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TCP Models

TCP Models. Objective Given the loss probability, how fast does TCP send? Deterministic model?. drops. wmax. cwnd. wmax/2. time. Wmax/2* RTT. Simple Stationary model. Data rate = cwnd/RTT. Total packet sent=. drops. wmax. cwnd. wmax/2. time. Wmax/2* RTT. Simple Stationary model.

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TCP Models

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  1. TCP Models Objective Given the loss probability, how fast does TCP send? Deterministic model?

  2. drops wmax cwnd wmax/2 time Wmax/2* RTT Simple Stationary model Data rate = cwnd/RTT Total packet sent=

  3. drops wmax cwnd wmax/2 time Wmax/2* RTT Simple Stationary model

  4. More complicated model

  5. The PDF of the cwnd for a Simplified TCP 0.8 0.7 =1 0.6 The mth moment around the origin scales like -m/2, i.e., 0.5 =0.1 p(cwnd) 0.4 0.3 =0.05 =0.01 0.2 =0.005 0.1 C1 =1.3, C2 = 2.0, C3 = 3.5, C4 = 7.1, … 0 0 5 10 15 20 25 30 cwnd The median scales = 1.2/1/2

  6. Distribution of cwnd Cwnd is nearly distributed according to the negative binomial distribution Gamma function is factorial if argument is an integer Where: c1~sqrt(3/2) E(w²)-E(w)²=(γ/δ) γ≈0.3

  7. 1%

  8. 5% 10%

  9. Time-out model Rate of going to time-out =

  10. Timeout model If a retransmission is not dropped (only if 1 and 2 didn’t apply). Total rate of entering timeout is: = ’ + ’’

  11. Time-out . Let I₁(t), denote the rate that flows enter timeout at time t

  12. Time out prob

  13. Dynamics of cwnd if proper stochastic calculus is applied, the correct dynamics for the mean are Approximately: SDE gives Using:

  14. Models of slow-start are in the works

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