ELEG 667-013 Spring 2003


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.

• 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

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.

Modeling Internet Topology [1]: domains/autonomous systems transit domains exchange point border routers peering hosts/endsystems routers stub domains lowly worm access networks

Barabasi Albert Model (BA Model):
 Basis for most current topology generators
 Very simplistic model
 Network evolves in size over time.
 Preferential Connectivity
 Probability that a newly added node will attach to node ‘i’

( k i
)

 k i j k j
 Many extensions.

Waxman Model:

Router level model

Nodes placed at random in 2D space with dimension L

Probability of edge (u,v):
(-d / (bL) )
, where d is
Euclidean 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 u d(u,v) v

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

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 a random graph, making sure that it is connected.

Inet:
Generate degree sequence
Build spanning tree over nodes with 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 using preferential connectivity
Add remaining edges using preferential connectivity

BRITE:
Generate small backbone, with nodes placed:

 randomly or concentrated (skewed)
Add nodes one at a time
(incremental growth)
New node has constant # of edges connected using:

 preferential connectivity and/or locality

Complex Networks:

Two limiting-case topologies have been extensively considered in the 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 in natural 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 links between vertices increases: the Erdös-Rényi 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.

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.

Complex Networks:

In contrast to these two limiting topologies, empirical evidence suggests that many biological, technological or social 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 and j 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 a given vertex from any other vertex. This is the foremost property of random networks, which is not fulfilled by regular networks.

Complex Networks:

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 fraction p of the links of the regular network.

Initial structure ( p=0 ) is the one-dimensional regular network where each vertex is connected to its z nearest neighbors.
 For 0 < p < 1 , we denote these networks disordered.
 for the case p=1 , we have a completely random network.

Complex Networks:
 Watts and Strogatz report that for a small value of the parameter p , there is an onset of
“small-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 of neighborhood is preserved.

The effect of a change in p 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:

The scientific question we are trying to answer is: Does the onset of the small-world behavior occurs at a given value of p or does it occur for a value of the system size n which depends on p ?
 To investigate this question, we need to look at the behavior of the system as a function of p for different values of n .

Complex Networks:

Complex Networks:

The appearance of the small-world behavior is not a phasetransition but a crossover phenomena.

The average distance l is: l (n,p) ~ n * F ( n / n * ) where:
F(u << 1) ~ u , and F(u >> 1) ~ ln u , and n * is a function of p .

When the average number of rewired links, pnz/2 , is much less than one, the network should be in the large-world regime. On the other hand, when pnz/2 >> 1 , the network should be a small-world.

Scale-free networks:
 It was proposed by Barabási and Albert that real-world networks in general are scale-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 growing network 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 .

What are Power Laws ?
 Distribution that fits :
P ( k )
 k
 
 Characteristic property of “Scale free networks”

Occur very often in Complex Systems literature.

Many complicated real world networks obey power laws

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 world power law networks support this).

However, it is not clear whether
Power Law

Hierarchy

Origin of Power Law:
 Power laws are an observed (empirical) phenomenon.
 The mechanisms that produce these can only be guessed at (for now!)
 Very typical in self organizing systems and chaotic systems.

Scale-free networks:

Scale-free networks:
(a) the neuronal network of the worm C. elegans.
(b) world-wide web.
(c) the network of citations of scientific papers.

Scale-free networks:
 broad-scale networks: or truncated scale-free networks, characterized by a connectivity distribution that has a powerlaw 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 or
Gaussian

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.

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 k other pages
-2.1
pointing to it is ~k (Power law)
• Probability that a random page points to k other pages is
-2.7
~k (Power law)

Search in power-law networks: GNUTELLA [3].

Most of the P2P networks display a power-law distribution in their node degree. This distribution reflects 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 network’s ad hoc nature, the node holding 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.

Search in power-law networks: GNUTELLA [3].
 GNUTELLA is a peer-to-peer file-sharing system that treats all client nodes as functionally equivalent and lacks a central server 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 to all 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.

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

Search in power-law networks: GNUTELLA [3].

Typically, a GNUTELLA client wishing to join the network must find the IP address of an initial node to connect to.
Currently, ad hoc lists of ‘‘good’’ GNUTELLA clients exist.

It is reasonable to suppose that this ad hoc method of growth would bias new nodes to connect preferentially to nodes that are already fairly well connected, since these nodes are more likely to be ‘‘well known.’’

Based on models of graph growth where the ‘‘rich get richer,’’ the power-law connectivity of ad hoc peer-to-peer networks may be a fairly general topological feature.

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


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

The Internet has a hierarchical structure.
At the highest level are large national Internet
Service Providers that interconnect through Network
Access Points (NAPs).
There are about a dozen NAPs in the U.S., run by common carriers such as Sprint and Ameritech, and many more around the world.
Regional ISPs interconnect with national ISPs which provide services to local ISPs who, in turn, sell access to individuals.

As the number of ISPs has grown, a new type of network access point, called a metropolitan area exchange (MAE) has arisen.
There are about 50 such MAE around the U.S. today.
Sometimes large regional and local ISPs also have access directly to NAPs.

ISP at the same level usually do not charge each other for exchanging messages.
This is called peering.
Higher level ISPs, however, charge lower level ones
(national ISPs charge regional ISPs which in turn charge local ISPs) for carrying Internet traffic.
Local ISPs, of course, charge individuals and corporate users for access.

ISPs provide access to the Internet through a Point of
Presence (POP).
Individual users access the POP through a dial-up line using the PPP protocol.
The call connects the user to the ISP’s modem pool, after which a remote access server (RAS) checks the userid and password.
Once logged in, the user can send TCP/IP/[PPP] packets over the telephone line which are then sent out over the Internet through the ISP’s POP.

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 POP’s CSU/DSU device. Channel Service Unit/Data Service Unit.
The CSU is a device that connects a terminal to a digital line. The DSU is a device that performs protective and diagnostic 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 expensive modem . Such a device is required for both ends of a T-1 or
T-3 connection, and the units at both ends must be set to the same communications standard.

Individual
Dial-up Customers
ISP Point-of Presence
Modem Pool
ISP POP
ISP POP
Corporate
T1 Customer
Corporate
T3 Customer
T1 CSU/DSU
T3 CSU/DSU
Layer-2
Switch
ATM
Switch
ISP POP
Corporate
OC-3 Customer
Remote
Access
Server
ATM Switch
NAP/MAE

CN
POP ISP
CN
CN
CN
POP BSP POP
CN
CN
NAP
POP
ISP
POP BSP
POP
CN
BSP
NAP
ISP POP
NAP
CN
ISP = Internet Service Provider
BSP = Backbone Service Provider
NAP = Network Access Point
POP = Point of Presence
CN = Customer Network

Clients
LAN
Servers
Ethernet
10 Mb/s
Router
WAN
T1 Link
1.54 Mb/s

ISP ISP ISP
Backbone
Operator
Route
Server
Routers
High-Speed LAN (FDDI, ATM, GigE)
Routers
Backbone
Operator
ISP
Backbone
Operator
NAP

Internet structure: network of networks roughly hierarchical at center: “tier-1” ISPs (e.g., UUNet, BBN/Genuity, Sprint,
AT&T), national/international coverage
 treat each other as equals
Tier-1 providers interconnect
(peer) privately
Tier 1 ISP
Tier 1 ISP
NAP
Tier 1 ISP
Tier-1 providers also interconnect at public network access points
(NAPs)

Sprint US backbone network

POP
The backbone is a set of POPs (usually one per city)
Point-of-Presence (POP)
:
A collection of routers and switches housed in a single location

“Tier-2” ISPs: smaller (often regional) ISPs

Connect to one or more tier-1 ISPs, possibly other tier-2 ISPs
Tier-2 ISP pays tier-1 ISP for connectivity to rest of Internet
 tier-2 ISP is customer of tier-1 provider
Tier-2 ISP
Tier 1 ISP
Tier 1 ISP
Tier-2 ISP
Tier-2 ISP
Tier-2 ISP
NAP
Tier 1 ISP
Tier-2 ISPs also peer privately with each other, interconnect at NAP
Tier-2 ISP

“Tier-3” ISPs and local ISPs
 last hop (“access”) network (closest to end systems)
Local and tier-
3 ISPs are
customers of higher tier
ISPs connecting them to rest of Internet local
ISP Tier 3
ISP
Tier-2 ISP
Tier 1 ISP local
ISP
Tier-2 ISP local
ISP local
ISP
Tier 1 ISP local
ISP
Tier-2 ISP local
ISP
NAP
Tier 1 ISP
Tier-2 ISP local
ISP
Tier-2 ISP local
ISP

a packet passes through many networks!
local
ISP Tier 3
ISP
Tier-2 ISP local
ISP
Tier 1 ISP local
ISP
Tier-2 ISP local
ISP
NAP
Tier 1 ISP local
ISP
Tier-2 ISP local
ISP
Tier 1 ISP
Tier-2 ISP local
ISP
Tier-2 ISP local
ISP

Backbone links
Access
Router
ISPs
Backbone
Router
Backbone
Router
Peering
Access
Router
Corporate networks
Access
Router
Web Servers
Access
Router
Dial-up

Access Network Architecture



Dial-up
ISDN
DSL


Dedicated Leased lines
Frame Relay Service

Central Office
Modem Circuit
Switch
ISP POP
Modem Pool
Web Cache
Router
Internet Backbone

ISDN service access links terminate at the ISP POP
Digital signal. Due to signal strength limitations, ISDN subscribers must be within 18000 feet of the CO
At the customers end, an ISDN adapter card is required.

Central Office
Modem DSLAM Circuit
Switch
ISP POP
Modem Pool
Web Cache
Router
Internet Backbone

DSL typically provisioned at 1.5Mbps from ISP to customer and at 128kbs in the reverse direction.
DSL Access Multiplexer (DSLAM) at CO terminates DSL signals from hundreds of customers.
The IP data is multiplexed into a single
ATM connection by DSLAM and forwarded to the ISP POP

Leased lines from 56Kbs to
155Mbps.
No multiplexing of other customer’s traffic. Can lead to higher operational cost.
Lines terminate at routers in the
POP.

Network resembles a star topology, with one leg of the star connected to ISP and other legs connected to different customers.
Router
Router
Router
Frame Relay
Network
ISP
Router

Backbone router
ISP 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 .

Backbone Node
Backbone Node
ISP Backbone
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.

Customers such as smaller ISPs and enterprises
(Downstream)
Access Router
ISP Backbone
Dial-in POP
(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 a point of presence (POP) . Modem entry points are known as dial-in POPs or dial-in hubs. Entry points for other types of networks are known as broadband POPs .

Broadband POP
Access Router
ISP Backbone
Backbone Router
Large dial-in POP
(Downstream)
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.

Upstream ISP
ISP Backbone
Peer ISP Gateway Router
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 backbone
Router.
So, a gateway router leads to a peer or upstream provider, whereas an access router leads to a downstream network.

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 and response
- Other aspects of protocol performance (Internet path selection)
 Real topologies are not publicly available
- Confidential




Selecting Measurements
 Directed probing
 Path reduction
Alias Resolution
 IP identifier
Router identification and Annotation


To employ BGP tables to identify relevant traceroutes and prune the remainder

To identify redundant traceroutes
 Only one traceroutes needs to be taken when two traceroutes enter and leave the ISP network at the same point


Sending traceroute-like probe(to a highnumbered UDP port but with a TTL of 255) directly to the potentially aliased IP address
 Requirement: routers need to be configured to send the “UDP port unreachable” response with the address of the outgoing interface as the source address: Two aliases should respond with the same source



Mercator’s IP address-based method
Comparing IP identifier field of the responses




Ally, a tool for alias resolution, sends a probe packet to the two potential aliases
Port unreachable responses, including the IP identifiers x and y
Ally sends a third packet to the address that responded first

Rocketfuel 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 AS reductions, and generate jobs for execution
Public traceroute servers
Alias resolution: Using IP identifier technique to resolve alias problem
Database


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. Barthélémy, & 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 exponent from Simon’s 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
Topologies with Rocketfuel