Adaptive Routing
Proshanto Mukherji
CSC 457: Computer Networks
University of Rochester
Introduction
 Networks are not static. They are subject to
three classes of change:



Topologies change as nodes are added and
removed
Traffic patterns change cyclically
Overall network load changes
 So, routing algorithms that assume that the network
is static don’t work in this setting
Rotten Algorithms 1: DV
50
A
C
“I can reach C with cost 10”
20
Host
Next
Cost
B
B
20
C
CB
50 30
10
B
Host
Next
Cost
A
A
20
C
C
10
Rotten Algorithms 2: LS
“I see B (cost 10), and A (cost 50)”
50
A
C
“I see C (cost 10), and A (cost 20)”
20
10
50
A
20
10
C
B
Host
Next
Cost
B
B
20
C
B
30
B
Analyses
 Distance Vector:


No. of messages:
O( |E|.diam )
Size of each message: O( n )
 Link State


Diameter of graph
Number of edges
Number of hosts
No. of messages:
O( n.|E| )
Size of each message: O( e )
Edges per host
 Each generates O( n.|E| ) = O( n3 ) bytes of traffic!
 Perhaps ok for single execution, but not every time the load on the network
changes
 When will you run the algorithm?
A New Model
 We want instead to think of the routing
protocol as always active
 Model the network as a dynamical system in
the topology and link costs
Q-Routing
 Qx(d, y) is the time that node x estimates it will take to
deliver a packet to node d via its neighbor y
 When y receives the packet, it sends back a message (to
node x), containing its (i.e. y’s) best estimate of the time
remaining to get the packet to d, i.e.
t = min(Qy(d, z)) over all z neighbors( y )
 x then updates Qx(d, y) by: RTT: x  y Time spent in queue at x


[Qx(d, y)]NEW = [Qx(d, y)]OLD + .(s+q+t - [Qx(d, y)]OLD )
new estimate
old estimate
Q-Routing (contd.)
message
message to d
y
x
Dest
Next Qx(d, y)
…
d
y
20 22
d
w
21
…
min(Qy(d, zi)) = 13;
RTT = s = 11
Qy(d, z1) = 25
Qy(d, z2) = 17
Qy(d, ze) = 70
w
[Qx(d, y)] += (0.25).[(11+17) - 20 ]
Q-Routing (contd.)
message to d
y
x
Dest
Next Qx(d, y)
…
d
y
22
d
w
21
…
message
w
Qw(d, z1)
Qw(d, z2)
Qw(d, ze)
Use this path next time
Ants
Ants Online: Routing Tables
 Each router x in the network maintains for each
destination node d a list of the form:
p = P(msg to d forwarded via y )
<d, <y1, p1>, <y2, p2>, …, <ye, pe>>,
where y1, y2, …, ye are the neighbors of x, and
p1 + p2 + …+ pe = 1
i
 This is a parallel (multi-path) routing scheme
 This also multiplies the number of degrees of
freedom the system has by a factor of |E|
i
Ants Online: Generation
Every destination host hd periodically generates
an “ant” to a random source host hs

An “ant” is a 3-tuple of the form:
< hd, hs, cost>

cost is a counter of the cost of the path the ant has covered
so far
Ants Online: Updation
When a router x receives an ant < hd, hs, cost>
from neighbor yi, it:
1.
2.
Updates cost by the cost of traversing the link
from x to yi (i.e. the cost of the link in reverse)
Updates entry for host (<hd, <y1, p1>, <y2, p2>, …, <ye, pe>>)
p = k / cost, for some k
pi = pi + p
1 + p
for j i, pj =
normalizing sum of probabilities to 1
pj
1 + p
Ants Online: Propagation (1)
 Two sub-species of ant:


Regular Ants:
P( ant sent to yi ) = pi
Uniform Ants:
P( ant sent to yi ) = 1 / e
 Regular ants use learned tables to route ants
 Uniform ants explore randomly
Ants Online: Propagation (2)
Regular Ants
Uniform Ants
Explore best paths very
Explore all paths equally
thoroughly; others hardly at all
Propagate “bad news”
extremely quickly, “good
news” extremely slowly
Propagate “good” and “bad”
news equally fast
Tends to find shortest paths
Natural parallel (multi-path)
routers
Does not converge to QRouting
Algorithm converges to QRouting in a static network
Q-Routing vs. Ants
 Q-Routing only changes its currently
selected route when the cost of that route
increases, not when the cost of an alternate
route decreases
 Q-Routing involves overhead linear in the
volume of traffic in the network; ants are
effectively free in moderate traffic
 Q-Routing cannot route messages by
parallel paths; uniform ants can
Summary




Routing algorithms that assume a static network
don’t work well in real-world networks, which are
dynamic
Adaptive routing algorithms avoid these
problems, at the cost of a linear increase in the
size of the routing tables
Q-Routing is a straightforward application of QLearning to the routing problem
Routing with ants is more flexible than Q-Routing
Finis
that’s all, folks