Chapter 4 Distance Vector Routing

1
Chapter 4Distance Vector Routing

• Professor Rick Han
• University of Colorado at Boulder
• rhan_at_cs.colorado.edu

2
Announcements

• Programming assignment 2 is due Saturday March 1
  by 1159 pm
• Short Homework 3 due Thurs Feb. 20
• Homework 1 solutions should be up soon
• Midterm probably week of March 11 13
• Next, more on IP routing,

3
Recap of Previous Lecture

• ARP
• IP Forwarding Tables
• Destination and Output Port
• IP Routing
• Distributed algorithm to create Forwarding Tables
• Calculate shortest path to each node

• Distance Vector (RIP)
• Send distance vectors to neighbors
• Update route to each destination thru closest
  neighbor
• If neighbor X is closer than neighbor Y to
  destination D, then route thru X to D

4
Link Failure Causes Bouncing Effect
dest
cost
dest
cost
via
via
1
X
A
B
B
A
1
1
B
A
C
2
C
1
B
C
1
25
C
dest
cost
via
A
2
B
B
1
B
5
B Notices A-B Link Failure
B notices failure, resets cost via A to infinity
dest
cost
dest
cost
via
via
A
B
B
A
1
B
C
2
C
1
B
C
1
25
C
dest
cost
via
A
2
B
B
1
B
6
C Sends Dist. Vector to B
dest
cost
dest
cost
via
via
A
B
B
A
3
1
B
C
C
2
C
1
B
C
1
25
C
dest
cost
via
A
2
B
B
1
B
7
B Updates Distance to A
dest
cost
dest
cost
via
via
A
B
B
A
3
C
1
B
C
2
C
1
B
C
Packet sent to A from C bounces between C and
B until TTL0!
1
25
C
8
B Sends Dist. Vector to C
dest
cost
via
dest
cost
via
A
B
B
A
3
C
1
B
C
2
B
C
1
C

• C updates distance to A from 2 to 4. Why
  increase the distance?
• Because shortest path was thru B B just
  advertised a new distance

1
25
C
9
C Sends Dist. Vector to B
dest
cost
dest
cost
via
via
A
B
B
A
5
C
1
B
C
2
C
1
B
C
B adds one to Cs advertised distance to A.
(overrides its stored distance of 3 to A with
5, larger value)
1
25
C
dest
cost
via
A
4
B
B
1
B
10
Link Failure Bad News Travels Slowly
dest
cost
dest
cost
via
via
A
B
B
A
25
C
26
C
C
25
C
1
C
C
After 20 exchanges, routing tables look like
this
1
25
Assume A has advertised its link cost of 25 to C
during Blt-gtC exchanges. C ignores these as too
large (or could store in its distance table (not
shown))
C
dest
cost
via
A
24
B
B
1
B
11
Bad News Travels Slowly (2)
dest
cost
dest
cost
via
via
A
B
B
A
25
C
26
C
C
25
C
1
C
C
B sends its dist Vector, C updates dist to A to
26 via B
1
25
C
12
Bad News Travels Slowly (3)
dest
cost
dest
cost
via
via
A
B
B
A
25
C
26
C
C
25
C
1
C
C
A sends its distance vector to C, so C chooses
shorter path of 25 via A
1
25
C
13
Bad News Travels Slowly (4)
dest
cost
dest
cost
via
via
A
B
B
A
26
C
26
C
C
25
C
1
C
C
After 25 B-C exchanges, finally converge
to stable routing
1
25
C
dest
cost
via
A
25
A
B
1
B
14
Link Failure Causes Counting to Infinity Effect
dest
cost
dest
cost
via
via
1
X
A
B
B
A
1
1
B
A
C
2
C
1
B
C
1
25
C
dest
cost
via
A
2
B
B
1
B
15
B Notices A-B Link Failure
dest
cost
dest
cost
via
via
A
B
B
A
1
B
C
2
C
1
B
C
1
25
C
dest
cost
via
A
2
B
B
1
B
16
C Sends Dist. Vector to B
dest
cost
dest
cost
via
via
A
B
B
A
3
C
1
B
C
2
C
1
B
C
1
25
C
dest
cost
via
A
2
B
B
1
B
17
A-C Link Fails
dest
cost
via
A
B
A
3
C
C
1
C
1

• C detects link to A has failed, but no change in
  Cs routing table. Why?
• Shortest path to A is via B, not C

C
dest
cost
via
A
2
B
B
1
B
18
B and C Count to Infinity
dest
cost
via
A
B
A
3
C
C
1
C
1
C
dest
cost
via
A
4
B
B
1
B
19
B and C Count to Infinity (2)
dest
cost
via
A
B
A
5
C
C
1
C
1
C
dest
cost
via
A
4
B
B
1
B
20
How are These Loops Caused?

• Observation 1
• Bs metric increases
• Observation 2
• C picks B as next hop to A
• But, the implicit path from C to A includes
  itself (C ) !

21
Solution 1 Holddowns

• If metric increases, delay propagating
  information
• In our example, B sees its metric increase and
  delays advertising its distance vector
• C eventually thinks Bs route is gone, picks its
  own route
• B then selects C as next hop
• Adversely affects convergence from failures

22
Other Solutions

• Split horizon
• Cs distance vector does not advertise routes
  thru B that it learned from B
• Poisoned reverse
• Cs distance vector advertises routes thru B that
  it learned from B with infinite distance
• Works for two node loops
• Does not work for loops with more nodes

23
B Notices A-B Link Failure
dest
cost
dest
cost
via
via
A
B
B
A
1
B
C
2
C
1
B
C
1
25
C
dest
cost
via
A
2
B
B
1
B
24
Split Horizon
dest
cost
dest
cost
via
via
A
B
B
A


1
B
C
2
C
1
B
C
25
C
dest
cost
via
A
25
A
C updates its path to A through A (knows its
link cost to A)
B
1
B
25
Split Horizon (2)
dest
cost
dest
cost
via
via
A
B
B
A
26
C
1
B
C
2
C
1
B
C
1
25
dest
cost
C
dest
cost
via
A B 1
25
A
25
A
B
1
B
26
Split Horizon With Poisoned Reverse
dest
cost
dest
cost
via
via
A
B
B
A

--
1
B
C
2
C
1
B
C
1
25
dest
cost
C
dest
cost
via
A

A
2
B
B
1
B
1
B
If lowest cost path is via B, then when updating
B send infinite cost
27
Example Where Split Horizon Fails

• When link breaks, C marks D as unreachable and
  reports that to A and B
• Suppose A learns it first
• A now thinks best path to D is through B
• A reports D unreachable to B and a route of
  cost3 to C
• C thinks D is reachable through A at cost 4 and
  reports that to B
• B reports a cost 5 to A who reports new cost to C
• etc...

1
A
B
1
1
C
X
1
D
28
Avoiding the Counting to Infinity Effect

• Select loop-free paths
• One way of doing this
• Each route advertisement carries entire path
• If a router sees itself in path, it rejects the
  route
• BGP does it this way
• Space proportional to diameter

29
Loop Freedom at Every Instant?

• Does bouncing effect avoid loops?
• No! Transient loops are still possible
• Why? Because implicit path information may be
  stale
• See this in BGP convergence
• Only way to fix this
• Ensure that you have up-to-date information by
  explicitly querying

30
Loop Prevention in Practice

• RIP and RIP2
• Uses split-horizon/poison reverse
• BGP
• Propagates entire path
• Path also used for effecting policies

31
Bellman-Ford Equation

• Distance vector RIP based on distributed
  implementation of Bellman-Ford algorithm
• Bellman-Ford equation
• Label routers iA, B, C,
• Let D(i,j) distance for best route from i to
  remote j
• Let d(i,j) distance from router i to neighbor j
• Set to infinity if ij or i and j not immediate
  neighbors

32
Bellman-Ford Equation (2)

• Bellman-Ford equation
• D(i,j) min d(i,k) D(k,j) for all iltgtj
• k
• neighbors
• Ex. D(B,F) min d(B,k) D(k,F)
• kA,C,E

33
Bellman-Ford Algorithm

• Bellman-Ford equation
• D(i,j) min d(i,k) D(k,j) for all iltgtj
• k neighbors
• Bellman-Ford Algorithm solves B-F Equation
• To calculate D(i,j), node i only needs d(i,k)s
  and D(k,j)s from neighbors
• Problem dont know D(k,j)s
• Solution
• For each node i, first find shortest distance
  path from i to j using one link, D(i,j)1
• Shortest distance path using two or fewer links,
  D(i,j)2, must depend on the shortest distance
  path using one link, namely D(i,j)2 min
  d(i,j) D(i,j)1

34
Bellman-Ford Algorithm (2)

• Key observation
• By induction, the best (h1 or fewer)-hop path
  between nodes i and j must be arise from an
  i-to-neighbor link connected with a (h or
  fewer)-hop path from neighbor to j
• D(i,j)h1 min d(i,k) D(k,j)h
• Bellman-Ford Algorithm
• D(i,j)h1 min d(i,k) D(k,j)h for all
  iltgtj, h0,1,
• k neighbors
• Iterate h0,1,2, until reach diameter DM of
  graph
• D(i,j)DM is the originally desired B-F solution
  D(i,j) !
• At each h, calculate D(i,j)h1 for all iltgtj
• At h0, D(i,j)0 0 for ij, infinity
  otherwise
• D(i,i)h link cost on which dist. vector is
  sent - 1

35
Bellman-Ford Algorithm Example

• Suppose C wants to find shortest path to each
  destination
• First, calculate shortest one-link paths from
  each node easy, D(i,j)1d(i,j)

• D(C,B)1, D(C,D)1, and
• D(B,A)1, D(B,E)1, D(B,C)1, and
• D(D,E)1, D(D,C)1, and
• D(A,B)1, D(A,E)1, D(A,F)1, and
• D(E,A)1, D(E,B)1, D(E,D)1, D(E,F)1, and
• D(F,A)1, D(F,E)1

36
Bellman-Ford Algorithm Example (2)

• Second, calculate shortest 2-or-fewer hop paths
  from each node
• Example for node C to F
• D(C,F)2 min (d(C,k) D(k,F)1) for all j
• k neighbors
• min d(C,B) D(B,F)1, d(C,D)
  D(D,F)1

• No one-link path from B to F, so D(B,F)1 is
  infinity, same for D(D,F)1
• Calculate D(i,j)2 for all other combinations of
  iltgtj

37
Bellman-Ford Algorithm Example (3)

• Third, calculate shortest 3-or-fewer hop paths
  from each node
• Example for node C to F
• D(C,F)3 min d(C,B) D(B,F)2, d(C,D)
  D(D,F)2
• No more unknowns
• D(B,F)2 is known by now and was calculated in
  the last iteration, mind(B,k) D(k,F)1
• D(D,F)2 is also known

• Since diameter 3, were done and have found all
  shortest distance paths D(i,j)

38
Distributed Bellman-Ford Algorithm

• Bellman-Ford Algorithm
• D(i,j)h1 min d(i,k) D(k,j)h for all
  iltgtj, h0,1,
• k neighbors
• One way to implement in a real network
• Flood d(i,j) first to every router in the network
• Calculate B-F Algorithm in each router
• Drawbacks
• Generates lots of overhead
• Requires much computation on each router
• Duplication of many of calculations on each
  router
• Consider an alternative to distribute calculations

39
Distributed Bellman-Ford Algorithm (2)

• Bellman-Ford Algorithm
• D(i,j)h1 min d(i,k) D(k,j)h for all
  iltgtj, h0,1,
• k neighbors
• Key observations
• We had to calculate D(i,j)h for each node i in
  the graph, at each step h in the iteration
• At every iteration h, we only needed information
  about the h-1 or fewer hop paths to calculate
  D(i,j)h

40
Distributed Bellman-Ford Algorithm (3)

• Therefore, in a real network,
• Physically distribute the calculation of
  D(i,j)h to router i only, and
• No duplication
• Less calculation
• Exchange the results of your D(i,j)h with
  neighboring routers at each iteration h
• Less overhead
• Satisfies condition that D(i,j)h only needs
  info on h-1 or less hop paths.
• At iteration h, d(i,j) within radius h-1 will be
  propagated to all routers within radius h-1

41
Distributed Bellman-Ford Algorithm (4)

• In practice, convergence will eventually occur
  even if different routers are slow to propagate
  or calculate their D(i,j)h and/or d(i,j)
• Bertsekas and Gallagher proved this, in the
  absence of topology changes
• Distributed routing algorithm where each router
  only performs a small but sufficient part of the
  overall B-F algorithm
• Node i calculates and sends D(i,j)h to its
  neighbors this is a distance vector
• Distributed Bellman-Ford Algorithm Distance
  Vector Algorithm

42
Distance Table

• Bellman-Ford Algorithm
• D(i,j)h1 min d(i,k) D(k,j)h for all
  iltgtj, h0,1,
• k neighbors
• Each router i must maintain a distance table
• Must store d(i,k), D(k,j)h for each neighbor k
  and destination j

43
Distance Table (2)

• In reality, each cell in distance table stores
  d(i,k) D(k,j)h, not just D(k,j)h
• Must store d(i,k) or receive it within a
  neighbors distance vector advertisement
• If d(i,k) is a hop, then d(i,j)1 always, so no
  need to store

44
Routing Table

• Easy to derive a Routing Table from a distance
  table choose the minimum distance in the row