Topology Pp t

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Network Topology

ELEG 667-013 Spring 2003


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Outline:

Why Network Topology is Important ?

Modeling Internet Topology

Complex Networks

Scale-free Networks Power-laws of the Web

Search in power-law networks: GNUTELLA, a P2P

example.


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Design Efficient Protocols

Solve Internetworking Problems:

- routing

- resource reservation

- administration

Create Accurate Model for Simulation

Derive Estimates for Topological Parameters

Study Fault Tolerance and Anti-Attack Properties

Why Topology is Important ?


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Modeling Internet Topology [1]:

Graph representation

Router-level modeling

- vertices are routers

-edges are one-hop IP connectivity

Domain- (AS-) level model (high degree of abstraction)

- vertices are domains (ASes)

- edges are peering relationships

Nodes can be assigned numbers rep. e.g. buffer

capacity

Edges migth have weights rep. e.g.prop. delay,

bandwidth capacity.


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Modeling Internet Topology [1]:

access networks

hosts/endsystems

routers

domains/autonomous systemsexchange point

stub domains

transit domains

border routerspeering

lowly worm


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Barabasi Albert Model (BA Model):

Basis for most current topology generators Very simplistic modelNetwork evolves in size over time.Preferential Connectivity

Probability that a newly added node will attach to node i

Many extensions.

jj

ii

k

kk

)(


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Waxman Model:

Router level model Nodes placed at random in 2D

space with dimension L

Probability of edge (u,v):

a*e(-d / (bL) )

, where d isEuclidean distance (u,v), a and

b are constants

Models locality

- no sense of backbone or hierarchy

-does not guarantee connected

network

- as #nodes the #links

proportionally

v

ud(u,v)


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Transit-Stub Model:

Router level model

Transit domains

placed in 2D space

populated with routers connected to each other

Stub domains

placed in 2D space

populated with routers

connected to transit domains

Models hierarchy

Edge count, guaranteed connectivity


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Transit-Stub Model:

No concept of a host all nodes are routers. Two level hierarchy First generate a number of transit domains,then generate a set of stub networks.

Given average edge-count, produce arandom graph, making sure that it isconnected.


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Inet:

Generate degree sequence

Build spanning tree over nodeswith degree larger than 1, using

preferential connectivity randomly select node u not in

tree

join u to existing node v with

probability d(v)/

d(w)Connect degree 1 nodes usingpreferential connectivity

Add remaining edges using

preferential connectivity


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BRITE:

Generate small backbone, withnodes placed:

randomly or

concentrated (skewed)

Add nodes one at a time(incremental growth)

New node has constant # ofedges connected using:

preferential connectivityand/or

locality


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Complex Networks:

Two limiting-case topologies have been extensively considered inthe literature [4],[5].:

regular network(lattice), the chosen topology of innumerable

physical models such as the Ising model or percolation.

random graph,studied in mathematics and used both innatural and social sciences. Properties studied in detail by Pal

Erdos.

Most of Erdos work concentrated on the case in which the

number of vertices is kept constant but the total number of linksbetween vertices increases: the Erds-Rnyi result states that for

many important quantities there is a percolation-like transition at

a specific value of the average number of links per vertex.


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Complex Networks:

random networks are used in:

Physics: in studies of dynamical problems, spin

models and thermodynamics, random walks, and

quantum chaos.

Economics and social sciences: to model interacting

agents.


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In contrast to these two limiting topologies, empirical

evidence suggests that many biological, technological orsocial networks appear to be somewhere in between these

extremes.

many real networks seem to share with regular

networks the concept of neighborhood, which means that

if vertices i andj are neighbors then they will have many

common neighbors --- which is obviously not true for a

random network.

On the other hand, studies on epidemics show that it

can take only a few ``steps'' on the network to reach agiven vertex from any other vertex. This is the foremost

property of random networks, which is not fulfilled by

regular networks.

Complex Networks:


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Complex Networks:


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Complex Networks:

The Watts-Strogatz model [5]. :

To bridge the two limiting cases, Watts and Strogatz

[Nature 393, 440 (1998)] have introduced a new type of

network which is obtained by randomizing a fractionp ofthe links of the regular network.

Initial structure (p=0) is the one-dimensional regular

network where each vertex is connected to itsznearest

neighbors.

For0 < p < 1, we denote these networks disordered. for the casep=1, we have a completely random

network.


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Watts and Strogatz report that for a small value of the

parameterp, there is an onset ofsmall-world behavior.

It is characterized by the fact that the distance between

any two vertices is of the order of that for a random

network and, at the same time, the concept ofneighborhood is preserved.

The effect of a change inp is extremely nonlinear,

where a very small change in the connectivity of the

network leads to a dramatic change in the distance

between different pairs of vertices.

Complex Networks:


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The scientific question we are trying to answer is: Does

the onset of the small-world behavior occurs at a given value

ofp or does it occur for a value of the system size n which

depends onp?

To investigate this question, we need to look at the

behavior of the system as a function ofp for different values

ofn.

Complex Networks:


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Complex Networks:


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Complex Networks:

The appearance of the small-world behavior is not a phase-

transition but a crossover phenomena.

The average distance lis:

l (n,p) ~ n* F ( n / n* )

where:F(u > 1) ~ln u, and n* is a function ofp.

When the average number of rewired links,pnz/2, is much less

than one, the network should be in the large-world regime. On theother hand, whenpnz/2 >> 1, the network should be a small-world.


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Scale-free networks:

It was proposed by Barabsi and Albert that real-world

networks in general arescale-free networks.

Scale-free networks have a distribution of connectivities that

decays with a power-law tail.

Scale-free networks emerge in the context of a growingnetwork in which new vertices connect preferentially to the

more highly connected vertices in the network. Scale free

networks are also small-world networks because (i) they have

clustering coefficients much larger than random networks, and(ii) their diameter increases logarithmically with the number of

vertices n.


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What are Power Laws ?

kkP )( Distribution that fits :

Characteristic property of Scale free networks

Occur very often in Complex Systems literature.

Many complicated real world networks obey power laws


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Implications of Power Laws:

Majority of nodes have small connectivity.

Few nodes have very large connectivity.

Good resistance to random failure.

Small resistance to planned attack.

Could imply existence of some hierarchy (all real worldpower law networks support this).

However, it is not clear whether

Power Law Hierarchy


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Power laws are an observed (empirical) phenomenon.

The mechanisms that produce these can only beguessed at (for now!)

Very typical in self organizing systems and chaoticsystems.

Origin of Power Law:


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(a) the neuronal network of the worm C. elegans.

(b) world-wide web.(c) the network of citations of scientific papers.



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broad-scale networks: or truncated scale-free networks,

characterized by a connectivity distribution that has a power-law regime followed by a sharp cut-off, like an exponential or

Gaussian decay of the tail.

single-scale networks: characterized by a connectivity

distribution with a fast decaying tail, such as exponential orGaussian


Aging of the vertices: The vertex is still part of the network

and contributing to network statistics, but it no longer receives

links. The aging of the vertices thus limits the preferential

attachment preventing a scale-free distribution of connectivities.

Cost of adding links to the vertices or the limited capacity of

a vertex: physical costs of adding links and limited capacity of a

vertex will limit the number of possible links attaching to a

given vertex.


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Power-laws of the Web [2].:

How many links on a page (outdegree)?

How many links to a page (indegree)?

Probability that a random page has kother pages

pointing to it is ~k-2.1

(Power law)

Probability that a random page points to kother pages is~k

-2.7(Power law)


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In-degree Distribution


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Out-degree Distribution


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Search in power-law networks: GNUTELLA [3].

Most of the P2P networks display a power-law

distribution in their node degree. This distributionreflects the existence of a few nodes with very high

degree and many with low degree.

In P2P networks, the name of the target file may be

known, but due to the networks ad hoc nature, the nodeholding the file may not be known until a real-time

search is performed.

A simple strategy to locate files, implemented by

NAPSTER, is to use a central server that contains an

index of all the files every node is sharing as they join

the network.

GNUTELLA and FREENET do not use a central

server.


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GNUTELLA is a peer-to-peer file-sharing system that treats

all client nodes as functionally equivalent and lacks a centralserver that can store file location information. This is advantageous

because it presents no central point of failure.

The obvious disadvantage is that the location of files is unknown.

When a user wants to download a file, he sends a query toall the nodes within a neighborhood of size ttl, the time to

live assigned to the query. Every node passes on the query to

all of its neighbors and decrements the ttl by one. In this

way, all nodes within a given radius of the requesting node

will be queried for the file, and those who have matching

files will send back positive answers.


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This broadcast method will find the target file quickly,

given that it is located within a radius of ttl. However, broadcasting

is extremely costly in terms of bandwidth.

Such a search strategy does not scale well. As query traffic

increases linearly with the size of GNUTELLA graph, nodes

become overloaded.


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Typically, a GNUTELLA client wishing to join the networkmust find the IP address of an initial node to connect to.

Currently, ad hoclists of good GNUTELLA clients exist.

It is reasonable to suppose that this ad hocmethod of

growth would bias new nodes to connect preferentially tonodes that are already fairly well connected, since these

nodes are more likely to be well known.

Based on models of graph growthwhere the rich get richer,

the power-law connectivity of ad hocpeer-to-peer networks may

be a fairly general topological feature.



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By passing the query to every single node in the network,the GNUTELLA algorithm fails to take advantage of the

connectivity distribution [3].

To take advantage of the power-law distribution, we can modify

each node to keep lists of files stored in first and second neighbor. Instead of passing the query to every node, now we can pass it

only to the nodes with highest connectivity.

High degree nodes are presumably high bandwidth node that can

handle the query traffic.


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Outline:

Internet Structure&Organization

Internet Hierarchical Structure ISPs, interconnection and organization [ref. 7].

POP Architecture and Load Balancing

ISP Architecture [ref. 7]. in detail

Topology Mapping Tool: Rocketfuel[ref. 8] Discussion

ELEG 667-013 Spring 2003


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Basic Internet Architecture


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Basic Architecture: NAPs and nationalISPs

The Internet has a hierarchical structure.

At the highest level are large national InternetService Providers that interconnect through Network

Access Points (NAPs).There are about a dozen NAPs in the U.S., run bycommon carriers such as Sprint and Ameritech, andmany more around the world.

Regional ISPs interconnect with national ISPs whichprovide services to local ISPs who, in turn, sell accessto individuals.


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Basic Architecture: MAEs and local ISPs

As the number of ISPs has grown, a new type ofnetwork access point, called a metropolitan areaexchange (MAE) has arisen.

There are about 50 such MAE around the U.S. today.Sometimes large regional and local ISPs also haveaccess directly to NAPs.


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Internet Packet Exchange Charges

ISP at the same level usually do not charge eachother for exchanging messages.

This is called peering.

Higher level ISPs, however, charge lower level ones(national ISPs charge regional ISPs which in turncharge local ISPs) for carrying Internet traffic.

Local ISPs, of course, charge individuals and

corporate users for access.


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Connecting to an ISP

ISPs provide access to the Internet through a Pointof Presence (POP).

Individual users access the POP through a dial-up

line using the PPP protocol.The call connects the user to the ISPs modem pool,after which a remote access server (RAS) checks theuserid and password.

Once logged in, the user can send TCP/IP/[PPP]

packets over the telephone line which are then sentout over the Internet through the ISPs POP.


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Connecting to an ISP (contd.)

Corporate users might access the POP using a T-1, T-3

or ATM OC-3 connections provided by a common carrier.

T-1 and T-3 lines connect to the ISP POPs CSU/DSUdevice. ChannelServiceUnit/DataServiceUnit.

The CSU is a device that connects a terminal to a digital

line. The DSU is a device that performs protective anddiagnostic functions for a telecommunications line. .Typically, the two devices are packaged as a single unit.

You can think of it as a very high-powered and expensivemodem. Such a device is required for both ends of a T-1 orT-3 connection, and the units at both ends must be set tothe same communications standard.
http://www.webopedia.com/TERM/C/modem.htmlhttp://www.webopedia.com/TERM/C/T_1_carrier.htmlhttp://www.webopedia.com/TERM/C/T_3_carrier.htmlhttp://www.webopedia.com/TERM/C/T_3_carrier.htmlhttp://www.webopedia.com/TERM/C/T_3_carrier.htmlhttp://www.webopedia.com/TERM/C/T_3_carrier.htmlhttp://www.webopedia.com/TERM/C/T_1_carrier.htmlhttp://www.webopedia.com/TERM/C/T_1_carrier.htmlhttp://www.webopedia.com/TERM/C/T_1_carrier.htmlhttp://www.webopedia.com/TERM/C/modem.html


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ISP Point-of Presence

Modem Pool

IndividualDial-up Customers

CorporateT1 Customer

T1 CSU/DSU

CorporateT3 Customer

T3 CSU/DSU

CorporateOC-3 Customer

ATM Switch

Layer-2Switch

ISP POP

ISP POP

ISP POP

NAP/MAE

RemoteAccessServer

ATMSwitch

Inside an ISP Point of Presence


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Internet Organization

NAP

NAP

NAP

BSP

ISP

ISP

ISP = Internet Service Provider

BSP = Backbone Service Provider

NAP = Network Access Point

POP = Point of Presence

CN = Customer Network

POP

POP

POP

ISPPOP

BSP

BSPPOP

POP

CN

CN

CN

CNCN

CN

CN

CN

POP


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Customer Network

Clients

Servers

LAN

WAN

Ethernet10 Mb/s

T1 Link

1.54 Mb/s

Router


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NAP Architecture

ISPBackboneOperator

ISP ISP

BackboneOperator

BackboneOperator

ISP NAP

Routers

Routers

High-Speed LAN (FDDI, ATM, GigE)RouteServer


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Internet structure: network of networks

roughly hierarchicalat center: tier-1 ISPs (e.g., UUNet, BBN/Genuity, Sprint,AT&T), national/international coverage

treat each other as equals

Tier 1 ISP

Tier 1 ISP

Tier 1 ISP

Tier-1providersinterconnect

(peer)privately

NAP

Tier-1 providersalso interconnectat public networkaccess points(NAPs)


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Tier-1 ISP: e.g., Sprint

Sprint US backbone network


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Tier-1 IP backbone

POP

Point-of-Presence (POP) : A collection of routers andswitches housed in a single location

The backbone is a set of POPs (usually one per city)


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Tier-2 ISPs: smaller (often regional) ISPs Connect to one or more tier-1 ISPs, possibly other tier-2 ISPs

Tier 1 ISP

Tier 1 ISP

Tier 1 ISP

NAP

Tier-2 ISPTier-2 ISP

Tier-2 ISP Tier-2 ISP

Tier-2 ISP

Tier-2 ISP paystier-1 ISP forconnectivity torest of Internet tier-2 ISP is

customeroftier-1 provider

Tier-2 ISPsalso peerprivately witheach other,interconnectat NAP


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Tier-3 ISPs and local ISPs last hop (access) network (closest to end systems)

Tier 1 ISP

Tier 1 ISP

Tier 1 ISP

NAP



Tier-2 ISP

local

ISP

local

ISP

local

ISP

localISP

localISP Tier 3

ISP

local

ISP

local

ISP

localISP

Local and tier-3 ISPs arecustomersofhigher tierISPs

connectingthem to restof Internet

I t t t t t k f


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Internet structure: network ofnetworks

a packet passes through many networks!

Tier 1 ISP

Tier 1 ISP

Tier 1 ISP

NAP



Tier-2 ISP

local

ISP

local

ISP

local

ISP

localISP

localISP Tier 3

ISP

local

ISP

local

ISP

localISP


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Architecture of a POP

Backbone

Router

Backbone links

Peering

Access

Router

Access

Router

Access

Router

ISPs Corporate

networks

Web Servers Dial-up

Access

Router

Backbone

Router


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ISP Architecture

Access Network Architecture

Dial-up

ISDN

DSL

Dedicated Leased lines

Frame Relay Service


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Dial-up Access Network

Modem Circuit

Switch

Internet Backbone

Modem Pool

Router

Central Office

ISP POP

Web Cache


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ISDN

ISDN service access linksterminate at the ISP POP

Digital signal. Due to signal

strength limitations, ISDNsubscribers must be within 18000feet of the CO

At the customers end, an ISDN

adapter card is required.


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DSL

Modem Circuit

Switch

Internet Backbone

Modem Pool

Router

Central Office

ISP POP

Web Cache

DSLAM


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DSL Access

DSL typically provisioned at 1.5Mbpsfrom ISP to customer and at 128kbs inthe reverse direction.

DSL Access Multiplexer (DSLAM) at COterminates DSL signals from hundredsof customers.

The IP data is multiplexed into a single

ATM connection by DSLAM andforwarded to the ISP POP


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Dedicated Access

Leased lines from 56Kbs to155Mbps.

No multiplexing of othercustomers traffic. Can lead tohigher operational cost.

Lines terminate at routers in the

POP.


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Frame Relay Service

Network resembles a star topology, withone leg of the star connected to ISP andother legs connected to different

customers.

Frame RelayNetwork

Router

Router

Router

ISP

Router

ISP Architecture: The Backbone


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ISP Architecture: The Backbone

The backbone of a large ISP is typically a WAN spread out across a large

geographic area.

Backbone routers connect the individual links composing the backbone .

ISP Backbone

Backbone router

ISP Architecture: Backbone Nodes


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ISP Architecture: Backbone Nodes

ISP Backbone

Backbone Node

For reasons of robustness and load management, multiple backbone routers

can be located in the same geographic location and connected via a LAN.

We consider all of the backbone routers and the connecting LAN to be

a backbone node.

These backbone nodes, whether they contain one or more routers, will serve

as the points of connection from the outside world to the backbone.

Backbone Node


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ISP Architecture: Access Routers

Dial-in POP(Downstream)

ISP Backbone

Access Router

Customers such

as smaller ISPsand enterprises

(Downstream)

Customers, including smaller ISPs, enterprise, are connected to backbone nodes

via access routers. Access routers gain their connectivity to the backbone,

because they are on the same LAN as one or more backbone routers.

Remember, the backbone nodes contain backbone routers, as well as these access

routers.

Any backbone entry point is known as apoint of presence (POP). Modem entry

points are known as dial-in POPs ordial-in hubs. Entry points for other types of

networks are known as broadband POPs.

ISP Architecture: In Practice


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ISP Architecture: In Practice

Large dial-in POP(Downstream)

ISP Backbone

Access Router

In practice, only the largest customers connect directly to access routers. Other

customers are aggregated at broadband points of presence (broadband POPs).These are basically LANs. The customers connect to routers on these LANs, and

then these LANs connect to the access nodes

Additionally, some very large dial-in POPs do connect directly to backbone routers.

These typically service very large corporate offices.

Broadband POP

BackboneRouter

ISP A hit t G t


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ISP Architecture: Gateways

Peer ISP

ISP Backbone

Gateway Router

Upstream ISP

Gateway routers, which are also connected via LANs to backbone routers,

connect ISPs to each other. The router is known as a gateway router, if it connects

a peer or upstream ISP.

Downstream ISPs generally connect via an access router, or directly to a backboneRouter.

So, a gateway router leads to a peer or upstream provider, whereas an access router leads to

a downstream network.

M i ISP T l i ith R k tf l[8]


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Measuring ISP Topologies with Rocketfuel[8]:

Rocketfule internet topology mapping engine

The goal is to obtain realistic, router-level maps of ISP networks.

Important influence on:

- The dynamics of routing protocols

- The scalability of multicast- The efficacy of proposals for denial-of-service tracing andresponse- Other aspects of protocol performance (Internet pathselection)

Real topologies are not publicly available- Confidential


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Mapping techniques

Three categories of mapping techniques:

Selecting Measurements

Directed probing

Path reduction

Alias Resolution

IP identifier

Router identification and Annotation


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Selecting Measurements

Directed probing

To employ BGP tables to identify relevant

traceroutes and prune the remainderPath reduction

To identify redundant traceroutes

Only one traceroutes needs to be taken whentwo traceroutes enter and leave the ISPnetwork at the same point


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Alias resolution

Mercator method

Sending traceroute-like probe(to a high-

numbered UDP port but with a TTL of 255)directly to the potentially aliased IPaddress

Requirement: routers need to be configured to

send the UDP port unreachable responsewith the address of the outgoing interface asthe source address: Two aliases shouldrespond with the same source


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Alias method

Proposed methods by Spring etc.

Mercators IP address-based method Comparing IP identifier field of the

responses


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IP identifier hints

IP identifier helps to identify a packetfor reassembly after fragmentation

IP identifier is commonly implementedusing a counter that is incrementedafter sending a packet

Ali l ti b IP id tifi


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Alias resolution by IP identifierProcess of alias resolution by IP identifier:

Ally, a tool for alias resolution, sends aprobe packet to the two potential aliases

Port unreachable responses, including the IP

identifiers x and yAlly sends a third packet to the address that

responded first

Router Identification &


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Router Identification &Annotation

Using DNS to determine routers ownedby mapped ISP, their geographical

location and role in the topology


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Mapping engine: RocketfuelRocketfuel includes modules:

BGP table from RouteViews Egress discovery: To find egress routers

Tasklist generation: To generate a list of directed probes

Path reductions: To apply ingress and next-hop ASreductions, and generate jobs for execution

Public traceroute servers Alias resolution: Using IP identifier technique to resolve

alias problem

Database


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References:

[1] Kenneth Calvert, Matthew Doar, Ellen Zegura, Modeling Internet

Topology.

[2]. Michalis Faloudsos, Petros Faloudsos, Christos Faloudsos, On

Power-law Relationships of the Internet Topology

[3]. Lada A. Adamic,1, Rajan M. Lukose,1, Amit R. Puniyani,2, and

Bernardo A. Huberman1, Search in power-law networks.[4]. L. A. N. Amaral, A. Scala, M. Barthlmy, & H. E. Stanley, 1997,

Classes of small-world networks.

http://polymer.bu.edu/~amaral/Content_network.html

[5]. Ellen Zegura, Kenneth Calvert, How to model an Internetwork

[6]. Stefan Bornholdt, Holger Ebel, World Wide Web scaling exponentfrom Simons 1955 model

[7]. S. Halabi and D. McPherson,Internet Routing Architectures, 2nd

ed., Cisco Press, Indianapolis, 2000.

[8]. Neil Spring Ratul Mahajan David Wetherall, Measuring ISP

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