d local e l3 8

52 onclusion from xample 2 The costs to b,c,e grow unbounded ount to Infinity the true costs are infinite this is the expected behaviour of ellman Ford In practice, we enforce convergence by setting large number e.g. RIP: ut we can do better 2

53 3 Route poisoning and Split Horizon Two practical heuristics in order to Prevent count to infinity Prevent ping pong loops Route poisoning : if detects that route to x is not reachable, immediately sends «distance to x =» to neighbours Further, when a distance = is received for x, any further update about x is ignored for some time (holddown timer) Split Horizon : if routes packets to x via, does not announce this route to

54 xample 2 with Route Poisoning and Split Horizon a local b l 2 c l 3 d l3 2 e l3 3 ll link costs = from : d c, e: a l3 2 b l3 3 c NR d local e NR l3 l4 a l 2 b local c l2 2 d l4 3 e l4 2 l2 l a l6 3 b l4 2 c l 2 d l6 2 e local a l2 3 b l2 2 c local d l 3 e l 2 detects failure immediately sends update to with poisoned routes ( distances) Routes to a and b are not advertized (split horizon)

55 fter processing this update, what are the a local b l 2 c l 3 d l3 2 e l3 3 ll link costs = from : d c, e: a l3 2 b l3 3 c NR d local e NR distances at to c and e? l3. None of the above 6. I don t know $$$$=3, $$$$ 0% 2% 9% 24% Noneof theabov 0% I don t know %

56 6 Solution a local b l 2 c l 3 d l3 2 e NR from : d c, e: a l3 2 b l3 3 c NR d local e NR l3 applies F : is not the next hop to c, therefore computes distance is 3, no change is the next hop to e, therefore computes distance is, i.e. e is unreachable

57 xample 2 with Route poisoning and Split Horizon a local b l 2 c l 3 d l3 2 e NR ll link costs = from : d c, e: a l3 2 b l3 3 c NR d local e NR l3 detects failure a local b NR c NR d l3 2 e NR from : a b,c,e a l3 2 b NR c NR d local e NR l3 No count to infinity fter some time, the distances are removed by timeout 7

58 RIP (Routing Information Protocol) Implements F ost of one link is by default osts are unidirectional, it is possible to have,, 6; therefore network span limited to Split horizon and route poisoning UP port 20 and multicast address / ff02::9 Sends distance vector update every 30 seconds (by default) or when change is detected ( triggered update ) Route not announced during 3 minutes becomes invalid RIP keeps a database of all best paths, called Routing Information ase (RI), which is different (superset of) forwarding table unlike slides in part theory this is to allow several different processes to update the forwarding table ; example: manual configuration + RIP uthentication in RIPv2 by M (shared secret) RIP for IPv4, RIPng for IPv6 8

59 IGRP (nhanced Interior Gateway Routing Protocol) Proprietary protocol by ISO Metric that estimates the global delay Maintains several routes of similar cost load sharing No limit of number of routers included in messages roadcast every 90 sec Typically one process for IPv4 and one process for IPv6 9

60 Metric example Metric Trans = /andwidth (time to send 0 Kb) delay = (sum of elay)/0 m = [K *Trans + (K 2 *Trans )/(26 load) + K 3 *delay] default: K=, K2=0, K3=, K4=0, K=0 if K 0, m = m * [K /(Reliability + K 4 )] andwidth in Kb/s, elay in s t Venus: Route for 72.7/6: Metric = /784 + ( )/0 = 48 t Saturn: Route for 2./8: Metric = /224 + ( )/0 =

61 In a fully connected network, say what is true :. F converges to the correct distances whatever the initial conditions 2. F converges to the correct distances whatever the initial conditions 3. and 2 4. None. I don t know 0% 0% 0% 0% 0% F converges to the correct... F converges to the correc... and 2 None I don t know 6

62 4. Per Flow Forwarding In principle, an IP router uses the destination address and longest prefix match to decide where to send a packet Some networks want more control; e.g. handle mission critical traffic with high priority; e.g. ban non HTTP traffic This is why some routers can be configured with per flow forwarding rules When a packet has to be forwarded, such a router does: Look for a rule match in the list of (priority ordered) perflow forwarding rules (also called flow table) if one or several matches exist, follow the rule with highest priority If no rule matches, go to the IP forwarding table and do longest prefix match Same can be used in switches (per flow tables then complement the M forwarding table) 62

63 63 Which way at R for packets from Lisa and. Lisa:, Homer:. Lisa:, Homer: 2. Lisa:2, Homer:. Lisa:2, Homer: 2. None of above F. I don t know 72% Homer to nterprise server? Lisa.H Homer.H Flow table at R Flow spec action prio input=0; dest=.* output 2 0 dest=..* drop 0 IP Forwarding table at R to output to output * 2 *..* 2.* 0.* 3.* router R router R2 2 3 nterprise server..h2 Lisa:, Homer: % Lisa:, Homer: 2 0% Lisa:2, Homer: 6% Lisa:2, Homer: 2 % None of above I don t know 2% to output *.* 2 router R4 2 IP Forwarding table

64 Solution nswer Packets from Lisa to enterprise server match the two flow rules; the first one has higher priority and is applied. Packets are forwarded to port 2. Since there is a match in flow table, the IP forwarding table is not used. Packets from Homer to enterprise server match the second flow rule and are dropped by R. The combined effect of the flow table and the IP forwarding table at R is such that. all traffic to..* is killed except if arriving on input 0 2. traffic to..* that is not killed is forwarded to output 2 3. traffic to.* and not..* is forwarded to output 64

65 Software efined Networking Local controller Local controller Local controller entral controller router R router R2 router R3 Local controller router R4 What? Manage the flow tables in a collection of routers or switches from a central application How? central controller decides rules and communicates them to local controllers on routers Local controller writes the per flow tables on router Protocol between local controller and central controller is e.g. OpenFlow, over TP connections. 6

66 o we need RIP (or another routing protocol) if we have SN?. No because flow tables can replace IP forwarding tables. Yes because flow tables cannot replace IP forwarding tables. Yes because the central controller needs a way to communicate with local controllers 8% 8% 63% 0%. I don t know No because flowtables can Yes because flowtables can Yes because the central con I don t know 66

67 67 Solution nswer The central controller communicates with the local controllers in routers over TP connections. This needs that IP forwarding tables are functional, which in turn requires RIP or some other routing protocol.

68 68 onclusion istance vector is smart Fully distributed, little information stored Simple ut: relatively slow Not suited for large and complex networks Link State protocols should be used instead Routing tables can be complemented with flow tables, controlled by an outside application (SN)