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Distance Vector Routing Protocols

Distance Vector Routing Protocols. Apr. 5, 2012. Control protocols error reporting e.g. ICMP. Control protocols - router “ signaling ” e.g. RSVP. Network layer protocol (e.g., IP) addressing conventions packet format packet handling conventions. Routing protocols path selection

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Distance Vector Routing Protocols

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  1. Distance Vector Routing Protocols Apr. 5, 2012

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

  3. 5 3 5 2 2 1 3 1 2 1 A D E B F C Routing Recap: 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

  4. Basis of RIP, IGRP, EIGRP routing protocols Positive costs assigned to network links Distributedshortestrouting conceptually, runs for each destination separately hence we consider one dest only state: each node maintains a current estimate to the destination di denotes the distance estimation from node i to dest update rule: based on Bellman-Ford alg. 5 3 5 2 2 1 3 1 2 1 A D B E F C Distance Vector Routing

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

  6. A D E B C Synchronous Bellman-Ford (SBF) 1 7 2 8 10 2 • Nodes update in rounds: • there is a global clock; • 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 A B E C D

  7. Outline • Network overview • Control plane: routing overview • Distance vector protocols • synchronous Bellman-Ford (SBF) • - SBF/

  8. A D E B C SBF/ 1 7 2 8 10 2 • Initialization (time 0):

  9. 1 7 2 8 10 2 1232 2 0 2 2 0 1032 2 0 1032 2 0   0 d(0) d(4) d(2) d(3) d(1) A D B E C Example Consider D as destination; d(t) is a vector consisting of estimation of each node at round t A B C E D Observation: d(0)  d(1)  d(2)  d(3)  d(4) =d*

  10. A Nice Property of SBF: Monotonicity • 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+1)  d’(t+1) • i.e., each node has a higher estimate in d than in d’ after one round of synchronous update.

  11. Correctness of SBF/ • Claim: di(h) is the length Li(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., Li(h)=di(h), Li(h-1)=di(h-1), …

  12. since di(h) ≤ di(h-1) Correctness of SBF/ • consider ≤ h+1 hops:

  13. Bellman Equation • We referred to the equations as Bellman equations (BE): where dD = 0. • SBF/ solves the equations in a distributed way • Does the equation have a unique solution (i.e., the shortest path one)?

  14. 1 7 2 8 10 2 A D E B C 1 1 1 1 Uniqueness of Solution to BE • Assume another solution d, we will show that d = d* case 1: 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* 2 3 Dest. 10 2

  15. Uniqueness of Solution to BE Case 2: 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*

  16. Outline • Network overview • Control plane: routing overview • Distance vector protocols • synchronous Bellman-Ford (SBF) • SBF/ • SBF/-1

  17. A D E B C SBF at another Initial Configuration: SBF/-1 1 7 2 8 10 2 • Initialization (time 0):

  18. 1 7 2 8 10 2 -1-1 -1 -1 0 103 3 2 0 9 3 3 2 0 8 2 2 2 0 7 1 1 2 0 6 0 0 2 0 103 3 2 0 d(5) d(4) d(3) d(6) d(1) d(0) d(2) A D B E C Example Consider D as destination A B C E D Observation: d(0)  d(1)  d(2)  d(3)  d(4)  d(5) = d(6) = d*

  19. Bellman Equation and Correctness of SBF/-1 • SBF/-1 converges due to monotonicity • At equilibrium, SBF/-1 satisfies the set of equations called Bellman equations (BE) where dD = 0. • Another solution is shortest path solution d* • Since there is a unique solution to the BE equations; thus SBF/-1 converges to shortest path Question: will SBF converge under other non-negative initial conditions? Problems of running synchronous BF?

  20. Outline • Network overview • Control plane: routing overview • Distance vector protocols • synchronous Bellman-Ford (SBF) • asynchronous Bellman-Ford (ABF)

  21. Asynchronous Bellman-Ford (ABF) • No notion of global iterations • each node updates at its own pace • Asynchronously each node i computes using last received value dij 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. j i Asynchronous Bellman-Ford (ABF) • In general, nodes are using different andpossibly inconsistent estimates dj dij di

  23. 1 distance table E sends to its neighbors 7 A: 10 B: 8 C: 4 D: 2 E: 0 2 8 10 2 A D E B C Distance Table: Example Below is just one step! The protocol repeats forever! distance tablesfrom neighbors computation E’s distance table d () A B C D A B D A B D E 10 15  0 7  A: 10 B: 8 7 0  17 8  destinations D: 4 1 2 9 4 0 2 D: 2 10 8 2

  24. Asynchronous Bellman-Ford (ABF) • ABF will eventually converge tothe shortest path • links can go down and come up – but if topology is stabilized after some timet, ABF will eventually converge to theshortest path ! • Ifthe 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/-1; call the sequence L()

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

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

  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 • Lj (0) ≤ dj≤ Uj (0) for all dj state at node j • Lj (0) ≤ dij≤ Uj (0) • Lj (0) ≤ update messages dij≤ Uj (0)

  29. dj di ABF Convergence • dj • after at least one update at node j: dj falls between Lj (1) ≤ dj ≤ Uj (1) • dij : • eventually all dij that are only bounded by Lj (0) and Uj (0) are replaced with inLj(1) and Uj(1) dij dij

  30. 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 Asynchronous Bellman-Ford: Summary

  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

  34. 1 7 2 8 1 2 A D E B C The Reverse-Poison (Split-horizon) Hack If the path to dest is through neighbor h, report  to neighbor h for dest. distance tables from neighbors computation E’s distance table distance table E sends to its neighbors E D () A B C D A 0 7   1 c(E,A) B 7 0 1  8 c(E,B) A 1 8   D   2 0 2 c(E,D) B 15 8 9  D   4 2 1, A 8, B 4, D 2, D To B A: 1 B:  C: 4 D: 2 E: 0 To A A:  B: 8 C: 4 D: 2 E: 0 To D A: 1 B: 8 C:  D:  E: 0 destinations distance through neighbor

  35. An Example Where Split-horizon Fails 1 1 1 1 • 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 1982 • Link cost: 1 • Distance metric: # of hops • Distance vectors • exchanged every 30 sec via Response Message (also called advertisement) using UDP • each advertisement: route to up to 25 destination nets

  37. RIP (Routing Information Protocol) z ... w x y A I B C Destination Network Next Router Num. of hops to dest. w A 2 y B 2 z B 7 x -- 1 …. …. .... Routing table in I

  38. RIP: Link Failure and Recovery If no advertisement heard after 180 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 = 16 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 224.0.0.10, 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

  42. Default Hello Intervals and Hold Time for EIGRP

  43. Backup Slides

  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)

  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

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