Distance Vector Routing Protocols. Apr. 5, 2012

Transcription

1 Distance Vector Routing Protocols Apr. 5, 0

2 Recap: Internet Network Layer Protocols Transport layer Routing protocols path selection e.g., RIP, OSPF, BGP Control protocols error reporting e.g. ICMP Control protocols - router signaling e.g. RSVP Network layer forwarding Network layer protocol (e.g., IP) addressing conventions packet format packet handling conventions Link layer physical layer

3 Recap: Routing Routing Goal: determine good paths (sequences of routers) thru network from source to dest. Graph abstraction for the routing problem: graph nodes are routers graph edges are physical links links have properties: delay, capacity, $ cost, policy A 5 B D 3 3 C E 5 F 3

4 Distance Vector Routing Basis of RIP, IGRP, EIGRP routing protocols Positive costs assigned to network links Distributed shortest routing conceptually, runs for each destination separately hence we consider one dest only state: each node maintains a current estimate to the destination d i denotes the distance estimation from node i to dest update rule: based on Bellman-Ford alg. A 5 B D 3 3 C E 5 F

5 Distance Vector Routing: Update At node i, the basic update rule d = min ( d + i j N i) ij d ( j ) destination where - d i denotes the distance estimation from i to the destination, - N(i) is set of neighbors of node i, and - d ij is the distance of the direct link from i to j d i i d ij j d j 5

6 A Synchronous Bellman-Ford (SBF) Nodes update in rounds: there is a global clock; A 0 at the beginning of each round, each node sends its estimate to dest to all of its neighbors; at the end of the round, updates its estimation d(0)? d ( h + ) = min ( d + d ( h)) i j N ( i) ij j 7 B E 8 C D B E C D 6

7 Outline q Network overview q Control plane: routing overview Ø Distance vector protocols Ø synchronous Bellman-Ford (SBF) - SBF/ 7

8 SBF/ Initialization (time 0): 7 A 0 B E 8 C D d i (0) = 0 i = dest otherwise 8

9 Example Consider D as destination; d(t) is a vector consisting of estimation of each node at round t 7 A 0 B E 8 C D A B C E D d(0) 0 d() 0 d() 3 0 d(3) d(4) Observation: d(0) d() d() d(3) d(4) =d* 9

10 ( h + ) = min j N ( i) ( dij d j ( h)) A Nice Property of SBF: Monotonicity d i + Consider two configurations d(t) and d (t) If d(t) d (t) i.e., each node has a higher estimate in d than in d, then d(t+) d (t+) i.e., each node has a higher estimate in d than in d after one round of synchronous update. 0

11 Correctness of SBF/ d ( h + ) = min j N ( i) ( dij d j ( h)) i + Claim: d i (h) is the length L i (h) of a shortest path from i to the destination using h hops base case: h = 0 is trivially true assume true for h, i.e., L i (h)= d i (h), L i (h-)= d i (h-),

12 Correctness of SBF/ d ( h + ) = min j N ( i) ( dij d j ( h)) i + consider h+ hops: L i (h + ) = min( Li ( h), min j N ( i) ( dij + L j ( h))) = min( di ( h), min j N ( i) ( dij + d j ( h))) = min( d ( h), d ( h + )) since d i (h) d i (h-) d i i ( h + ) = min j N ( i) ( dij + d j ( h)) min j N ( i) ( dij + d j ( h )) di ( h) i = L i ( h + ) = d ( h + ) i

13 Bellman Equation We referred to the equations as Bellman equations (BE): d = min ( d + i j N i) ij d ( j ) where d D = 0. - SBF/ solves the equations in a distributed way - Does the equation have a unique solution (i.e., the shortest path one)? 3

14 Uniqueness of Solution to BE d i = min j N i) ( dij + d ( j ) Assume another solution d, we will show that d = d* case : we show d d* Since d is a solution to BE, we can construct paths as follows: for each i, pick a j which satisfies the equation; since d* is shortest, d d* 0 7 A 0 3 B 8 E C D Dest. 4

15 Uniqueness of Solution to BE d i = min j N i) ( dij + d ( j ) Case : we show d d* assume we run SBF with two initial configurations: one is d another is SBF/ (d ), -> monotonicity and convergence of SBF/ imply that d d* 5

16 Outline q Network overview q Control plane: routing overview Ø Distance vector protocols Ø synchronous Bellman-Ford (SBF) - SBF/ - SBF/- 6

17 SBF at another Initial Configuration: SBF/- 7 A 0 B E 8 C D Initialization (time 0): d i (0) = 0 i = dest otherwise 7

18 Example Consider D as destination 7 A 0 A B C E D B E 8 C D d(0) d() d() 7 0 d(3) 8 0 d(4) d(5) d(6) Observation: d(0) d() d() d(3) d(4) d(5) = d(6) = d* 8

19 Bellman Equation and d ( h + ) = min j N ( i) ( dij d j ( h)) i + Correctness of SBF/- SBF/- converges due to monotonicity At equilibrium, SBF/- satisfies the set of equations called Bellman equations (BE) d = min ( d + i j N i) ij d ( j ) where d D = 0. Another solution is shortest path solution d* Since there is a unique solution to the BE equations; thus SBF/- converges to shortest path Question: will SBF converge under other non-negative initial conditions? Problems of running synchronous BF? 9

20 Outline q Network overview q Control plane: routing overview Ø Distance vector protocols o synchronous Bellman-Ford (SBF) Ø asynchronous Bellman-Ford (ABF) 0

21 Asynchronous Bellman-Ford (ABF) No notion of global iterations each node updates at its own pace Asynchronously each node i computes d = min ( d + i j N ( i) ij d i j ) using last received value d i j from neighbor j. Asyncrhonously node j sends its estimate to its neighbor i: there is an upper bound on the delay of estimate packets (no worry for out of order)

22 Asynchronous Bellman-Ford (ABF) In general, nodes are using different and possibly inconsistent estimates j d j i d i j d i

23 Distance Table: Example Below is just one step! The protocol repeats forever! d () E distance tables from neighbors A B D computation A B D A E s distance table 0 7 B E 8 C D distance table E sends to its neighbors A A: 0 A: 0 destinations B C B: 8 D: 4 B: 8 C: 4 D 0 D: D: 0 8 E: 0

24 Asynchronous Bellman-Ford (ABF) ABF will eventually converge to the shortest path links can go down and come up but if topology is stabilized after some time t, ABF will eventually converge to the shortest path! If the network is connected, then ABF converges in finite amount of time, if conditions are met

25 ABF Convergence There are too many different runs of ABF, so need to use monotonicity Consider two sequences: SBF/ ; call the sequence U() SBF/-; call the sequence L()

26 System State j i where can distance estimate from node j appear?

27 System State d i d i j d i j dj three types of distance estimates from node j: - d j : current distance estimate at node j - d i j : last d j that neighbor i received - d i j : those d j that are still in transit to neighbor i

28 ABF Convergence Consider the time when the topology is stabilized as time 0 U(0) and L(0) provide upper and lower bound at time 0 on all corresponding elements of states L j (0) d j U j (0) for all d j state at node j " L j (0) d i j U j (0) " L j (0) update messages d i j U j (0)"

29 ABF Convergence d j d i j : after at least one update at node j: d j falls between L j () d j U j () eventually all d i j that are only bounded by L j (0) and U j (0) are replaced with in L j () and U j () d i dj d i j d i j

30 Asynchronous Bellman-Ford: Summary Distributed: each node communicates its routing table to its directly-attached neighbors Iterative: continues periodically or when link changes, e.g. detects a link failure Asynchronous: nodes need not exchange info/iterate in lock step! Convergence in finite steps, independent of initial condition if network is connected

31 Properties of Distance-Vector Algorithms Good news propagate fast

32 Properties of Distance-Vector Algorithms Bad news propagate slowly (link A-B broke) This is called the counting-to-infinity problem Question: why does counting-to-infinity happen?

33 What is a Routing Loop? A routing loop is a global state (consisting of the nodes local states) at a global moment (observed by an oracle) such that there exist nodes A, B, C, E such that A (locally) thinks B as down stream, B thinks C as down stream, E thinks A as down stream Counting-to-infinity because of routing loops 33

34 The Reverse-Poison (Split-horizon) Hack destinations If the path to dest is through neighbor h, report to neighbor h for dest. E D () A B C D distance tables from neighbors A 0 7 c(e,a) B c(e,b) D 0 c(e,d) A 8 computation B D 4 A E s distance table, A 8, B 4, D, D distance through neighbor 7 B E 8 C D distance table E sends to its neighbors To A A: B: 8 C: 4 D: E: 0 To B A: B: C: 4 D: E: 0 To D A: B: 8 C: D: E: 0

35 An Example Where Split-horizon Fails When the link between C and D fails, C will set its distance to D as However, unfortunate timing can cause problem - A receives the bad news ( ) from C, A will use B to go to D - A sends the news to C - C sends the news to B Question: what is the routing loop formed?

36 Example: RIP ( Routing Information Protocol) Distance vector Included in BSD-UNIX Distribution in 98 Link cost: Distance metric: # of hops Distance vectors exchanged every 30 sec via Response Message (also called advertisement) using UDP each advertisement: route to up to 5 destination nets

37 RIP (Routing Information Protocol) w x y A I B... z C Destination Network Next Router Num. of hops to dest. w A y B z B 7 x Routing table in I

38 RIP: Link Failure and Recovery If no advertisement heard after 80 sec --> neighbor/ link declared dead routes via neighbor invalidated new advertisements sent to neighbors neighbors in turn send out new advertisements (if tables changed) link failure info quickly propagates to entire net reverse-poison used to prevent ping-pong loops set infinite distance = 6 hops (why?)

39 EIGRP Neighbor Discovery EIGRP routers actively establish relationships with their neighbors EIGRP routers establish adjacencies with neighbor routers by using small hello packets. The Hello protocol uses a multicast address of , and all routers periodically send hellos.

40 EIGRP Neighbor Discovery On hearing hellos, the router creates a table of its neighbors. The continued receipt of these packets maintains the neighbor table By forming adjacencies, EIGRP routers do the following: Dynamically learn of new routes that join their network Identify routers that become either unreachable or inoperable Rediscover routers that had previously been unreachable

41 Neighbor Discovery - 3 4

42 Default Hello Intervals and Hold Time for EIGRP

43 Backup Slides 43

44 Using Virtual Circuit to Implement Network Services In order to provide some functionalities, a network may choose virtual circuit, e.g., Virtual Private Network (VPN) 44

45 Using Datagram to Implement the Most Basic Network Service A datagram network generally provides simple services: the forwarding of packets from src to dest. We will focus on datagram networks which provide best effort service extensions to provide more services will be discussed in the multimedia networking part of the course 45