Fluid-based analysis of TCP and RED

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Fluid-based analysis ofTCP and RED

• Rajarshi Gupta
• WebTP Group
• April 3, 2000

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Paper being Presented

• Fluid-based Analysis of a Network of AQM Routers
  Supporting TCP Flows with an Application to RED
• AQM Active Queue Management
• Authors
• Vishal Misra
• Don Towsley
• et al. (?)
• Work in progress, early Preprint

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Previous Work

• Recall Stochastic Differential Equation Modeling
  and Analysis of TCP-Windowsize Behavior, Vishal
  Misra, Wei-Bo Gong, Don Towsley
• Presented at Performance99, Istanbul,
  Turkey, October99
• ftp//gaia.cs.umass.edu/pub/Misra99-TCP-Stochastic
  .ps.gz
• Presented by RG _at_ WebTP 11/08/99

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Key Ideas of Old Paper

• Consider network as source of losses and sources
  as recipient of these signals
• Model loss arrival as independent Poisson process
• Use Stochastic Differential Equations Queuing
  Theory to estimate Rate
• Compare with existing data and analytical model
  (Padhye - SIGCOMM98)

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Themes of Current Paper

• Use SDE to model COMPLETE system
• TCP characteristic
• Action of AQM routers (RED)
• Evaluate solution of system of equations
• Corollary RED is bad !
• Suggested improvements to RED filtering mechanisms

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Assumptions

• Model of complete system
• Pkt losses no longer independent parameter
• TCP window size depends on RTT and RED pkt
  discard function
• Pkt loss is function of Q estimate and Q lengths
• Q length is a function of window sizes
• Pkt losses to flow i are described by Poisson
  process Ni (t) with rate ?i (t)
• RTT Ri (t) Ai (t) q(t)/C

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TCP Window Size

• Window size defined by
• Taking expectations

• Here Ex ?x
• Approximation used was Ef(x) ? f(Ex)
• Hence,

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Pkt Loss Function

• RED discards
• Let x be exponentially weighted MA sampled every
  ? seconds

• Converting to DE and sampling
• Comparing coefficients and taking expectations

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Behavior of q

• Differential version of Lindleys equation
• -1q(t)C is pkt servicing
• Wi / Ri (q) is arrival of pkts from TCP flow i

• Then,
• For a bottlencked Q, q(t)gt0 w.p. 1
• Hence,

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Building Entire System

• N2 coupled equations
• N2 unknowns (?x,?q,?Wi )
• Solve numerically
• These values can yield
• R
• ?
• etc

• We have,

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Extensions to a Network

• Generalize
• variables to vectors
• vectors to matrices
• Subscript v denotes a specific router
• Then,

• Replacing the old system of equations
• is same (for V routers)

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2
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So we get a total of N2V unknowns to solve
numerically
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Further Complications

• Timeout losses
• Slow-Start
• Aggregation of identical flows
• Same route and same RTT
• Different variations of TCP

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Application RED

• Compare the system with a network with RED as the
  AQM policy in routers
• Network simulated using ns
• Differential equation solver done in Matlab
• RED updates estimate every arrival
• Here, choose ?v 1/Cv where Cv is the link
  capacity in pkts/sec

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Topology

• Two RED routers
• S2 goes through both
• S1, S3 use only Q1
• S4, S5 use only Q2
• Symmetric case (both Q capacities 5 MB/s)
• Asymmetric case (Q1 5 MB/s, Q2 2.5 MB/s)

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DiffEq Model works well (1/4)
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DiffEq Model works well (2/4)
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DiffEq Model works well (3/4)
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DiffEq Model works well (4/4)
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Effect of Packet Size (1/2)
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Effect of Packet Size (2/2)
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Effect of value of ?
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Flaws in RED

• If a busy state is followed by long silence, RED
  does not notice the silence
• When there are rapid arrivals, average queue size
  closely follows instantaneous value
• Discontinuity in drop function also bad and
  should be eradicated

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Suggestions for RED

• Adaptive nature of sampling interval is harmful
  and leads to oscillations
• Oscillations caused by many factors like pkt
  size, link bw, load level etc
• Need to incorporate an appropriate sampling
  interval ? in the sampling mechanism
• Trying to design a better filter with nicer
  capabilities (Claims to be nearly there -)

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Contributions

• An improved methodology of TCP modelling
• Analytical
• Computationally efficient
• Models the complete system
• Matches well with simulation
• Demonstrates inefficiencies of RED under certain
  circumstances
• Working on improved averaging mechanism