Loss Model of TCP

1
Loss Model of TCP

• Presented by
• Rajarshi Gupta
• WebTP Group

2
Paper being Presented

• Stochastic Differential Equation Modeling and
  Analysis of TCP-Windowsize Behavior
• Authors
• Vishal Misra, completing PhD, UMass EE
• Wei-Bo Gong, faculty, UMass EE
• Don Towsley, faculty, UMass CS
• Presented at Performance99, Istanbul,
  Turkey, October99
• ftp//gaia.cs.umass.edu/pub/Misra99-TCP-Stochastic
  .ps.gz

3
Key Ideas

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

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Loss Model

• Loss arrival may be modeled by Poisson process
• Connection travels through many hops
• Khinchines Theorem
• Many flows at each router
• Probabilistic thinning
• Kallenbergs Theorem

• Denote arrival processes
• dNTD 3-dup-ack loss
• dNTO timeout loss

5
Window Size Model

• Congestion Avoidance
• Let W window size
• Terms
• 1st additive increase
• 2nd multiplicative decrease (TD loss)
• 3rd window cutback to 1 (TO loss)

• Slow Start
• Cong Avoidance
• Tslow-start threshold
• Denote
• ?TDTD loss arrival rate
• ?TOTO loss arrival rate

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Analysis (no slow-start)

• Throughput Expected window size / RTT
• Then,
• NOTE We havent considered effect of
• maximum window size (important effect)
• timeout backoff

Taking t??
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Maximum Window Size

• We solve for PWM by looking at Window Size
  Evolution for TCP as the Virtual Waiting Time in
  an M/G/1 queue with finite buffer
• Then,
• Here
• ?1 ?TO
• ?1 ?TD
• K service rate 1 / RTT
• As before, Throughput EW/RTT

M is the maximum window size
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Timeout Backoff

• After a timeout, the window does not grow for a
  period of T0
• Need to replace indicator function IM with IMIT0
  where IT0 is 0 for T0 seconds after a timeout
• Events WM and W?TO are mutually exclusive

• Two corrections needed for silent time
• EW during active stage only
• Scaling RTT to account for the silent periods
• Throughput EWactive / RTT scaled for active
  period

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Comparing with other Models

• To compare with traditional TCP analysis
• loss/sec ?1?2
• pkts/sec R
• loss/pkt p (?1?2 )/R
• No timeout is likely in the case of TCP SACK
• In short connections, TO gt TD

• No TO losses (?10)
• Unlimited window (M??),

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Experiments

• Used the datasets collected by Padhye et al for
  the SIGCOMM98 paper
• Used the sets of 100 ?100 sec traces
• Plotted against SIGCOMM formula values
• On the plots, the 100 points are arranged in
  descending order of throughput
• Formula works badly for very low throughputs
• multiple timeouts
• ?TO too low since throughput is low
• loss rates of 60-80 is non-poisson

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Results
Throughput
Experiment Sequence Number
Experiment Sequence Number
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More Results
Throughput
Experiment Sequence Number
Experiment Sequence Number
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Still More Results
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Poisson ?

• For Poisson Arrivals, need to test for
• independent inter-arrival times
• exponential inter-arrival times
• Note that exponentiality alone is not enough
• Use the following tests
• Independence Lewis and Robinson test (gt90)
• Exponentiality Anderson-Darling test (60-80)
• Independence property more important than
  exponential property

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Poisson Experiments
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Conclusions

• Losses modeled as Poisson arrivals from network
• SDE gives closed form solution for comprehensive
  TCP model
• Experimental verification with real data