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Lecture 21 Distance Vector Routing Protocols 11/14/2013

Computer Networks. Lecture 21 Distance Vector Routing Protocols 11/14/2013. Outline. Admin and recap Distance vector protocols. Admin. Any questions on Assignment 4?. Recap: Resource Allocation Framework. Forward (design) engineering: how to determine objective functions

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Lecture 21 Distance Vector Routing Protocols 11/14/2013

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  1. Computer Networks Lecture 21 Distance Vector Routing Protocols 11/14/2013

  2. Outline • Admin and recap • Distance vector protocols

  3. Admin • Any questions on Assignment 4?

  4. Recap: Resource Allocation Framework • Forward (design) engineering: • how to determine objective functions • given objective, how to design effective alg • Reverse (understand) engineering: • understand current protocols (what are the objectives of TCP/Reno, TCP/Vegas?)

  5. Network layer functions: • 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

  6. Recap: Data (Forwarding) Plane routing and call setup

  7. Routing Recap: Routing Design Space • Routing has a large design space • who decides routing? • source routing: end hosts make decision • network routing: networks make decision • how many paths from source s to destination d? • multi-path routing • single path routing • does the route(s) provide QoS? • QoS • best effort, shortest path • will routing adapt to network traffic demand? • adaptive routing • static routing Goal: determine “good” paths (sequences of routers) thru network from source to dest.

  8. Routing Design Space: Adaptive Routing • Routing has a large design space • who decides routing? • source routing: end hosts make decision • network routing: networks make decision • how many paths from source s to destination d? • multi-path routing • single path routing • does the route(s) provide QoS? • QoS • best effort, shortest path • will routing adapt to network traffic demand? • adaptive routing • static routing

  9. Represent network as a graph, with positive costs assigned to network links The path from a source to a destination chosen by the routing protocol is a shortest (lowest cost) path among all possible paths 5 3 5 2 2 1 3 1 2 1 A D B E F C Shortest/Lowest Cost Path Routing

  10. Assume link costs reflect current traffic Link costs reflect current traffic intensity 0 0 0 0 1+e 1 2+e 0 0 1 1+e e 0 0 0 1 1 e t=1 t=0 0 2+e 0 D D D D A A A A B C C B B B C C 0 B C D A 2+e 0 0 1 1+e 1 1+e e 0 t=2 t=3 Routing: Single-Path, Adaptive Routing 1 1 e Solution: Link costs are a combination of current traffic intensity (dynamic) and topology (static). To improve stability, the static topology part should be large. Thus less sensitive to traffic; thus non-adaptive.

  11. Example: Cisco Proprietary  Recommendation on Link Cost • Link metric: • metric = [K1 * bandwidth-1 + (K2 * bandwidth-1) / (256 - load) + K3 * delay] * [K5 / (reliability + K4)] By default, k1=k3=1 and k2=k4=k5=0. The default composite metric for EIGRP, adjusted for scaling factors, is as follows: BWmin is in kbps and the sum of delays are in 10s of microseconds. EIGRP : Enhanced Interior Gateway Routing Protocol

  12. 5 3 5 2 2 1 3 1 2 1 A D B E F C Example: EIGRP Link Cost • The bandwidth and delay for an Ethernet interface are 10 Mbps and 1 ms, respectively. • The calculated EIGRP BW metric is as follows: • 256 × 107/BW = 256 × 107/10,000 • = 256 × 10000 • = 256000

  13. Outline • Admin and recap • Distance vector protocols

  14. Basis of RIP, IGRP, EIGRP routing protocols Distributed alg to computeshortest paths conceptually, runs for each destination separately hence we consider one dest only state: each node maintains a current estimate of distance 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

  15. 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

  16. 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

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

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

  19. 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 • Observations: • d(0)  d(1)  d(2)  d(3)  d(4) • After a few iterations d(n) = d(n+1) = d*

  20. 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.

  21. 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), …

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

  23. Bellman Equation • We referred to the update rules 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)?

  24. 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

  25. 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*

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

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

  28. 1 7 2 8 10 2 -1-1 -1 -1 0 103 2 2 0 9 3 2 2 0 8 2 2 2 0 7 1 1 2 0 6 0 0 2 0 103 2 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*

  29. Correctness of SBF/-1 • SBF/-1 converges due to monotonicity • At equilibrium, SBF/-1 satisfies Bellman equations: 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

  30. Discussion • How do you prove that SBF converges under other non-negative initial conditions?

  31. Toolbox • A key technique for proving convergence (liveness) of distributed protocols: two extreme configurations to sandwich any real configurations

  32. Discussion • Problem of SBF? A B E C D

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

  34. 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)

  35. 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

  36. j i Asynchronous Bellman-Ford (ABF) • In general, nodes are using different andpossibly inconsistent estimates dj dij di

  37. 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

  38. 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()

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

  40. 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

  41. 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)

  42. 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

  43. 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

  44. Properties of Distance-Vector Algorithms • Good news propagate fast

  45. 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?

  46. 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

  47. 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

  48. An Example Where Split-horizon Fails 1 1 1 1 • C and D fails, C will set its distance to D as  • C sends the bad news () to A • A switches to use use B to go to D • A sends the news to C • C sends the news to B I can reach D w/ cost 3 Question: what is the routing loop formed?

  49. Outline • Admin and recap • Distance vector protocols • synchronous Bellman-Ford (SBF) • asynchronous Bellman-Ford (ABF) • RIP, EIGRP

  50. 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

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