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Cooperative cost sensitive IP Routing
(Authors: Dean H.Lorenz Ariel Orda Danny Raz Yuval Shavitt)
Presenting : Vadim Drabkin
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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 perflow 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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Main Contributions
• 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 ) (N is a
number of nodes in the network)
• OSPF is (N ) worse than per flow routing
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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.
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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 : u, v, i1, i2, j  V 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 ai, i=1,…,n
elements with sizes s(ai) 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
n
B
 i1ai  B
(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 (N ) 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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IP-R vs RS-R1 and OSPF-R
IP-R
Network
congestion factor
is N
1
IP-R
throughput
is 1
1
1
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IP-R vs RS-R1 and OSPF-R
• RS-R1
1
RS-R1
Network congestion
factor is 1
RS-R1
throughput
is N
1
1
27
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IP-R vs RS-R1 and OSPF-R
• OSPF-R
1
OSPF-R
throughput
is N
OSPF-R
Network congestion
factor is 1
1
1
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Disadvantage 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
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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.
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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.
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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)
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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 sourcedestination 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 = i , j d i, j )
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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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