Statistical Modeling for PerHop QoS

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Statistical Modeling for Per-Hop QoS

• Mohamed El-Gendy
• (mgendy_at_eecs.umich.edu)
• In collaboration with
• Abhijit Bose, Haining Wang, and Prof. Kang G.
  Shin
• Real-Time Computing Laboratory
• EECS Department
• The University of Michigan_at_Ann Arbor
• June 4th, 2003

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Outline

• 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

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DiffServ 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

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Per-Hop QoS

• Throughput (BW), delay (D), jitter (J), and loss
  (L) experienced by traffic crossing a PHB

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Motivations

• 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

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Related Work

• Study of TCP ACK marking in DiffServ IWQoS01
• 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

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Related Work

• Performance of TCP Vegas Infocom00
• 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

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Approach to Statistical Characterization

• 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

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Input 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

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Alternative PHB Realizations
EF-EDGE
EF-CORE
EF-CBQ

• Different PHB realizations have different
  functional relationships between inputs and
  outputs

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Configuration 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

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Statistical Analysis

• Analysis of Variance (ANOVA)
• Models
• Output response as a linear combination of the
  main effects and their interactions
• Allocation of variation
• Calculate the percentage of variation in the
  output response due to factors at each level,
  their interactions, and the errors in the
  experiments
• ANOVA
• Statistically compare the significance of each
  factor as well as the experimental error

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ANOVA

• 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

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ANOVA

• Squaring both sides we get

SSE sum of squared errors
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ANOVA
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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
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Statistical Analysis - Regression

• 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

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Regression
Linear model for one dependent variable y and k
independent variables x
Polynomial model for two independent variables
x1, x2
Transformation to fit into linear model
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Experimental 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

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Experimental Framework, contd

• 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

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Experimental Framework, contd

• Network Setup
• Using ring topology for one-way delay measurements

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Full Factorial Design of Experiments

• If we have k factors, with ni levels for the
  i-th factor, and repeat r times
• Total number of experiments

LARGE!!

• Use factor clustering and automated experimental
  framework

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Scenarios 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)

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Scenarios of Experiments, contd

• 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

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EF 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

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EF PHB OP, EF-EDGE w/o BG traffic

• J model and visual tests

Significant factors are assured rate ( ar ),
number of assured flows ( an ), and assured
packet size (apkt)
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EF PHB UP, EF-EDGE w/o BG traffic

• ANOVA results for L
• Significant factors are assured rate ( ar ),
  number of assured flows ( an ), and the token
  bucket rate ( efr )

• Regression model for L

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EF PHB OP, EF-EDGE w/ BG traffic

• ANOVA results for BW, D, and J
• Significant factors are BG packet size ( bpkt ),
  number of BG flows ( bn ), and ratio of assured
  to BG traffic ( Rab )

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EF PHB EF-CORE w/o BG traffic

• J surface response
• Significant factors are assured packet size (
  apkt ) and number of assured flows ( an ), R2
  64

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EF PHB EF-CORE w/o BG traffic

• J visual tests

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EF PHB OP, EF-CBQ w/o BG traffic

• ANOVA results for BW, D, and J
• Significant factors are assured rate ( ar ),
  assured packet size ( apkt ) and number of
  assured flows ( an )

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EF PHB OP, EF-CBQ w/ BG traffic

• ANOVA results for L
• Significant factors are BG packet size ( bpkt ),
  number of BG flows ( bn ), and ratio of assured
  to BG traffic ( Rab )

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EF PHB OP, EF-CBQ w/ BG traffic

• D regression model
• R2 89

• D approximate model

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AF PHB

• ANOVA results for BW, D, J, and L
• Significant factors are assured rate ( ar ),
  assured peak rate ( ap ), assured packet size (
  apkt ), max. threshold ( maxth ) , and min.
  threshold ( minth )

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Discussion

• 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

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Errors

• Experimental errors due to experimental methods
  captured in ANOVA
• Model errors due to factor truncation
• Statistical and fitting errors due to
  regression captured in coefficient of
  determination (R2 )

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A 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

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Conclusions

• 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

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Extensions and Future Work

• 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

• The framework presented is general to be applied
  for studying edge-to-edge (Per-Domain Behavior or
  PDB) in DiffServ

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Multi-Hop Case

• First approach

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Multi-Hop Case

• Second approach

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Questions ?