capturing network traffic...
TRANSCRIPT
![Page 1: Capturing Network Traffic Dynamicsrudolf.riedi.home.hefr.ch/Publ/TALKS/Riedi-TUK-TrafficSmall-Web.pdf · High Multiplex vs Large Scale. Rudolf Riedi Rice University stat.rice.edu/~riedi](https://reader035.vdocument.in/reader035/viewer/2022071011/5fc95989ef2f020b6c24dd73/html5/thumbnails/1.jpg)
Capturing Network Traffic DynamicsSmall Scales
Stochastic Systems and Modelling in Networking and FinancePart II
Dependable Adaptive Systems and Mathematical ModelingKaiserslautern, August 2006
Rolf Riedi
Dept of Statistics
![Page 2: Capturing Network Traffic Dynamicsrudolf.riedi.home.hefr.ch/Publ/TALKS/Riedi-TUK-TrafficSmall-Web.pdf · High Multiplex vs Large Scale. Rudolf Riedi Rice University stat.rice.edu/~riedi](https://reader035.vdocument.in/reader035/viewer/2022071011/5fc95989ef2f020b6c24dd73/html5/thumbnails/2.jpg)
Rudolf Riedi Rice University stat.rice.edu/~riedi
Model and Physical Reality
PhenomenonPhysical System
StatisticalModel Physical
Model
StochasticModel
Convergence of ON-OFF to fBm
LRDSelf-similarity
Queuing predictionEstimation of LRD
User responsiblefor bursts at large scale
Large scaleswell understood
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Failure of classical prediction
• Interarrival times – Not exponential– Not independent
Paxson-Floyd, 1995
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Multiscale
Hurst
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Measured Data• Time series (Ak,Zk) collected at gateway of LAN
– k= number of data packet– Ak= arrival time of packet– Bk= size of packet
• Work load until time t:
••Working arrival per m time units
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Long Range Dependence
• High variability at large scales caused by correlation
• Auto-covariance function
• LRD– Slowly decaying auto-covariance
• Cox: for ½ < H < 1 (presence of LRD)
– Var-time-plot: simple first diagnostics for LRD
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Rudolf Riedi Rice University stat.rice.edu/~riedi
ON-OFF: Physical Traffic Model
(Taqqu Levy 1986)
![Page 8: Capturing Network Traffic Dynamicsrudolf.riedi.home.hefr.ch/Publ/TALKS/Riedi-TUK-TrafficSmall-Web.pdf · High Multiplex vs Large Scale. Rudolf Riedi Rice University stat.rice.edu/~riedi](https://reader035.vdocument.in/reader035/viewer/2022071011/5fc95989ef2f020b6c24dd73/html5/thumbnails/8.jpg)
Rudolf Riedi Rice University stat.rice.edu/~riedi
fBm Historic facts• Brown (1820): observes particle motion• Markov (1900+): Markov chains • Einstein (1905): Heat equ for Brownian motion• Wiener (1923): continuous Markov process• Kolmogorov (1930’s): theory of stochastic processes• Kolmogorov (1940): fBm• Levy, Lamperti: H-sssi processes (1962)• Mandelbrot & VanNess: integral representation (1965)
• Adler: fractal path properties of fBm• Samorodnitsky & Taqqu:
self-similar stable motion
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Connection-level Analysis and
Modeling of Network Traffic
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Aggregate Traffic at small scales• Trace:
– Time stamped headers– Sender-Receiver IP !!
• Large scales– Gaussian– LRD (high variability)
• Small scales– Non-Gaussian– Positive process– Burstiness
Objective :– Origins of bursts
Auckland Gateway (2000)Aggregate Bytes per time
Gaussian: 1%Real traffic: 3%
Kurtosis - Gaussian : 3- Real traffic: 5.8
Mean
99%
0 0.5 1 1.5 2 2.5 3x 105
0
50
100
150
200
250
300
350
400
450histogram
Gaussian: 1%Real traffic: 3%
0 2000 4000 60000
0.5
1
1.5
2
2.5
3x 105
time (1 unit=500ms)nu
mbe
r of b
ytes
Mean
99%
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Rudolf Riedi Rice University stat.rice.edu/~riedi
• ON/OFF model – Superposition of sources– Connection level model
• Explains large scale variability: – LRD, Gaussian– Cause: Costumers– Heavy tailed file sizes !!
Bursts in the ON/OFF framework
• Small scale bursts:– Non-Gaussianity– Conspiracy of sources ??– Flash crowds ??
(dramatic increase of active sources)
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Non-Gaussianity: A Conspiracy?
• The number of active connections is close to Gaussian; provides no indication of bursts in the load
• Indication for:- No conspiracy of sources- No flash crowds
Load: Bytes per 500 ms
Number of active connections
Mean
99%
Mean
99%
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Non-Gaussianity: a case studyTypical bursty arrival(500 ms time slot)
Histogram of load offered in same time bin per connection:One connection dominates
150 Kb
Typical Gaussian arrival(500 ms time slot)
Histogram of load offered in same time bin per connection:Considerable balanced “field” of connections
10 Kb
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Non-Gaussianity and Dominance
• Dominant connections correlate with bursts
Circled in Red: Instances where one connections contributes over 50% of load(resolution 500 ms)
Mean
99%
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Non-Gaussianity and Dominance
Systematic study: time series separation• For each bin of 500 ms:
remove packets of the ONE strongest connection• Leaves “Gaussian” residual traffic
Overall traffic Residual traffic1 Strongest connection
= +Mean
99%
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Separation on Connection Level
Definition:• Alpha connections:
Peak rate > mean arrival rate + 1 std dev
• Beta connections: Residual traffic
• Findings are similar for different time series– Auckland (2000+2001), Berkeley, Bellcore, DEC– 500ms, 50ms, 5ms resolution
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Alpha Traffic Component
• There are few Alpha connections – < 1% (AUCK 2000: 427 of 64,087 connections)
– 3% of load
Alpha is extremely bursty
Beta is little bursty
Overall traffic is quite bursty
• Alpha connections cause bursts:
Multifractal spectrum:Wide spectrum means bursty
Balanced (50% alpha) very bursty
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Multifractal spectrum: Microscope for Bursts
α=.7 α=.9 α=.8
• Collect points t with same α :
aLarge Deviation type result
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Beta Traffic Component
• Constitutes main load• Governs LRD properties of overall traffic• Is Gaussian at sufficient utilization (Kurtosis = 3)
• Is well matched by ON/OFF model
Beta traffic Number of connections = ON/OFF
Variance time plot
Mean
99%
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Simple Connection Taxonomy
Careful analysis on connection level shows : this is the onlysystematic reason
Bursts arise from largetransfers over fast links.
RTTrate
bandwidth =But:
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Cwnd or RTT?
Correlation coefficient=0.68
RTT has strong influence on bandwidth and dominance.
103
104
105
106
10-1
100
101
102
peak-rate (Bps)
1/R
TT (1
/s)
Correlation coefficient=0.01
103
104
105
10610
2
103
104
105
peak-rate (Bps)
cwnd
(B)
Colorado State University trace, 300,000 packets
cwnd 1/RTT
ratepeak →
Beta Alpha Beta Alpha
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Examples of Alpha/Beta Connections
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
-200
0
200
400
600
800
1000
1200
1400
one beta connection
packet arrival time (second)
pack
et s
ize
(byt
es)
forward direction
reverse direction
41.3 41.35 41.4 41.45
-200
0
200
400
600
800
1000
1200
1400
one alpha connection (96078, 196, 80, 59486)
packet arrival time (second)
pack
et s
ize
(byt
es)
forward direction
reverse direction
Alpha connections burst because of short round trip time, not large rate
Notice the different time scales
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Modeling Network Traffic
Physical Model• Traffic (user): superposition of ON/OFF
sources requesting files with heavy tailed size• Network: heterogeneous bandwidth
variable sending-rates (fixed per ON/OFF source)
• Explains properties of traffic:–LRD: heavy tailed transfer of beta sources (crowd)
–Bursts: few large transfers of few alpha sources
Mathematical Model•…accommodate this insight within ON-OFF?
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Modeling of Alpha Traffic• ON/OFF model revisited:
High variability in connection rates (RTTs)
Low rate = beta High rate = alpha
fractional Gaussian noise Non-Gaussian limit??
+
=
+
+
=
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Modeling of Alpha Traffic• ON/OFF model revisited:
High variability in connection rates (RTTs)
Low rate = beta High rate = alpha
fractional Gaussian noise Non-Gaussian limit
0 2000 4000 60000
0.5
1
1.5
2
x 105
time (1 unit=500ms)
num
ber o
f byt
es
0 2000 4000 60000
0.5
1
1.5
2
2.5
3x 105
time (1 unit=500ms)
num
ber o
f byt
es
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Towards mathematical models
Renewal reward processes
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Stable distributions• Parameters:
• Equivalent definitions:– Stable– Limit of iid sums
• Known special cases:– Gaussian– Cauchy
• Characteristic fct
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Rudolf Riedi Rice University stat.rice.edu/~riedi
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Rudolf Riedi Rice University stat.rice.edu/~riedi
High Multiplex vs Large Scale
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Different Limits for ON-OFF model
• Recall limitsof ON-OFF sourcesmultiplexed
• Possible limits of renewal reward aggregateWillinger Paxson R Taqqu
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Rudolf Riedi Rice University stat.rice.edu/~riedi
ON-OFF traffic model
…revisited
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Modeling of Alpha Traffic• ON/OFF model revisited:
High variability in connection rates (RTTs)
Low rate = beta High rate = alpha
fractional Gaussian noise stable Levy noise
+
=
+
+
=
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Impact: Simulation
• Simulation: ns topology to include alpha links
Simple: equal bandwidth Realistic: heterogeneousend-to-end bandwidth
• Congestion control• Design and management
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Inpact: Understanding• LRD
– Large time scales – approx. Gaussian – Client behavior– Bandwidth over Buffer
• Multifractal– Small time scale– Network topology– Control at flow level– Simulation
Structure: Multiplicative AdditiveModel: hybrid tree
Mixture of Gaussian - Stable
packetscheduling
sessionlifetime
networkmanagement
round-triptime
< 1 msec msec-sec minutes hours
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Impact: Performance• Beta Traffic rules the small Queues• Alpha Traffic causes the large Queue-sizes
(despite small Window Size)
Alpha connections
Queue-size overlapped with Alpha PeaksTotal
traffic
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Self-similar Burst Model• Alpha component = self-similar stable
– (limit of a few ON-OFF sources in the limit of fast time)
• This models heavy-tailed bursts – (heavy tailed files)
• TCP control: alpha CWND arbitrarily large – (short RTT, future TCP mutants)
• Analysis via De-Multiplexing:– Optimal setup of two individual Queues to come closest to
aggregate Queue
De-Multiplexing:Equal critical time-scales
Q-tail ParetoDue to Levy noise
Beta (top) + Alpha
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Rudolf Riedi Rice University stat.rice.edu/~riedi
ON-OFF Burst Model• Alpha traffic = High rate ON-OFF source (truncated)• This models bi-modal bandwidth distribution• TCP: bottleneck is at the receiver (flow control
through advertised window)• Current state of measured traffic• Analysis: de-multiplexing and variable rate queue
Beta (top) + Alpha Variable Service Rate Queue-tail Weibull(unaffected) unless
• rate of alpha traffic larger than capacity – average beta arrival • and duration of alpha ON period heavy tailed
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Rudolf Riedi Rice University stat.rice.edu/~riedi
On-off parameters
• Free parameters in on-off model?– File size = duration * rate : these variables are dependent– Assuming two of them are independent leads to following models:
• Simulation: same “behavior” for entire traffic results in poor match. Different models (power/patience) for alpha and beta?
Power modelFile size and rate independent
Patience model:File size and duration independent
Real trace Real trace
Simulation using observed size and rate independently
Simulation using observed size and duration independently
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Rudolf Riedi Rice University stat.rice.edu/~riedi
Duration (s)
Rat
e (b
ytes
per
sec
)
Duration and Rate (Beta)
0.1 10 1000 10
1k
100k
0
10
20
30
40
50
60
70
80
90
Size (bytes)
Rat
e (b
ytes
per
sec
)
Filesize and Rate (Alpha)
10 1k 100k 10M 10
1k
100k
0
2
4
6
8
10
12
14
16
Size (bytes)
Rat
e (b
ytes
per
sec
)
Filesize and Rate (Beta)
10 1k 100k 10M 10
1k
100k
0
10
20
30
40
50
60
70
80
90
Duration (s)
Rat
e (b
ytes
per
sec
)
Duration and Rate (Alpha)
0.1 10 1000 10
1k
100k
0
2
4
6
8
10
12
Free parameters: statistical analysis
Alpha Beta
Duration- Rate
Size- Rate
X
• Beta users: rate determines file size• Alpha users are “free”
![Page 40: Capturing Network Traffic Dynamicsrudolf.riedi.home.hefr.ch/Publ/TALKS/Riedi-TUK-TrafficSmall-Web.pdf · High Multiplex vs Large Scale. Rudolf Riedi Rice University stat.rice.edu/~riedi](https://reader035.vdocument.in/reader035/viewer/2022071011/5fc95989ef2f020b6c24dd73/html5/thumbnails/40.jpg)
Rudolf Riedi Rice University stat.rice.edu/~riedi
0 1000 2000 3000 4000 5000 6000 70000
1
2
3
4
5
6
7
8
9x 10
5 Bytes per time (overall)
Time bin (1 unit = 500ms)
Byt
es
0 1000 2000 3000 4000 5000 6000 70000
1
2
3
4
5
6
7
8
9x 10
5 Bytes per time (Alpha)
Time bin (1 unit = 500ms)
Byt
es
0 1000 2000 3000 4000 5000 6000 70000
1
2
3
4
5
6
7
8
9x 10
5 Bytes per time (Beta)
Time bin (1 unit = 500ms)
Byt
es
0 2000 4000 60000
2
4
6
8
x 105 Bytes per time (overall)
Time bin (1 unit = 500ms)
Byt
es
0 2000 4000 60000
2
4
6
8
x 105 Bytes per time (Alpha)
Time bin (1 unit = 500ms)
Byt
es
0 2000 4000 60000
2
4
6
8
x 105 Bytes per time (overall)
Time bin (1 unit = 500ms)
Byt
es
Scheme RD:Rate Durationindependent
Total
Scheme SD:Size Durationindependent
Scheme SR: Size Rate
independent
Alpha
Beta
0 2000 4000 60000
0.5
1
1.5
2
2.5
3
x 107 Bytes per time (overall)
Time bin (1 unit = 500ms)
Byt
es
0 2000 4000 60000
1
2
3
4
5
6
x 107 Bytes per time (Beta)
Time bin (1 unit = 500ms)
Byt
es
0 2000 4000 60000
2
4
6
8
10x 10
6 Bytes per time (Beta)
Time bin (1 unit = 500ms)
Byt
es
0 2000 4000 60000
2
4
6
8
x 105 Bytes per time (Alpha)
Time bin (1 unit = 500ms)
Byt
es
0 2000 4000 60000
2
4
6
8
x 105 Bytes per time (Beta)
Time bin (1 unit = 500ms)
Byt
es
Real Trace
0 2000 4000 60000
2
4
6
8
x 105 Bytes per time (overall)
Time bin (1 unit = 500ms)
Byt
es
Free parameters: SIMULATION
![Page 41: Capturing Network Traffic Dynamicsrudolf.riedi.home.hefr.ch/Publ/TALKS/Riedi-TUK-TrafficSmall-Web.pdf · High Multiplex vs Large Scale. Rudolf Riedi Rice University stat.rice.edu/~riedi](https://reader035.vdocument.in/reader035/viewer/2022071011/5fc95989ef2f020b6c24dd73/html5/thumbnails/41.jpg)
Rudolf Riedi Rice University stat.rice.edu/~riedi
Network-User Driven Traffic model
CONCLUSION: • Rates for alpha drawn to be large, beta drawn to be
small but:– Alpha: power model: Rate independent of Size– Beta: patience factor: Rate independent of Duration
• New limiting results needed for novel ON-OFF settings
0 1000 2000 3000 4000 5000 6000 70000
1
2
3
4
5
6
7
8
9x 10
5 Bytes per time (overall)
Time bin (1 unit = 500ms)
Byt
es
0 1000 2000 3000 4000 5000 6000 70000
1
2
3
4
5
6
7
8
9x 10
5 Bytes per time (overall)
Time bin (1 unit = 500ms)
Byt
es
Original trace (Bellcore) Alpha (SR) + Beta (RD)
![Page 42: Capturing Network Traffic Dynamicsrudolf.riedi.home.hefr.ch/Publ/TALKS/Riedi-TUK-TrafficSmall-Web.pdf · High Multiplex vs Large Scale. Rudolf Riedi Rice University stat.rice.edu/~riedi](https://reader035.vdocument.in/reader035/viewer/2022071011/5fc95989ef2f020b6c24dd73/html5/thumbnails/42.jpg)
Rudolf Riedi Rice University stat.rice.edu/~riedi
Model and Physical Reality
PhenomenonPhysical System
StatisticalModel
ON-OFF withasympt. regimes. Renewal Reward.
StochasticModel
Two component model(alpha/beta users)
Self-similar limitsare fBm (multiplexed beta)or Levy stable (fast alpha)
Queuing predictionDetection of alpha users User responsible
for bursts at large scale
Small scalessufficiently understood.
Choice of physical model not clear