Seminar in Packet Networks
1
Cooperative cost sensitive IP Routing
(Authors: Dean H.Lorenz Ariel Orda Danny Raz Yuval Shavitt)
Presenting : Vadim Drabkin
Seminar in Packet Networks
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A Short Introduction to IP
Routing
•
Every host interface has it’s own IP address
•
5 address
classes(A,B,C,D(multicast),E(reserved)
•
Interior routing protocols
–
Distance

vector routing and RIP
–
Link state routing and OSPF
•
How does a host perform routing
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IP packet format
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IP packet format (cont.)
•
Header Length (because of the options field)
•
Total length includes header and data
•
Service Type
–
lets user identify his needs in terms of
bandwidth and delay (for example QoS)
•
Time to Leave prevents a packet from looping forever
•
Protocol, indicates the sending protocol
(TCP,UDP,IP…)
•
Source Address
•
Destination Address
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Unicast Routing
•
We need to know the
next hop
to reach a particular
network number (can be done with a routing table)
•
The routing table
is a simple database held by every
router. It tells the router how to forward packets
whose destination IP address is not equal to router IP
address.
•
Theoretically ,the routing table needs an entry for
every network in the Internet. Practically, most of the
networks are mapped into a single “
default
” entry.
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An Autonomous System (AS)
•
A
region of the Internet
that is under the
administrative control of a single entity and has a
single routing policy.
•
The routing problem is divided into :
–
Routing within a single AS (
intra domain
routing
)
–
Routing between AS (
inter domain routing
)
•
An AS can run whatever intra

domain routing
protocols it chooses
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Internet routing protocols
•
Interior routing protocols :
–
RIP (routing information protocol)
•
A distance vector algorithm
–
OSPF (open shortest path first)
•
A link state algorithm
–
IS

IS
–
a link state protocol and quite similar to OSPF
•
Exterior routing protocols
–
EGP
–
BGP (border gateway protocol), based on path vectors than
on distance vectors
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Distance Vector routing
•
A node tells its neighbors it’s best idea of distance to
every other node in the network
•
Node receives these distance vectors from it’s
neighbors
•
Node then updates its notion of the cost of the best
path to each destination, and the next hop for this
destination
•
A distributed implementation of the Bellman

Ford
algorithm
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Distance Vector routing (cont.)
•
RIP is simple for implementation but is
inadequate for larger and complex autonomous
systems because of the long convergence
following failures.
•
RIP is being replaced by OSPF (Open Shortest
Path First), which uses link

state rather then
distance

vector routing.
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Link

state routing
•
Each router creates a set of link

state packets (LSPs)
that describe it’s links
•
Each LSP is distributed to every router using a
controlled flooding algorithm.
•
Each router can independently compute optimal paths
to every destination.
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The advantages of link

state over
distance vector
•
Fast, loopless convergence
•
Can support routing according to different metrics
–
Each link is associated with a value for each metric
–
A routing table is computed for every metric
•
A Link

state protocol, the preferred choice for interior
routing
–
OSPF version 2 is defined in RFC

2328
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Introduction
•
In the traditional IP scheme both the packet
forwarding and routing protocols (RIP and OSPF) are
source invariant
i.e., their decisions depend solely on
the destination IP address
•
Recent protocols allow routing and forwarding
decisions to
depend on both the source and
destination addresses
•
The
benefit
of the per

flow forwarding is well
accepted as well as the practical complication of its
deployment
.
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Introduction (cont.)
•
In particular any solution that requires to consider
some
quadratic number of source

destination pairs
(rather than a linear number of destinations) is far
from being scalable.
•
This work
aims
at investigating the performance gap
between
source invariant
and
per

flow schemes
.
•
Facing the gap between the two basic schemes, in this
study
we propose a novel source invariant scheme
.
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Introduction (cont.)
•
The scheme exhibits a significantly improved
performance over the standard source invariant
scheme, and comes close to the performance of per

flow schemes.
•
At the same time it maintains the practical
advantage
of independence of source addresses
.
•
But it requires a
higher degree of centralization
.
•
However increased centralization is one of the
processes that can be observed in the evolution of the
Internet.
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•
We show that theoretically any routing algorithm
based on
static weights
can perform
as bad as
any source invariant scheme
•
We show that the gap in performance between IP
routing and OSPF may be as bad as (N is a
number of nodes in the network)
•
OSPF is worse than per flow routing
Main Contributions
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Main Contributions (cont.)
•
Thus, we present a family of centralized
algorithms that set forwarding tables in IP
networks, based on
dynamically changing
weights.
•
The centralized algorithm input is the
network
topology
and a
flow demand matrix
that based
on long term traffic statistics.
Seminar in Packet Networks
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Model and Problem Formulation
•
The network is defined as a graph G(V,E), V = n, E = m.
Each link has a capacity Ce,Ce>0. A demand matrix,
D={Di,j}, defines the demand Di,j, between each source i
and destination j.
•
We
define
the following
routing paradigms
:
•
Unrestricted Splitable Routing
(US

R)
–
a flow can be
split
among the outgoing links
arbitrarily
•
Restricted Splitable Routing
(RS

R)

a flow can be
split
over a predefined number
L
of outgoing links
•
RS

R1
–
a special case of RS

R, when L = 1, which is
known as the
unsplitable flow problem
.
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Model and Problem Formulation
(cont.)
•
A
routing assignment
is a function R:V^4

>[0..1],
such that Fu,v(i,j)
(i=source,j=destination)
is the
relative amount
of (i,j) flow that is routed from a
node
u
to neighbor
v
•
A routing is called
source invariant
if :
Fu,v(i1,j)=Fu,v(i2,j)= Fu,v(j)
(flow amount depends on destination j only)
•
Standard IP Forwarding Routing
(IP

R)
–
The
special case of source invariant RS

R1
, for each u
and j belongs to V, exists v and Fu,v(j) = 1
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Model and Problem Formulation
(cont.)
•
OSPF routing
(OSPF

R)
–
A class of source
invariant routing assignments that
split flow
evenly among next hops
.
•
We denote Ď =Ď(G,D,R) the allocation matrix that
results from the
application of the rule
(for
example max

min fairness) on network G,demand
matrix D and routing assignment R.
The
throughput of the matrix is the sum of its
components.
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Model and Problem Formulation
(cont.)
•
Link congestion factor
is the ratio between the
flow routed over the link and its capacity; the
network congestion factor
is the
largest
link
congestion factor.
•
For a network G,routing assignment R and
demand matrix D are said to be
feasible
if the
resulting congestion factor is
at most 1
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Optimization Problems
•
Problem Congestion Factor
–
Given a routing
paradigm, a network G(V,E) with link capacities
and a demand matrix D, find a routing assignment
R that
minimizes the network congestion factor
.
•
Problem Max Flow

Given a routing paradigm, a
network G(V,E) with link capacities and a demand
matrix D,
find a routing assignment R
such that
allocation matrix Ď(G,D,R) has
maximum
throughput.
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Hardness Results
•
Finding an optimal IP routing(Problem Congestion
factor with IP

R) is NP

hard
even for a single
destination
.
•
Theorem 1
: The decision optimal IP routing problem
is at least as hard as the
subset sum problem
. (The
subset problem is defined as follows: given a
i,
i=1,…,n
elements with sizes s(a
i
)
belongs to Z+ and a positive
integer B, find a subset of the elements whose size
sum equals to B.
)
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Hardness Results (cont.)
•
Proof: we build the
reduction from subset problem to IP
routing decision problem
•
Because subset sum problem is NP

hard , we conclude that
the decision optimal IP routing problem is NP

hard as well.
•
Every node
i
creates a flow
i
to destination
and the question is
how to route the flow
(to x or to y) to destination
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Theoretical Bounds
•
In this section we study the differences among the
routing paradigms by showing upper and lower
bounds on the worst case ratio between the
performance of these paradigms.
•
IP

R vs RS

R1 and OSPF

R
•
We show that IP

R can be than RS

R1 and
OSPF

R with respect to both optimization criteria.
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IP

R vs RS

R1 and OSPF

R
•
All link capacities are 1.
Every node creates a flow
1
to destination.
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1
1
1
IP

R
throughput
is 1
IP

R
Network
congestion factor
is N
IP

R vs RS

R1 and OSPF

R
Seminar in Packet Networks
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•
RS

R1
27
1
1
1
RS

R1
throughput
is N
RS

R1
Network congestion
factor is 1
IP

R vs RS

R1 and OSPF

R
Seminar in Packet Networks
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•
OSPF

R
1
1
1
OSPF

R
throughput
is N
OSPF

R
Network congestion
factor is 1
IP

R vs RS

R1 and OSPF

R
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Disa
dvantage of static weight
in routing
•
Sometimes
weight assignment cannot make
easier maximum flow problem
, because once
the link weights are determined ,the
routing is
insensitive to the load
already routed through
the link.
•
Now we will see the improved routing algorithm
Seminar in Packet Networks
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Algorithm
•
The aim of the algorithm to
improve the
performance of centrally controlled IP networks
.
•
We showed that
SPR
(Shortest path Routing) has such
a bad load ratio
because once the weights of the links
are determined,
the routing is insensitive to the load
already routed through a link.
•
Thus
we suggest a centralized algorithm
that is
given as input a
network graph
and a
flow demand
matrix
. The demand matrix is build from long term
gathered statistics about the flow through the network.
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Algorithm (cont.)
•
Working off

line enables the algorithm to
assign costs
to links dynamically
while the routing is performed,
and thus to achieve a
significant improvement over
other algorithms
.
The routing of each flow triggers
a cost increase along the links used for the routing
.
•
For links cost function the algorithm uses the
function
family
e

a(Ce
–
FLOWe)
which was found by Awerbuch
to have good performance for related problems.
Seminar in Packet Networks
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Algorithm (cont.)
•
The parameter
a
determine how sensitive is the
routing to the load on the link.
•
Question: What can u say about
a
=0 ?
•
Answer :For
a
=0, the routing is simply minimum
hop routing which is load insensitive.
•
For higher values of
a
the routing sensitivity
to the load increases with
a
.
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Algorithm (cont.)
•
If the routing is too sensitive
to the load, will prefer
routes
that are much longer
than the shortest path and the
total flow
in the network may
increase
.
•
Thus, we look for a
good trade

off between minimizing
the
maximum load
in the network and
minimizing the total flow.
•
Each flow is routed along the least cost route from the source to
the destination, with the
restriction
that if the new route
hits another route to the
same destination
, the algorithm must
continue along the
previous route
as we assume IP forwarding.
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Algorithm (cont.)
•
The
calculation
can be done using any
SPR
algorithm
(Bellman

Ford for example) (under the
above mentioned IP restriction)
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Algorithm performance
evaluation
•
The algorithm was tested under 3 heuristics :
–
rand
–
the flows are examined at some
random order
–
sort
–
the flows between each
source

destination pairs
are
cumulated, and then examined
in decreasing order
.
–
dest
–
the total flows to each destination are
cumulated
and
then the flows to the destinations
with more flows are
examine first
with sources weights used as the second sort
key.
Seminar in Packet Networks
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Algorithm performance
evaluation (cont.)
•
To test the algorithm were generated two types of random
networks ,and two type of random matrices.
•
Networks :
–
Inet
–
preferential attachment networks that are now widely
considered to represent the Internet structure.
–
Flat, Waxman
network which were largely in use in pastand may
represent better the internal structure of ASs.
•
For the flow demand matrix the
destination
nodes were
uniformly
selected among the network nodes and
source
nodes
were selected either
uniformly
or according to
ZIPf

like
distribution (the distribution was shown to model well the web
traffic at the Internet)
Seminar in Packet Networks
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Algorithm performance
evaluation (cont.)
•
The network links were assumed to have a unit
capacity
Ce = 1
, for every e that belongs to E.
•
The flows had infinite bandwidth requirements, and
thus each flow contributes a unit capacity to the
demand matrix. (
Di,j can be greater than 1
if more
than one flow is selected between the same source

destination pair).
•
The cost function
e

a(Ce
–
FLOWe)
was tested with
a
=B/D, B= 0,1,20,100,D ,where D is total flow
demand (D = )
Seminar in Packet Networks
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Algorithm performance
evaluation (cont.)
•
Note that when
B=a=0
all the link costs are uniformly one
and the algorithm performs
minimum hop routing
.
•
Figures 5

8 show the
load of the most congested link
for
200,2000,20000 flows and 10 combinations of the 3
heuristics and B values.
•
All the bars in the graphs represent an average of 25
executions that are the result of applying 5 random demand
matrices on 5 random network topologies
•
When a mild dependency on the link load is used (
B = 20
or B =1
) the load on the
most congested link decreases
significantly.
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Load on most congested link (Inet,Zipf)
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Load on most congested link (Inet,Unif)
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Load on most congested link (Flat,Zipf)
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Load on most congested link (Flat,Unif)
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Algorithm performance
evaluation (cont.)
•
Figures 9

12 show that Only when
B=D there was a
significant increase in the traffic in the network
.
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Total Flow in the network (Inet,Zipf)
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Total Flow in the network (Inet,Unif)
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Total Flow in the network (Flat,Zipf)
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Total Flow in the network (Inet,Zipf)
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Conclusions
•
The differences between the heuristics for the order at which the
flows are examined by the algorithm are not big. The
random
order was the best policy
.
•
Thus we can conclude that exponential dynamic link
cost functions increase significantly the network
performance
•
B = D is the optimal
, because it simultaneously significantly
increases the traffic
in the network and
decreases the load on
most congested link.
•
For high demand (20000 flows) the decrease is greater
than 65% for Inet networks , up to 43% for Waxman
networks.
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