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Statistical Modeling for Per-Hop QoS. Mohamed El-Gendy ([email protected]) In collaboration with Abhijit Bose, Haining Wang, and Prof. Kang G. Shin Real-Time Computing Laboratory EECS Department The University of Michigan@Ann Arbor June 4 th , 2003. Outline. - PowerPoint PPT Presentation
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Statistical Modeling for Per-Hop Statistical Modeling for Per-Hop QoSQoS
Statistical Modeling for Per-Hop Statistical Modeling for Per-Hop QoSQoS
Mohamed El-Gendy([email protected])
In collaboration withAbhijit Bose, Haining Wang, and Prof. Kang G.
Shin
Real-Time Computing Laboratory EECS Department
The University of Michigan@Ann Arbor
June 4th, 2003
OutlineOutlineOutlineOutline
•Intro of DiffServ, PHB, and Per-Hop QoS•Motivations•Related Work•Approach to Statistical Characterization•Experimental Framework•Results and Analysis•A Control Example•Conclusions and Future Work
DiffServ and PHBDiffServ and PHBDiffServ and PHBDiffServ and PHB
•Scalable network-level QoS based on marked “traffic aggregates”
•Traffic is conditioned and marked with DSCP at edge
•Per-Hop Behaviors (PHBs) are applied to traffic aggregates at core
•QoS is achieved through different PHBs:– Expedited Forwarding (EF) for delay assurance– Assured Forwarding (AF) for bandwidth
assurance
Per-Hop QoSPer-Hop QoSPer-Hop QoSPer-Hop QoS
•Throughput (BW), delay (D), jitter (J), and loss (L) experienced by traffic crossing a PHB
DiffServ node
PHB
Input traffic c/c’sI
Output traffic c/c’sO (BW, D, J, L)
Configuration parametersC
MotivationsMotivationsMotivationsMotivations
• Why modeling Per-Hop QoS?– PHB is the key building block of DiffServ– Wide variety of PHB realizations– PHB control and configuration– Necessary for end-to-end QoS calculation
• Benefits of PHB modeling:– Facilitates the control and optimization of PHB
performance– Enables contribution of per-hop admission control to e2e
admission control decisions
Related WorkRelated WorkRelated WorkRelated Work
•Study of TCP ACK marking in DiffServ [IWQoS’01] :– Used full factorial design and ANOVA– Compared many marking schemes for TCP acks– Suggested an optimal strategy for marking the
acks for both assured and premium flows– Used ns simulation for analysis
•AF performance using ANOVA [IETF draft]:– Compared different bandwidth and buffer
management schemes for their effect on AF performance
Related WorkRelated WorkRelated WorkRelated Work
•Performance of TCP Vegas [Infocom’00] :– Used ANOVA to test the effect of ten congestion
and flow control algorithms– Clustered the ten factors into three groups
according to the the three phases of the TCP Vegas operation
Approach to Statistical Approach to Statistical CharacterizationCharacterization
Approach to Statistical Approach to Statistical CharacterizationCharacterization
•Identify the factors in I and C that affect output per-hop QoS most
•Construct statistical models of the per-hop QoS in terms of these important factors
Fullfactorialdesign
Run Exp. &collect
dataANOVA Tests Regression
Scenariofile
Adjust scenario parameters
Input Traffic Factors - IInput Traffic Factors - IInput Traffic Factors - IInput Traffic Factors - I
Dual Leaky Bucket (DLB) representation for I:– Average rate, peak rate, burst size, packet size,
number of flows per aggregate, and traffic type
– Ia : assured traffic, Ib: background traffic
– Used the ratio between assured to best-effort traffic, instead of absolute value
– Number of input interfaces to PHB node
Alternative PHB RealizationsAlternative PHB RealizationsAlternative PHB RealizationsAlternative PHB Realizations
Priority
EF
BE
RED
FIFO
CBQ/WFQ
EF
BE
RED
FIFO
EF TBF
Priority
BE
RED
EF-EDGE EF-CORE EF-CBQ
•Different PHB realizations have different functional relationships between inputs and outputs
Configuration Parameters- CConfiguration Parameters- CConfiguration Parameters- CConfiguration Parameters- C
Configuration parameters depend on PHB realization:– EF-EDGE: token rate, bucket size, and MTU– EF-CORE: queue length– EF-CBQ: service rate, burst size, and avg packet
size– AF: min. threshold, max. threshold, and drop
probability
Statistical AnalysisStatistical AnalysisStatistical AnalysisStatistical Analysis
Analysis of Variance (ANOVA)– Models
Output response as a linear combination of the main effects and their interactions
– Allocation of variationCalculate the percentage of variation in the output
response due to factors at each level, their interactions, and the errors in the experiments
– ANOVAStatistically compare the significance of each factor as
well as the experimental error
ANOVAANOVAANOVAANOVA
•For any three factors (k = 3), A, B, and C with levels a, b, and c, and with r repetitions, the response variable y can be written as:
rlckbjai
ey ijklABCijkBCjkACikABijkjiijkl
,,1 ,,1 ,,1 ,,1
ijkijklijkl
kjiBCjkACikABijijkABCijk
jiijABij
jjii
yye
y
y
yy
.
..
......
,
, ,
ANOVAANOVAANOVAANOVA
•Squaring both sides we get:
ijklijkl
ijkijk
jkjk
ikik
ijij
kk
jj
ii
ijklijkl
erarbrcr
abracrbcrabcry
22222
22222
SSESSABCSSBCSSACSSABSSCSSBSSASSSSY 0
0)( 2 SSSSYySSTijkl
ijkl
SSE: sum of squared errors
ANOVAANOVAANOVAANOVA
Effect SS %age DF MS F
SSY abcr
SS0 1
SST abcr-1
A SSA a-1
AB SSAB (a-1)(b-1)
ABC SSABC(a-1)(b-1)(c-
1)
e SSE abc(r-1)
....y
y
....yy
SST
SSA100
SST
SSAB100
SST
SSABC100
SST
SSE100
1aSSA
)1)(1( ba
SSAB
)1)(1)(1( cba
SSABC
)1( rabc
SSE
MSE
MSA
MSE
MSAB
MSE
MSABC
100
ANOVA Model Assumptions ANOVA Model Assumptions ANOVA Model Assumptions ANOVA Model Assumptions
• Assumptions:• Effects of input factors and errors are additive• Errors are identical, independent, and normally
distributed random variables• Errors have a constant standard deviation
• Visual tests:• No trend in the scatter plot of residuals vs. predicted
response• Linear normal quantile-quantile (Q-Q) plot of residuals
No assumptions about the nature of the statistical relationship between input factors and response variables
Statistical Analysis - Statistical Analysis - RegressionRegression
Statistical Analysis - Statistical Analysis - RegressionRegression
Polynomial regression– A variant of multiple linear regression– Any complex function can be expanded into
piecewise polynomials with enough number of terms
– Transformations to deal with nonlinear dependency
– Coefficient of determination (R2) as a measure of the regression goodness
RegressionRegressionRegressionRegression
ni
exbxbxbby ikikiioi
12211
iiiiiiioi exxbxbxbxbxbby 21522423
21211
Linear model for one dependent variable y and k independent variables x :
Polynomial model for two independent variables x1, x2:
iiiiiiiiiii xxzxzxzxzxz 21522423
21211
Transformation to fit into linear model:
Experimental FrameworkExperimental FrameworkExperimental FrameworkExperimental Framework
Framework components:– Traffic Generation Agent
•Generates both TCP and UDP traffic•Policed with a built-in leaky bucket for profiled traffic•BW, D, J, L are measured within the agent itself
– Controller and Remote Agents•Control the flow of the experiments according to a
distributed scenario file•Executes and keep track of the experiments steps and
other components
– Network and Router Configuration Agents•Configure traffic control blocks on router according to
experiment scenarios•Receive scenario commands from the Controller agent•Current implementation works on Linux traffic control
– Analysis Module•Performs ANOVA, model validation tests, and
polynomial regression on output data
Experimental Framework, Experimental Framework, cont’dcont’d
Experimental Framework, Experimental Framework, cont’dcont’d
Experimental Framework, Experimental Framework, cont’dcont’d
Experimental Framework, Experimental Framework, cont’dcont’d
Network Setup– Using ring topology for one-way delay
measurements
M
switch
Router ConfigurationAgent
Network ConfigurationAgent
NI
S
H
1 2 3 4 5 6
TrafficAgent
TrafficAgent
TrafficAgent
TrafficAgent
TrafficAgent
TrafficAgent
TrafficAgent
ControllerAgent
AnalysisModule
TrafficAgent
RemoteAgent
Full Factorial Design of Full Factorial Design of ExperimentsExperiments
Full Factorial Design of Full Factorial Design of ExperimentsExperiments
•If we have k factors, with ni levels for the i-th factor, and repeat r times
Total number of experiments =
k
i inr1
LARGE!!
•Use factor clustering and automated experimental framework
Scenarios of ExperimentsScenarios of ExperimentsScenarios of ExperimentsScenarios of Experiments
EF PHB– Factor sets: Ia, Ib, C
– PHB configurations: EF-EDGE, EF-CORE, EF-CBQ– Operating mode: over-provisioned (OP), under-
provisioned (UP), fully-provisioned (FP)EF
EF-EDGE EF-CORE EF-CBQ
Ia+C Ib
OP1
UP2
FP3
OP4
Ia+C5
Ib6
Ia+C Ib
OP7
UP8
FP9
OP10
experimentnumber
Scenarios of Experiments, Scenarios of Experiments, cont’dcont’d
Scenarios of Experiments, Scenarios of Experiments, cont’dcont’d
AF PHB– Use AF11 as assured traffic
– Use AF12 and AF13 as background traffic
– Change max. threshold, min. threshold, and drop probability for AF11 only
EF PHB – OP, EF-EDGE w/o BG trafficEF PHB – OP, EF-EDGE w/o BG trafficEF PHB – OP, EF-EDGE w/o BG trafficEF PHB – OP, EF-EDGE w/o BG traffic
BW surface response: significant factors are assured rate ( ar ) and number of assured flows ( an ), R2 = 96%
nrnrnr aahahahahahhBW 52
42
3210
EF PHB – OP, EF-EDGE w/o BG trafficEF PHB – OP, EF-EDGE w/o BG trafficEF PHB – OP, EF-EDGE w/o BG trafficEF PHB – OP, EF-EDGE w/o BG traffic
J model and visual tests
ar apkt an (ar, apkt) Error
1/J 4.12%
12.52%
46.58%
2.88% 25.34%
Significant factors are: assured rate ( ar ), number of assured flows ( an ), and assured packet size (apkt)
EF PHB – UP, EF-EDGE w/o BG trafficEF PHB – UP, EF-EDGE w/o BG trafficEF PHB – UP, EF-EDGE w/o BG trafficEF PHB – UP, EF-EDGE w/o BG traffic
•ANOVA results for LSignificant factors are: assured rate ( ar ), number of
assured flows ( an ), and the token bucket rate ( efr )
ar an efr
(ar,an
)(ar, efr) (an, efr) (ar, an ,efr)
1/L 6.06%20.81
%6.63% 15.1% 8.9% 16.21% 25%
•Regression model for L
318
217
216
315
21413
212
211
210
310
298
27
652
43210/1
rrn
rnnrrrnrnr
rrnrrrrnn
rrnrrrnr
efhefah
efahahefahefaahaah
efahaahahefhefahah
efahaahahefhahahhL
•ANOVA results for BW, D, and JSignificant factors are: BG packet size ( bpkt ), number of BG
flows ( bn ), and ratio of assured to BG traffic ( Rab )
EF PHB – OP, EF-EDGE w/ BG trafficEF PHB – OP, EF-EDGE w/ BG trafficEF PHB – OP, EF-EDGE w/ BG trafficEF PHB – OP, EF-EDGE w/ BG traffic
bpkt bn Rab (bpkt,bn) (bpkt, Rab) (bn, Rab)(bpkt,
bn ,Rab)
BW 0% 36.6% 2.65% 0% 0% 2.87% 4.4%
Log(D) 3.28% 8.98% 36.3% 3.54% 10.01% 27.07% 10.69%
J 3.36% 7.5% 39.14% 3.7% 9.72% 12.13% 22.77%
•J surface response:Significant factors are assured packet size ( apkt ) and
number of assured flows ( an ), R2 = 64%
EF PHB – EF-CORE w/o BG trafficEF PHB – EF-CORE w/o BG trafficEF PHB – EF-CORE w/o BG trafficEF PHB – EF-CORE w/o BG traffic
npktpktnpktn aahahahahahhJ 52
42
3210/1
•J visual tests
EF PHB – EF-CORE w/o BG trafficEF PHB – EF-CORE w/o BG trafficEF PHB – EF-CORE w/o BG trafficEF PHB – EF-CORE w/o BG traffic
•ANOVA results for BW, D, and JSignificant factors are assured rate ( ar ), assured packet
size ( apkt ) and number of assured flows ( an )
EF PHB – OP, EF-CBQ w/o BG trafficEF PHB – OP, EF-CBQ w/o BG trafficEF PHB – OP, EF-CBQ w/o BG trafficEF PHB – OP, EF-CBQ w/o BG traffic
ar apkt an efr
(apkt, an)
(an, efr) Error
BW 96.73%
0% 0% 0% 0% 0% 0%
1/D 0%94.55
%0% 0% 0% 0% 2.51%
1/J 0% 14.1% 37.5% 6.8% 2.0% 2.0% 22.55%
•ANOVA results for LSignificant factors are BG packet size ( bpkt ), number of BG
flows ( bn ), and ratio of assured to BG traffic ( Rab )
EF PHB – OP, EF-CBQ w/ BG trafficEF PHB – OP, EF-CBQ w/ BG trafficEF PHB – OP, EF-CBQ w/ BG trafficEF PHB – OP, EF-CBQ w/ BG traffic
bpkt bn Rab (bpkt,bn) (bpkt, Rab) (bn, Rab)(bpkt,
bn ,Rab)
Log(D) 0% 0% 83.23% 2.34% 3.53% 2.04% 7%
L 8.87% 2.38% 36.89% 5.14% 25.84% 4.8% 15.45%
•D regression modelR2 = 89%
EF PHB – OP, EF-CBQ w/ BG trafficEF PHB – OP, EF-CBQ w/ BG trafficEF PHB – OP, EF-CBQ w/ BG trafficEF PHB – OP, EF-CBQ w/ BG traffic
3232
22223
22
2
90.196.189.144.388.1
99.179.051.034.124.78
61.819.125.574.289.1
86.12103.633.265.4691.1)log(
npktabpktnabpktpktn
pktnnabpktabnabab
pktpktnnpktabnab
abpktnab
bbRbbRbbb
bbbRbRbRR
bbbbbRbR
RbbRD
2
2223
2
96.1
89.179.051.034.124.78
74.289.186.12165.4691.1)log(
pktab
pktnabnabpktabnabab
pktabnababab
bR
bbRbRbRbRR
bRbRRRD
•D approximate model
AF PHBAF PHBAF PHBAF PHB
•ANOVA results for BW, D, J, and LSignificant factors are: assured rate ( ar ), assured peak rate
( ap ), assured packet size ( apkt ), max. threshold ( maxth ) , and min. threshold ( minth )
ar ap apkt maxth minth (ar, ap)
BW 51.38%
12.51% 0% 2.67% 2.38% 13.27%
D 38.2% 25.42% 2.85% 0% 3.1% 25.06%
1/J 14.75%
17.35% 34.82% 0% 0% 18.94%
L 29.32%
17.12% 0% 7.14% 4.17% 16.98%
DiscussionDiscussionDiscussionDiscussion
• BW shows a square root relationship with factors in Ia in EF-CBQ only, and direct relation in the other EF realizations
• D shows a direct relation with Ia in EF-EDGE, and EF-CORE, and inverse relation in EF-CBQ
• D shows a logarithmic (multiplicative) relation with Ib
• J shows inverse relation with Ia and a direct relation with Ib
• J depends on the number of flows in the aggregate as well as the difference in packet size with other flows/aggregates
ErrorsErrorsErrorsErrors
1. Experimental errors: due to experimental methods; captured in ANOVA
2. Model errors: due to factor truncation3. Statistical and fitting errors: due to
regression; captured in coefficient of determination (R2 )
A PHB Control ExampleA PHB Control ExampleA PHB Control ExampleA PHB Control Example
•For OP, EF-CBQ w/ BG traffic: – For bpkt = 600 B, bn = 1, Rab = 2 D = 0.4136
msec
– For bpkt = 1470 B, bn = 3, D = 0.4136 msec Rab = ??
•Use the delay model to find Rab = 0.494 with accuracy of (1-R2) = 11%
Co
nfi
gu
rati
on
C(t
)
QoSSubSystem
Model-basedController
|O - O'|
InputI(t)
OutputO(t)
RequiredOutput (O')
ConclusionsConclusionsConclusionsConclusions
• Simple statistical models are derived for per-hop QoS using ANOVA and polynomial regression
• Statistical full factorial design of experiments is an effective tool for characterizing QoS systems
• Using automated experimental framework is shown to be effective in such studies
• Different PHB realizations show differences in dependency of per-hop QoS on input factors
Extensions and Future WorkExtensions and Future WorkExtensions and Future WorkExtensions and Future Work
•The framework presented is general to be applied for studying edge-to-edge (Per-Domain Behavior or PDB) in DiffServ
•More rigorous control analysis and study of suitable control algorithms
•Validate the models derived with analytical methods such as network calculus
•Use real-time measurements to update models and control criterion while operation
Multi-Hop CaseMulti-Hop CaseMulti-Hop CaseMulti-Hop Case
•First approach
Input(I)
Output(O)
Configuration(C)
EgressIngress
Multi-Hop CaseMulti-Hop CaseMulti-Hop CaseMulti-Hop Case
•Second approach
Input(I)
Output(O)
EgressIngress
I1 Ii InO1 Oi On
CnCiC1
QuestionsQuestions ? ?QuestionsQuestions ? ?