scaling phenomena in the internet - mathematical … and valverde, “information transfer and ......
TRANSCRIPT
Topics Covered
The Self-Similar Nature of Internet TrafficThe “Physics of Complex Systems” viewThe Networking viewJCD’s dream comes true: 1st INFOCOM paper
High Variability in Internet TopologyThe “Physics of Complex Systems” viewThe Networking viewJCD’s dream comes true: 1st SIGCOMM paper
A Look Ahead
Time scale: 100 sec
10 msec
Varibility scales like 10^(-0.8) at each step
Time scale: 100 sec
10 msec
Variab
ility s
cales
like 1
0^(-0
.5) at
each
step
The “Physics” View:Self-Organized Criticality (SOC)
Csabi, “1/f noise in computer network traffic”(1994)Ohira and Sawatari, “Phase transition in computer traffic models” (1998)Yuan, Ren, and Shan, “Self-organized criticality in a computer network model” (2000)Sole and Valverde, “Information transfer and phase transitions in a model of Internet traffic”(2001)
SOC and Internet Traffic
Can ignore Internet-specific “details” for the sake of addressing “fundamental” issuesSelf-similar Internet traffic is the result of a “critical” phase transitionAt criticality: 1/f-type traffic fluctuations, heavy-tailed queues and latencies, etc.There exist deep links between Internet traffic and highway traffic
The SOC-type Network Model
2-d lattice model with 4 nearest neighborsSome nodes are “hosts”, some are “routers”Hosts generate packets at rate λ (pick random dest.)Routers store or forward packets (rule-based)Unbounded queues at the routersNo congestion control!!“SOCnet”
Flowcapacity
AverageQueueAt each link
flow capacity l
lk l
k Kx c
∈
≤
≤
∑
Link
Flows
SOCnet and Criticality
At criticality (λ= λ*)• Self-similar fluctuations• Power law latencies and
queue lengths• Maximum efficiency,
information transfer
Phase transition at λ= λ*• Average latency bifurcates• Packet flow is maximized
Sole and Valverde(2001)
SOCnet and the Internet
There exists no “critical” rate!Self-similar traffic is observed for all load levelsBottom line
It is conceivable to build a SOCnetNo engineer would ever design a SOCnetNo user would ever get anything done using SOCnetChaos-based explanations for self-similar traffic have been proposed and are equally specious
The Networking View:High Variability I
Leland, Taqqu, Willinger, and Wilson, “On the self-similar nature of Ethernet traffic” (1993)Paxson and Floyd, “Wide area traffic: The failure of Poisson modeling” (1994)Crovella and Bestavros, “Self-similarity in World-Wide-Web traffic” (1996)Mandelbrot, “Long-run linearity, locally Gaussian processes, h-spectra, and infinite variances (1969)
Web servers
Application traffic (e.g., WWW)
is streamed out on the net
creating Internettraffic
Webclient
Let’s look at Internet traffic over some link
Link
Internet traffic
Web traffic …
… is streamed onto the Internet …
… creating “bursty-looking” link traffic
time
Mandelbrot-Cox Construction
Renewal reward processes and their aggregatesAggregate is made up of many constituents/flowsFlows arrive at randomEach flow has a “size” (number of packets)Each flow transmits it packets at some (constant) rate
Mathematical resultsIf flows arrive at random and if their sizes are heavy-tailed with infinite variance, then the aggregate traffic is perforce self-similar (exhibits long-range dependence)Aggregate traffic is Fractional Gaussian noise
Web traffic …
… is streamed onto the Internet …
… creating “bursty-looking” link traffic
time
(heavy-tailed HTTP requests/responses)
(fractional Gaussian noise)(TCP-type transport)
Typical web transfers
log(file size)
α > 1.0log(freq > size)
p ∝ s-α
Web servers
Heavy tailed Webrequests/responses
Are streamed out on the net.
Creating fractal Gaussian traffic on individual links
23 α−
=H
Measured IP Flow Property (Size)
High Variability and Internet Traffic
Coherent and mathematically rigorous framework for Internet traffic (large time scales)Flow measurements over the last 10 years have consistently shown heavy-tailed/infinite variance behavior Prime example for what is meant by a consistent, mathematically rigorous, networking-based, explanation with supporting measurementsSays nothing about Internet traffic over short time scales
2001: JDC’s 1st INFOCOM Paper
Provides an explanation of the origin of “heavy tails” in Web documentsSuggests that heavy tails are here to stayCompletes the explanation of self-similarityMotivates subsequent work on congestion control for “mice/elephant” traffic
Zhu, Yu, and Doyle, “Heavy tails, generalizedcoding, and optimal web layout”, Proc. IEEEInfocom’01
Topics Covered
The Self-Similar Nature of Internet TrafficThe “Physics of Complex Systems” viewThe Networking viewJCD’s dream comes true: 1st INFOCOM paper
High Variability in Internet TopologyThe “Physics of Complex Systems” viewThe Networking viewJCD’s dream comes true: 1st SIGCOMM paper
Lessons Learned
Internet Topology and Power LawsSource: Faloutsos et al (1999)
How to account for high variability in node degrees?How to explain high variability in node degrees?
Most nodes have few connections
A few nodes have lots of connections
The “Physics” View:Scale-Free Networks (SFN)
Barabasi and Albert, “Emergence of scaling in random networks” (1999) Albert, Jeong, and Barabasi, “Attack and error tolerance of complex networks”(2000)Barabsi, “Linked: The New Science of Networks” (2002)
SFN and Internet Topology
Ignore Internet-specific “details” for the sake of addressing “fundamental” issues High variability in node degrees: Power law!Preferential attachment leads to power law degree distributions (“scale-free” structure)Central core nodes with high degree (“hubs”): The “Achilles’ heel” of the InternetThere exist deep links between Internet topology, the power grid, airline network, metabolic networks, etc.
One ofthe most-read papers ever on
the Internet!
SFN and the Internet
The high-degree nodes are at the edge and not in the center of the networkThe Internet is extremely robust to hardware failures, but (by design!) very fragile to hijackings by malicious end usersBottom line
It is conceivable to build a SF InternetNo engineer would ever design a SF InternetNo user would ever get anything done using a SF InternetDespite getting it completely wrong, SFNs have had impact
The Networking View:High Variability II
What causes node degrees to be highly variable?Topology is more than connectivity
Routers (nodes) have max capacityLinks have max bandwidth
Economic factors impacting network designEnd user bandwidth demandsLink costsIncentive for multiplexing
Cisco 12000 Series Routers
80 Gbps41/812404
120 Gbps61/412406
200 Gbps101/212410
320 Gbps16Full12416
Switching CapacitySlotsRack sizeChassis
Modular in design, creating flexibility in configuration.Router capacity is constrained by the number and speed of line cards inserted in each slot.
Source: www.cisco.com
Technologically Feasible Region
0.01
0.1
1
10
100
1000
10000
100000
1000000
1 10 100 1000 10000
degree
Ban
dwid
th (M
bps) cisco 12416
cisco 12410
cisco 12406
cisco 12404
cisco 7500
cisco 7200
cisco 3600/3700
cisco 2600
linksys 4-port router
uBR7246 cmts(cable)cisco 6260 dslam(DSL)cisco AS5850(dialup)
Edge Shared media(LAN, DSL,
Cable, Wireless,Dial-up)
Corebackbone
High-end gateways
Older/cheapertechnology
1e-1
1e-2
1
1e1
1e2
1e3
1e4
1e21 1e4 1e6 1e8
Rank (number of users)
Dial-up~56Kbps
BroadbandCable/DSL~500Kbps
Ethernet10-100Mbps
POS/Ethernet1-10Gbps
Con
nect
ion
Spee
d (M
bps)
most users have low speed
connections
a few users have very high speed
connections
high performancecomputing
academic and corporate
residential and small business
Internet End-User Bandwidths
How to build a network that
satisfies these end user demands?
Hosts
Edges
CoresMesh-like core of fast,
low degree routers
High degree nodes are at the edges.
Heuristically Optimal Topology (HOT)Based on HOT framework (Carlson and Doyle)Economic and technology constraints:
Mesh-like core of high-speed, low-degree routersHigh-degree, low-speed nodes at the edge
Consistent with real observed network
SOX
SFGP/AMPATH
U. Florida
U. So. Florida
Miss StateGigaPoP
WiscREN
SURFNet
Rutgers
MANLAN
NorthernCrossroads
Mid-AtlanticCrossroads
Drexel
U. Delaware
PSC
NCNI/MCNC
MAGPI
UMD NGIX
DARPABossNet
GEANT
Seattle
Sunnyvale
Los Angeles
Houston
DenverKansas
City Indian-apolis
Atlanta
Wash D.C.
Chicago
New York
OARNET
Northern LightsIndiana GigaPoP
MeritU. Louisville
NYSERNet
U. Memphis
Great Plains
OneNetArizona St.
U. Arizona
Qwest Labs
UNM
OregonGigaPoP
Front RangeGigaPoP
Texas Tech
Tulane U.
North TexasGigaPoP
TexasGigaPoP
LaNet
UT Austin
CENICUniNet
WIDE
AMES NGIX
OC-3 (155 Mb/s)OC-12 (622 Mb/s)GE (1 Gb/s)OC-48 (2.5 Gb/s)OC-192/10GE (10 Gb/s)
Abilene BackbonePhysical Connectivity(as of December 16, 2003)
PacificNorthwestGigaPoP
U. Hawaii
PacificWave
ESnet
TransPAC/APAN
Iowa St.
Florida A&MUT-SWMed Ctr.
NCSA
MREN
SINet
WPI
StarLight
IntermountainGigaPoP
Internet Topologies
nodes=routersedges=links
25 interior routers818 end systems
High degree hub-like coreLow degree
mesh-like core
101
10210
0
101
degree
rank
identical power-law degrees
How to characterize / compare these two networks?
“scale-rich” vs. “scale-free”
Characterization of Topologies
Network performanceTechnology constraintEnd user demands, traffic matrixHow well is the network able to carry a given traffic?
Network likelihoodAll simple connected graphs with same node degree distributionAssign probability to each graphRelated to “degree of scale-free” and “degree of self-similarity”
LikelihoodHighLow
Good
Bad
Performance
Why such strikingdifferences with same
node degree distribution?
1
10
100
1000
10000
100000
10 100
degree
Ban
dwid
th (M
bps)
11
10
100
1000
10000
100000
10 100
degree1
Fast core
High-degree edge
Slow core
Slower edge
Performance LikelihoodLikelihood
HighLow
Fast
Slow
High Variability and Internet Topology
Newer measurements show that router node degrees are not consistent with a power law distributionDomain knowledge is crucialHigh variability in end user demands leads to high variability in node degreesHOT networks are unlikely to arise at randomBasic ingredient for studying topologies at higher layers (AS-graph, overlay networks)
2004: JDC’s 1st SIGCOM Paper
Provides an explanation of the origin of the high variability in node degreesResolves much of the confusion and controversy created by SFNMotivates the development of a rigorous mathematical treatment of SFNSFN may be ok for “virtual” networks
Li, Alderson, Willinger, and Doyle, “A first-principles approach to understanding the Internet’s router-level topology”, ACM SIGCOMM 2004
A Look Ahead
Internet-specific multiscale analysisInternet architecture defines an (unusual) multiscalestructureBytes, packets, IP-flows, OD-flows, AS-flowsLink, individual IP addresses, prefixes, ASesSeparate pieces in place, but no coherent approach exists
Towards a theory of the InternetFirst theoretical results on TCP confirm the ingenuity of the original architects of the InternetWhat will be the first negative result? Routing?