1. Routing: Distance Vector Algorithm
Networking
CS 3470, Section 1

2. Review
So how is routing different from forwarding?

3. The University of Adelaide, School of Computer Science
19 September 2018
Routing
Network as a Graph
The basic problem of routing is to find the lowest-cost path between any two nodes
Where the cost of a path equals the sum of the costs of all the edges that make up the path 5 3 B C 2 5 A 2 1 F 3 1 2 D E 1
Chapter 2 — Instructions: Language of the Computer

4. Routing Routing protocols need to be both dynamic and distributed
Deal with node and link failures, changing link costs, and scalability

5. Distributed Routing Algorithms
Two standard distributed routing algorithms
Link state routing
Distance vector routing
What link state routing protocol did we discuss last time?

6. Link State vs Distance Vector
Both assume that
The address of each neighbor is known
The cost of reaching each neighbor is known
Both find global information
By exchanging routing info among neighbors
Differ in info exchanged and route computation
LS: tells every other node its distance to neighbors
DV: tells neighbors its distance to every other node

7. Distance Vector Routing
A router tells neighbors its distance to every router
Communication between neighbors only
Each router maintains a distance table
A row for each possible destination
A column for each neighbor
DX(Y,Z) : distance from X to Y via Z
So far we have talked about link state routing. Under link state routing each router receives complete information about the network topology and computes shortest paths using Dijkstra’s algorithm. Now we will discuss a different routing protocol called distance vector Routing.
Under distance vector routing, a router informs its neighbors about the distance from that router to every other router in the network. Unlike in link state routing, here information is exchanged only between neighbors. It is based on Bellman-Ford algorithm for computing shortest paths. We will go through an example to see how this works.
Under distance vector routing, each router maintains a distance table. A row for each possible destination and a column for each neighbor. An entry in router X’s table corresponding to a row Y and a column Z is the distance from X to Y via Z.
Given a distance table we can find the shortest distance to a destination, i.e., the smallest value in the row corresponding to the destination. A list of <destination, shortest distance> tuples is called a distance vector and these distance vectors are exchanged between neighbors.

8. Distance Vector Routing
Given a distance table we can find the shortest distance to a destination
i.e., the smallest value in the row corresponding to the destination.
A list of <destination, shortest distance> tuples is called a distance vector
Current least cost to each destination
Exchanged between neighbors
Based on Bellman-Ford algorithm
Computes “shortest paths”

9. Distance Table: Example
Distance table at router E
D () A B C D 1 7 6 4 14 8 9 11 5 2 E
cost to destination via
destination A E D C B 7 8 1 2
Lets look at an example. Here A, B, C, D, and E are routers and the links are labeled with their costs. And this is a distance table at router E. You can see that there is one row per each destination an one column per each neighbor.
If you look at the third row, it says that you can reach C via A with cost 6, via B with cost 9 and via D with 4. So the shortest distance to C is 4 via D. If E were to advertise its distance vector it will send <A,1>,<B,5>,<C,4>,<D,2>.
If E were to advertise its distance vector, it would send <A,1>,<B,5>,<C,4>,<D,2>

10. Distance Table to Routing Table1 7 6 4 14 8 9 11 5 2 E
cost to destination via
destination
Outgoing link
to use, cost A B C D
A,1
D,5
D,4
D,2
What we are really interested in is the routing table. How do we create a routing table from this distance table. Pretty simple. For example, to reach B the shortest path is via D. So the next hop for routing to B is D. We can get the whole routing table this way.
Now the question is how do we compute this distance table. That’s where we use Bellman-Ford algorithm.
destination
Distance table
Routing table

11. Distance Vector Routing Algorithm
Now the real question…
How do we compute this distance table?
That’s where we use Bellman-Ford algorithm.

12. Distance Vector Routing Algorithm
iterative:
continues until no nodes exchange info.
self-terminating: no “signal” to stop
asynchronous:
nodes need not exchange info/iterate in lock step!
distributed:
each node talks only with directly-attached neighbors
Distance Table data structure
each node has its own
row for each possible destination
column for each directly-attached neighbor to node
example: in node X, for dest. Y via neighbor Z:
D (Y,Z) X
distance from X to
Y, via Z as next hop
c(X,Z) + min {D (Y,w)} Z w =

13. Distance Vector Routing: Overview
Each node:
Iterative, asynchronous: each iteration caused by:
local link cost change
message from neighbor: its least cost path change from neighbor
Distributed:
each node notifies neighbors only when its least cost path to any destination changes
neighbors then notify their neighbors if necessary
wait for (change in local link cost or msg from neighbor)
recompute distance table
if least cost path to any dest has changed, notify neighbors

14. Distance Vector Algorithm: ExampleZ 1 2 7 Y
D (Y,Z) X
c(X,Z) + min {D (Y,w)} w =
7+1 = 8 Z
At beginning, a node only knows the distance to their immediate neighbors. After a few iteration, a node progressively learns the distance to other nodes.
D (Z,Y) X
c(X,Y) + min {D (Z,w)} w =
2+1 = 3 Y

15. Distance Vector Algorithm: ExampleZ 1 2 7 Y
This process continues until no one changes the shortest path to others. Some later steps are not shown in the figure.

16. Distance Vector Algorithm: ExampleZ 1 2 7 Y
This process continues until no one changes the shortest path to others. Some later steps are not shown in the figure.

17. Convergence of DV Routing
router detects local link cost change
updates distance table
if cost change in least cost path, notify neighbors X Z 1 4 50 Y
“good
news
travels
fast”
algorithm
terminates
Now lets look at the convergence of distance vector routing. Here we show only the cost of reaching X from Y and Z.
Suppose that the cost of link between X and Y changes from 4 to 1. The router Y notices the change and updates its distance table. Since the shortest distance changed, it notifies Z. The router Z changes the distance to X via Y as 2 from the previous value 5. It then notifies Y since the shortest distance changed. Y once again changes the distance table. However, this time no change in the shortest distance.
This is the case when the link cost decreases which is a good news. Now lets see what happens when the link cost increases.

18. Problems with DV Routing
Link cost changes:
good news travels fast
bad news travels slow
“count to infinity” problem! X Z 1 4 50 Y 60
algorithm
continues
on!
Suppose that link cost is increased from 4 to 60. Once again router Y senses the change, updates the distance table. It sees that it can reach X via Z with distance 6. Since the shortest distance changed, it notifies the neighbor Z. The router Z in turn updates its table and informs Y. This goes on and on.
Do you know when it terminates? What will be the entries in distance table when it converges? It finally reaches steady state with distance from Y to X via Z as 51 and Z to X via Y as 52.
This is the problem with distance vector routing. Good news travels fast but bad news travels slow. This results in what is known as count to infinity problem.

19. Fixes to Count-to-Infinity Problem
Split horizon
A router never advertises the cost of a destination to a neighbor
If this neighbor is the next hop to that destination
Split horizon with poisonous reverse
If X routes traffic to Z via Y, then
X tells Y that its distance to Z is infinity
Instead of not telling anything at all
Accelerates convergence

20. Split Horizon with Poisoned ReverseX Z 1 4 50 Y 60
If Z routes through Y to get to X :
Z tells Y its (Z’s) distance to X is infinite (so Y won’t route to X via Z)
algorithm
terminates
Lets look at the earlier example again. Note that the initially the cost to reach Z from Y via X is infinity since Y is the next hop for Z to reach X. When the cost changes to 60, Y senses it, updates its table and notifies Z. The router Z realizes that direct link to X is shorter than going thru Y and updates its routing table. It then notifies Y which updates its table and makes Z its next hop to reach X. Then as per the rule, Y announces its cost to reach X as infinity. This way routers quickly converge to stable state.
Does this solution completely solve the count to infinity problem?

21. Count-to-Infinity ProblemX Y Z W
What happens when the link Y to Z goes down?
All three routers X, Y, and W together count to infinity.
Split horizon solution works only when two routers are involved in a loop.
What happens when the link Y to Z goes down. All three routers X, Y, and W together count to infinity. Split horizon solution works only when two routers are involved in a loop. So what is the solution?
To completely eliminate the problem, a router some how need to figure out the complete path to a destination. Obvious solution is to pass on the path information along with the distance vector. This path vector approach is used in BGP.
Split horizon with poison reverse does not help.

22. Count-to-Infinity ProblemX Y Z W
To completely eliminate the problem, a router some how need to figure out the complete path to a destination.
Obvious solution is to pass on the path information along with the distance vector.
This path vector approach is used in BGP.
What happens when the link Y to Z goes down. All three routers X, Y, and W together count to infinity. Split horizon solution works only when two routers are involved in a loop. So what is the solution?
To completely eliminate the problem, a router some how need to figure out the complete path to a destination. Obvious solution is to pass on the path information along with the distance vector. This path vector approach is used in BGP.
Split horizon with poison reverse does not help.

23. Link State vs Distance Vector
Tells everyone about neighbors
Controlled flooding to exchange link state
Dijkstra’s algorithm
Each router computes its own table
May have oscillations
Tells neighbors about everyone
Exchanges distance vectors with neighbors
Bellman-Ford algorithm
Each router’s table is used by others
May have routing loops
Now lets compare these two routing protocols. Under link state, a router tells everyone about its neighbors using controlled flooding. Distance vector case a router communicates with neighbors only to inform about everyone.
Link state each router gathers global information and computes its own table using Dijkstra’s algorithm. Distance vector performs distributed computation using other routers tables.
We saw that distance vector can cause routing loops. There may be frequent changes in routes in the case of link state. This results in out of order delivery of packets which is undesirable.
Both these approaches have advantages and disadvantages. Both are used in the Internet. OSPF is the most popularly used intra-domain routing protocol that is based on link state. RIP is based on distance vector which is being taken over by OSPF. BGP is an inter-domain protocol that uses path vectors.

24. RIP RIP == Routing Information Protocol
RIP is a distance vector implementation
Instead of advertising costs to the next router, RIP advertises the cost to the next network.
(network_address,
distance)
pairs