1. 14: Intro to Routing Algorithms
Last Modified:
11/16/ :32:13 PM
4: Network Layer

2. Routing
IP Routing – each router is supposed to send each IP datagram one step closer to its destination
How do they do that?
Static Routing
Hierarchical Routing – in ideal world would that be enough? Well its not an ideal world
Dynamic Routing
Routers communicate amongst themselves to determine good routes (ICMP redirect is a simple example of this)
Before we cover specific routing protocols we will cover principles of dynamic routing protocols
4: Network Layer

3. Routing Algorithm classification: Static or Dynamic?
Choice 1: Static or dynamic?
Static:
routes manually defined
change slowly over time or only one possible route
Appropriate in some circumstances, but obvious drawbacks (routes added/removed? sharing load?)
Not much more to say?
Dynamic:
Routes learned by communicating with other routers
routes change more quickly
periodic update
in response to link cost changes
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4. Routing Algorithm classification: Global or decentralized?
Choice 2, if dynamic: global or decentralized information?
Global:
all routers have complete topology, link cost info
“link state” algorithms
Decentralized:
router knows physically-connected neighbors, link costs to neighbors
iterative process of computation, exchange of info with neighbors (gossip)
“distance vector” algorithms
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5. Roadmap Details of Link State Details of Distance Vector Comparison
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6. Routing Routing protocol Graph abstraction for routing algorithms:E D C B F 2 1 3 5
Goal: determine “good” path
(sequence of routers) thru
network from source to dest.
Graph abstraction for routing algorithms:
graph nodes are routers
graph edges are physical links
link cost: delay, $ cost, or congestion level
“good” path:
typically means minimum cost path
other definitions possible
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7. Global Dynamic Routing
See the big picture; Find the best Route
What algorithm do you use? A E D C B F 2 1 3 5
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8. A Link-State Routing Algorithm
Dijkstra’s algorithm
Know complete network topology with link costs for each link is known to all nodes
accomplished via “link state broadcast”
In theory, all nodes have same info
Based on info from all other nodes, each node individually computes least cost paths from one node (“source”) to all other nodes
gives routing table for that node
iterative: after k iterations, know least cost path to k dest.’s
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9. Link State Algorithm: Some Notation
c(i,j): link cost from node i to j. cost infinite if not direct neighbors
D(v): current value of cost of path from source to dest. V
n(v): next hop from this source to v along the least cost path
N: set of nodes whose least cost path definitively known
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10. Dijsktra’s Algorithm 1 Initialization – know c(I,j) to start:
2 N = {A}
3 for all nodes v
if v adjacent to A
then D(v) = c(A,v)
else D(v) = infty 7
8 Loop
9 find w not in N such that D(w) is a minimum (optional?)
10 add w to N
11 update D(v) for all v adjacent to w and not in N:
D(v) = min( D(v), D(w) + c(w,v) )
13 /* new cost to v is either old cost to v or known
shortest path cost to w plus cost from w to v */
15 until all nodes in N
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11. Dijkstra’s algorithm: example
Step 1 2 3 4 5
start N A AD
ADE
ADEB
ADEBC
ADEBCF
D(B),n(B)
2,B
D(C),n(C)
5,C
4,D
3,D
D(D),n(D)
1,A
D(E),n(E)
infinity
2,D
D(F),n(F)
infinity
4,D A E D C B F 2 1 3 5
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12. Dijkstra’s Algorithm gives routing table
Outgoing Link A B C D E F
n(A) = A
n(B) = B
n (C)= D
n(D) = D
n(E) = D
n(F) = D
destination
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13. Complexity of Link State
Algorithm complexity: n nodes
each iteration
Find next w not in N such that D(w) is a minimum
Then for that w, check its best path to other destinations
=> n*(n+1)/2 comparisons: O(n2)
more efficient implementations possible using a heap: O(nlogn)
Picture not that clear!
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14. Distance Vector Routing Algorithm
distributed:
each node communicates only with directly-attached neighbors
iterative:
continues until no nodes exchange info.
self-terminating: no “signal” to stop
asynchronous:
nodes need not exchange info/iterate in lock step!
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15. Distance Vector Routing Algorithm
Column only for each neighbor
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:
cost to destination via X
D () Y Z
Dx(Y,Z)
destination
D (Y,Z) X
distance from X to
Y, via Z as next hop
c(X,Z) + min {D (Y,w)} Z w =
Rows for each possible dest !
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16. Example: Distance Table for E
Column only for each neighbor A E D C B 7 8 1 2
cost to destination via E
D () A B C D A 1 7 6 4 B 14 8 9 11 D 5 4 2
D (row, col) E
D (C,D) E
c(E,D) + min {D (C,w)} D w =
2+2 = 4
destination
D (A,D) E
c(E,D) + min {D (A,w)} D w =
2+3 = 5
Loop back through E!
Rows for each possible dest !
D (A,B) E
c(E,B) + min {D (A,w)} B w =
8+6 = 14
Loop back through E!
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17. Distance table gives routing table
= least cost
D () A B C D 1 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
destination
Distance table
Routing table
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18. Distance Vector Routing: overview
Iterative, asynchronous: each local 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
Each node:
wait for (change in local link cost of msg from neighbor)
recompute distance table
if least cost path to any dest has changed, notify neighbors
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19. Distance Vector Algorithm:
At all nodes, X:
1 Initialization (don’t start knowing link costs for all links in graph):
2 for all adjacent nodes v:
D (*,v) = infty /* the * operator means "for all rows" */
D (v,v) = c(X,v)
5 for all destinations, y
send min D (y,w) to each neighbor /* w over all X's neighbors */ X X X w
Then in steady state…
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20. Distance Vector Algorithm (cont.):
8 loop
9 wait (until I see a link cost change to neighbor V
or until I receive update from neighbor V) 11
12 if (c(X,V) changes by d)
/* change cost to all dest's via neighbor v by d */
/* note: d could be positive or negative */
for all destinations y: D (y,V) = D (y,V) + d 16
17 else if (update received from V wrt destination Y)
/* shortest path from V to some Y has changed */
/* V has sent a new value for its min DV(Y,w) */
/* call this received new value is "newval" */
for the single destination y: D (Y,V) = c(X,V) + newval 22
23 if we have a new min D (Y,w)for any destination Y
send new value of min D (Y,w) to all neighbors 25
26 forever X X w X X w X w
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21. z y x Dx(z) = min{c(x,y) + Dy(z), c(x,z) + Dz(z)} = min{2+1 , 7+0} = 3
Dx(y) = min{c(x,y) + Dy(y), c(x,z) + Dz(y)} = min{2+0 , 7+1} = 2
node x table
x y z x y z ∞
from
cost to
cost to
x y z x 2 3
X hears news from Y and Z
from y z
node y table
cost to x z 1 2 7 y
x y z x ∞ ∞ ∞ y
from z ∞ ∞ ∞
node z table
To start just know directly connected links…tell neighbors
cost to
x y z x
∞ ∞ ∞
from y ∞ ∞ ∞ z 7 1
time
Network Layer

22. z y x Dx(z) = min{c(x,y) + Dy(z), c(x,z) + Dz(z)} = min{2+1 , 7+0} = 3
Dx(y) = min{c(x,y) + Dy(y), c(x,z) + Dz(y)} = min{2+0 , 7+1} = 2
node x table
x y z x y z ∞
from
cost to
cost to
cost to
x y z
x y z x x
from y
from y z z
node y table
cost to
cost to
cost to x z 1 2 7 y
x y z
x y z
x y z x ∞ ∞ x ∞ x y
from y
from
from y z z ∞ ∞ ∞ z
node z table
In steady state, when have good news tell neighbor
cost to
cost to
cost to
x y z
x y z
x y z x x x
∞ ∞ ∞
from y
from y
from y ∞ ∞ ∞ z z z 7 1
time
Network Layer

23. Distance Vector: link cost changes
node detects local link cost change
updates distance table (line 15)
if cost change in least cost path, notify neighbors (lines 23,24) X Z 1 4 50 Y
algorithm
terminates
“good
news
travels
fast”
Anyone see
a problem?
t0 : y detects link-cost change, updates its DV, informs its neighbors.
t1 : z receives update from y, updates its table, computes new least cost to x , sends its neighbors its DV.
t2 : y receives z’s update, updates its distance table. y’s least costs do not change, so y does not send a message to z.
Y sends direct to X and Z sends through Y
Would be better example if X-Z was 4 to start with and Z initially sent direct but when X=Y gets
Better will go that way instead
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24. Distance Vector: 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!
Initially Y sends direct to X and Z sends through Y to reach X
When X-Y goes from 4 to 60, Y decides to use path through Z instead (Y doesn’t know that
This path is back through it)
When Xy goes from 4 to 60, Y tells Z I have a new minumum path to X it is not 4 anymore it is 6
Z says ok I guess that my path of 4+1 = 5 isn’t as good anymore – now it is 6+1 = 7 but still that
Is better than my direct route of 50
Z tells Y my new low cost route to X is 7
Y says 7+1 = 8 is still better than 60 and back and forth they go there respective alternatives
Of 50 and 60 look good enough to use
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25. Distance Vector: poisoned reverse
If Z routes through Y to get to X :
Originally, Z tells Y its (Z’s) distance to X is infinite (so Y won’t route to X via Z)
In end, Y tells Z infinity
will this completely solve count to infinity problem? X Z 1 4 50 Y 60
algorithm
terminates
Steps above – link changes and Y sees it changes 4 to 60
Y Tells its neighbors of the change – so Z learns 60 and then Z updates its path to X via Y to be 61 and that swtiches its best path to 50
Z tells neighbors of the changes from 5 to 50
When Y hears thisit is better than the 60 choice and so switches to it (51) and tells neighbors
Split horizon – don’t advertise routes to neighbor if learned them from that neighbor (poison reverse is an active version; split horizon is passive)
Hold down timers are another approach: Cisco Semester if get bad news then set hold down timer – take good news and cancel timer – if news gets worse ignore until timer expires “If at any time before the hold-down timer expires an update is received from a different neighboring router with a poorer metric, the update is ignored. Ignoring an update with a poorer metric when a hold-down timer is in effect allows more time for the knowledge of a disruptive change to propagate through the entire network”
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26. Bigger Loops and Poison ReverseC B 7 8 1 2
D (A,D) E
c(E,D) + min {D (A,w)} D w =
= 5
Loop back through E! Poison reverse will fix this
D tells E infinity because D’s route to A through E
D (A,B) E
c(E,B) + min {D (A,w)} B w =
8+6 = 14 A E D C B 7 8 50 2 1
Loop back through E! Poison reverse will not fix this
B’s route to A is through E but B doesn’t know that
so does not tell E infinity
B’s route is through C so no poison reverse
E will try to send through B
B does not route through E to get to A so if will advertise its path to A through C even
if it was the best one
Crisper example would be better here
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27. Count to Infinity Example with Bigger LoopD C B 1 8 2
B will learn bad news
C will have told B infinity because its route to A is through B, so B won’t reroute through C
E however will have told B about a good route to A through D (cost 6)
B will choose that route instead and advertise it as the new best to C (cost 6+8 = 14); it will be worse than the old one it advertised to C (old cost = 1)
C will propagate this updated “best” route to D (cost 15)
D will propagate this new “best” route to E (cost 17)
E will update the “best” route to B (cost 19)
Last time it advertised cost 6 to B
It will loop around adding 13 each time (cost of loop)
Will continue until cost E advertises to B is bigger than 500 A E D C B
500 8 2 1
Cisco’s protocols fix this yes?
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28. Comparison of LS and DV algorithms
Message complexity
LS: nodes send info on directly connections to all other nodes
More, smaller messages
DV: nodes send info on best paths to all destinations to neighbors
Fewer, larger messages
Speed of Convergence
LS: O(n2) algorithm
DV: convergence time varies
may be routing loops
count-to-infinity problem
Robustness: what happens if router malfunctions?
LS:
node can advertise incorrect link cost
each node computes only its own table
DV:
DV node can advertise incorrect path cost
each node’s table used by others
error propagate thru network
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29. Oscillations Assume: Initially start with slightly unbalanced routes
Link cost = amount of carried traffic
Link cost is not symmetric
B and D sending 1 unit of traffic; C send e units of traffic
Initially start with slightly unbalanced routes
Everyone goes with least loaded, making them most loaded for next time, so everyone switches
Herding effect!
Can happen with any routing protocol that uses dynamic load info A A D C B
2+e
1+e 1 A A D C B
2+e e
1+e 1 1
1+e
Picture not that clear!
2+e D B D B e 1 C
1+e C 1 1 e
… B,C,D go
clockwise
Initially start with
almost equal routes
… B and C go
clockwise to A
… B, C and D go
counterclockwise
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30. Preventing Oscillations
Avoid link costs based on experienced load
But want to be able to route around heavily loaded links…
Avoid “herding” effect
Avoid all routers recomputing at the same time
Not enough to start them computing at a different time because will synchronize over time as send updates
Deliberately introduce randomization into time between when receive an update and when compute a new route
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31. Outtakes
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32. Distance Vector Algorithm: example
To start just know directly connected links…tell neighbors X Z 1 2 7 Y
X hears news from Y and Z
D (Z,Y) X
c(X,Y) + min {D (Z,w)} w =
2+1 = 3 Y
D (Y,Z) X
c(X,Z) + min {D (Y,w)} w =
7+1 = 8 Z
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33. Distance Vector Algorithm: example
In steady state, when have good news tell neighbor X Z 1 2 7 Y
4: Network Layer

34. In distance vector algorithms, the installation of a looping route slows down the convergence of the algorithm. Virtually all of the modifications that have been made to distance vector routing since 1969 (e.g., split horizon, poison reverse, etc., etc.) have the same goal, to reduce the number of looping routes that are installed, and hence to decrease the convergence time.
In link state algorithms, the convergence time is completely unaffected by the installation of looping routes. Hence you don't usually see loop- suppression techniques being combined with link state routing. While forwarding loops are possible during the transients, these are not regarded as much of a problem. It is possible to combine loop-suppression techniques with link state routing, it just has never been regarded as worth the trouble.
With either kind of routing algorithm, TTL is used as a loop detection procedure in order to catch the case where something goes wrong.
4: Network Layer

35. DUAL
Loop-free routing algorithm that performs a “diffused” computation of a routing table
Researched and developed at SRI International by Dr. J.J. Garcia-Luna-Aceves
No need for route hold down
Enhanced IGRP integrates the capabilities of link-state protocols into distance vector protocols
DUAL enables EIGRP routers to determine whether a path advertised by a neighbor is looped or loop-free, and allows a router running EIGRP to find alternate paths without waiting on updates from other routers
4: Network Layer

36. J. J. Garcia-Luna-Aceves
J.J. Garcia-Luna-Aceves. Loop-Free Routing Using Diffusing Computations. IEEE/ACM Trans. Networking, 1: , February 1993.
4: Network Layer