can we model the internet? · number of networks year 0 20,000,000 40,000,000 60,000,000 80,000,000...
TRANSCRIPT
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Can we model the Internet? … and keep it simple
Don TowsleyDept. of Computer Science
UMass - Amherst
large supporting cast: N. Duffield, K. Hollot,W. Gong, Y. Liu, F. Lopresti, V. Misra
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Overview
! introduction! scalable models
" keep it simple!measurement-based models
" keep it simple! summary
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A (short) History of the Internet
after the big bang
changes in technology stimulated disruptiveapplications
increased bandwidth+ access ⇒ email
⇒ the web⇒ P2P applications
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Prior to the WebWWW
ftp
news email
other
! 1993 – almost no web traffic
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Transition to Web
! 1993 – almost no web traffic
! 1995 – starts to show up
ftp
other
WWW
news
1993
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The Web rules
! 1993 – almost no web traffic
! 1995 – starts to show up
! 2000 – almost 75% web traffic
ftp
streaming
emailother
1994
WWW
streaming
1993
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Transition to P2P! 1993 – almost no web
traffic! 1995 – starts to show up! 2000 – almost 75% web
traffic! 2001 – transition to P2P
2000
WWW
P2P other
ftp
1993 1994
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Exponential GrowthN
umbe
r of N
etw
orks
Year
0
20,000,000
40,000,000
60,000,000
80,000,000
100,000,000
120,000,000
140,000,000
160,000,000
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
source datawww.isc.com
Num
ber
of h
osts
OC192
OC48
OC12OC3OC156K
200019951990198519801970
[adapted from Hui 1997]9.6 G
2.5 G
band
widt
h
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how do we model?
understanding?
design?
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Invariants
! IP hourglass! predominance of TCP ! mice/elephants
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IP Hourglass
! network plane – IP!many protocols,
applications!many low-level technologies
email WWW phone...
HTTP ...
TCP UDP…
IP
ethernet PPP…
copper fiber radio...
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Predominance of TCPtraffic by protocol, bytes
traffic by protocol, packets
courtesy, D. Plonka
TCP makes up 95% of traffic1993199420002002•••
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Mice/Elephants
Flow size distributions! most flows 1 - 20 pkts! most pkts in long flows
" MP3 file – 1K – 10K pkts" movie – 50K – 600K pkts
! % pkts belonging to flows not captured in finite trace (CAIDA)" 48min – 22%" 24hr - 5%
presence of long-lived TCP flows
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Challenges
Appropriate model for TCP elephants?Level of abstraction?Control strategies?
Models and measurements?
Disclaimer: choice of research problems personal
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Themes
! fluids vs packets
! correlation in measurements
! simplicity in modeling
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Ingredients: TCP Source Model
! adapts sending rate to network congestion! window based rate control
#sends out a window W of packets each round trip time (RTT)
#W increases by 1 every RTT if no packet loss
sender
receiver
W
RTT
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Ingredients: TCP Source Model
! adapts sending rate to network congestion! window based rate control
#sends out a window W of packets each round trip time (RTT)
#W increases by 1 every RTT if no packet loss#W decreases by half upon packet loss
sender
receiver
W
RTT
x
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Scalable Modeling: Fluids
! network time scales" configuration: hours" routing: 10s of minutes" congestion: seconds⇒ flexibility of fluids
! granularity" packet, burst, flow,
aggregate! closed loop vs. open
loopTCP - closed loop
packet
burst
flow
aggregate
open loop
closed loop
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! network introduces" round trip time R" losses, Poisson(λ)
! Poisson assumption verified by measurements
! W – average window size
Network as a black box
data
ACKs
λ×−=2W
R1
dtdW
Additiveincrease
LossrateMult.
decrease
sender
rcvr
packet loss, λ
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! network introduces" round trip time R" losses, Poisson(λ)
! Poisson assumption verified by measurements
! W – average window size
as t → ∞
Network as a black box
data
ACKs
λ×−=2W
R1
dtdW
sender
R2W λ
=
rcvr
packet loss, λ
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Network as a black box! TCP session throughput
! validation with measurements" 85 100 sec. wide area
network traces" λ, R estimated from
traces 0
500
1000
1500
2000
2500
3000
3500
0 20 40 60 80 100Trace
Thro
ughp
ut
measured
Fluid
RWTput =
… but no session is an island
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Ingredients: Link Model
!drop tail - drop pkt when buffer fills
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Ingredients: Link Model
!drop tail - drop pkt when buffer fills
! active queue management (AQM)" proactively drop/mark packets
before buffer overflow" drop/mark pkt with
probability p(q); q - queue length
" example: RED (random early discard)
q(t)p(q(t))
tmin tmax
pmax
1
2tmaxM
arki
ng p
rob.
pavg queue length q
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Start Simple: One Congested Router
AQM router
C, p
TCP flow k,prop. delay Ai
! one bottlenecked AQM router" capacity {C (packets/sec) }" queue length q(t)" drop prob. p(t)
! N TCP flows" window sizes Wk(t)" round trip times
Rk (t) = Ak + q(t)/C
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Fluid Equations
Window Size:
Quantities are average values
)t(R1
k=
dtdWk −
2Wk )Rt(p
)Rt(R)Rt(W
kkk
kk −−−
Mult.decrease
Additiveincrease
Loss arrivalrate
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Fluid Equations
Window Size:
Quantities are average values
)t(R1
k=
dtdWk )Rt(p
)Rt(R)Rt(W
kkk
kk −−−−
2Wk
Incomingtraffic
∑+ )t(R)t(W
k
kQueue length: =dtdq
Outgoingtraffic
C1 0tq ])([ >−
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A Queue is not an IslandNetwork - set of AQM routers, V
sequence Vk for sessionk
Loss/marking probability - cumulative prob1 - pk (t) = Πv ∈Vk (1 - pv(t))
Round trip time - aggregate delayRk(t) = Ak + Σv∈Vk qv(t)/Cv
Link bandwidth constraints
Queue equations
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How well does it work?
OC-48
OC-12
! OC-12 – OC-48 links! RED with target delay
5msec! 2600 TCP flows
! decrease to 1300 at 30 sec.
! increase to 2600 at 90 sec.
t=30 t=90
2600 × j 2600 × j1300 × j
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Good queue length match
inst
anta
neou
s de
lay
time (sec)
simulationfluid model
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time (sec)
wind
ow s
ize
matches average window size
simulationfluid model
time (sec)
aver
age
wind
ow s
ize
simulationfluid model
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Lessons and opportunitiesstochastic
differentialequations
(distributions)
slow,accurate,off-line
fast,approximate,
on-line
! fluids right level of abstraction for TCP
!hierarchy of modeling abstractions
Language of control theory (Kelly, Low, Misra, Srikant, Vinnicombe,…)
differentialequations
(averages)
equilibria(steady state)
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Control: Insights
100flows
100flows
50flows
ns simulation, instantaneous queue length
fluid model avg. queue length
time
queu
e le
ngth
Control theoretic analysis predicts stability, decreases as" link capacity (C)
increases" no. of flows (N)
decreases" feedback delay (R)
increases
Link capacity (C/N) increases (high speed computing)
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Controller Design
CD
F (%
)
Response Time (ms)
Drop-tail, PI, & REM equivalent for shortest
80% of responses
Drop-tail, PI, & REM equivalent for shortest
80% of responses
PI best overallPI best overall
RED not competitiveRED not
competitive
! analysis reveals RED problems" q(t) estimator adds
feedback delaydesigned wo model
! PI controller" from model" faster response" decouples queue length,
load! UNC experimental
evaluation" http latency" 90% load
courtesy, K. Jeffay
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models and measurements
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Measurement-based Modeling (Network Tomography)
Goal: obtain detailed picture of a network/internet from end-to-end views
! infer topology /connectivity
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Network Tomography
Goal: obtain detailed picture of a network/internet from end-to-end views
! infer link-level" loss" delay" utilization
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Brain Tomography
unknownobject
counting &projection
Maximumlikelihood estimate
performinference
data
statistical modelbrain model
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Network Tomography
routing &counting
data
queuing behavior binomial
performinference
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MINC (Multicast Inference of Network Characteristics)
!multicast probes" copies made as needed
within network
source
receivers
source
receivers
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MINC (Multicast Inference of Network Characteristics)
!multicast probes" copies made as needed
within network! receivers observe
correlated performance! exploit correlation to get
link behavior" loss rates" delays
source
receivers
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Modeling Loss on Multicast Trees
source
receivers
kαk
!loss model"Bernoulli losses, αk
on link k " independent
between links!data
"observed losses at receivers
!goal "estimate link probabilities {αk }
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LossesMaximum likelihood
estimator (MLE) for link loss rates
!minimum variance! unbiased
MLE for link delay distributions
Topology discovery
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Lessons and Opportunities
! correlation powerful tool!" multicast, packet pairs, sandwiches, stripes
!measurement-based modeling rich, wide open research area" edge-based" router-based “monitor in the middle”" hybrid approaches" application-based
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Lessons and Opportunities (Scalability)
source
receivers
AS-level tomography
AS1
AS2
AS3
AS4AS5
!works for 10 - 50 routers
! 1000? !different ASes?
What is right model?
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Other modeling successes
! open loop traffic (Mitra, …)
! network calculus (Cruz, Chang, LeBoudec, …)
! security (Zou, …)
" malware as fluids
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Summary
! invariants permit reasoned approach to modeling
! fluids allow scalable modeling
need to go beyond data plane to control plane
! correlation key to measurement-based modeling" how to introduce, quantify, control?
still missing - a measurement science
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The end
Thanks!
Slides (will be) available athttp://gaia.cs.umass.edu/towsley/dtc03.pdf