Variance Estimation for Networking Congestion Avoidance Algorithm. - - PowerPoint PPT Presentation

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Variance Estimation for Networking Congestion Avoidance Algorithm. - - PowerPoint PPT Presentation

Variance Estimation for Networking Congestion Avoidance Algorithm. Olga I. Bogoiavlenskaia PetrSU, Department of Computer Science olbgvl@cs.karelia.ru TCP Congestion Control The paradigm of Distributed Control in Packet Switching Network


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SLIDE 1

Variance Estimation for Networking Congestion Avoidance Algorithm.

Olga I. Bogoiavlenskaia PetrSU, Department of Computer Science

  • lbgvl@cs.karelia.ru
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SLIDE 2

TCP Congestion Control

  • The paradigm of Distributed Control in Packet Switching Network
  • Transmission Control Program, 1974.
  • Congestion collapse
  • Variance not important yet

1

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SLIDE 3
  • S. Low tree

2

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SLIDE 4

Example of Tahoe Trajectory

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SLIDE 5

TCP Congestion Control Development

  • Jitter sensitive applications
  • TCP vs UDP
  • High BDP links utilization vs Congestion Control
  • Best effort vs QoS guarantees

4

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SLIDE 6

Variety of Experimental Versions

  • TCP CUBIC - cubical growth period. RTT independent
  • High Speed TCP (HSTCP), S. Floyd 2003. Congestion Avoidance
  • coeff. of linear growth and multiplicative decrease are convex functions
  • f current window size
  • Scalable TCP (STCP) T. Kelly, 2003. Decreases time of data recovery
  • H-TCP, Hamilton Institute, Ireland, 2004. Intended for links with

high BDP value. Uses RTT size to react on losses

  • TCP Hybla 2003-04. Developed for satellite links. Scales throughput

to mimic NewReno and utilize link at the same time.

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SLIDE 7

Variety of Experimental Versions

  • TCP Westwood, 2001. Tries to identify the reason behind losses.

Developed for wireless links.

  • TCP-Illinois uses dynamic function for defining Congestion Avoidance

parameters

  • TCP-LP (Low Priority)
  • TCP-YeAH

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SLIDE 8

TCP Variance

  • Why important?
  • A lot of models of average window size — Reno, NewReno, CUBIC
  • Asymptotic studies etc.
  • D. Towsley group for p > 0.025

T = MSS RTT

  • 2p

3 + RTOmin(1, 3

  • 3p

8 )p(1 + 32p2)

(1)

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SLIDE 9

TCP NewReno ’Saw’

wi

i+1

τ

w

α

t w(t)

w td td

i i+1 i i+1

τ

td i−1

’triple−duplicate’ periods

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SLIDE 10

Variance evaluation

  • Altman E., Avrachenkov K., Barakat C. A Stochastic model of TCP/IP

with Stationary Random Losses, Proceedings of ACM SIGCOMM’00. Stockholm, 2000. pp. 231-242.

  • Some ‘popular’ assumptions provide difficulties in estimating TCP

variance, e.g.

  • Variance is V ar[X] = E[X2] − (E[X]2)
  • Root square lows are derived thorough Goelders’s inequality i.e.

E[X] ≤

  • E[X2]

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SLIDE 11

Variance estimation

  • Using geometrical considerations one get from TCP ‘saw’

X2

n+1 = αX2 n + 2bSn,

  • Expanding, one gets

X2

k+n = 2b n

  • i=0

α2iSk+n−i

  • r
  • Xk+n =
  • 2b

n

  • i=0

α2iSk+n−i

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SLIDE 12

Variance estimation E[Xk+n] = E  

  • 2b

n

  • i=0

α2iSk+n−i   ≤ √ 2b

n

  • i=0

E

  • α2iSk+n−i
  • Now when n → ∞ one gets the following

E[X] = lim

n→∞ E[Xn] ≤ lim

√ 2b

n

  • i=0

E

  • α2iSi
  • =

√ 2b 1 − αE[

  • Sn]

For b = 1 and α = 1

2 and hence

E[X] ≤ 2 √ 2E[

  • Sn]

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SLIDE 13

Variance evaluation Now we have two estimations of sliding window size expectation

  • E[X] ≤ A =
  • 8

3E[S2 n]

  • E[X] ≤ B = 2

√ 2E[√Sn] Reminder. If B < A then it could be used for estimation variance V ar[X] ≤ A2 − B2. This holds if E[

  • Sn] <
  • E[Sn]

3 .

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SLIDE 14

Variance evaluation. Examples Lets p.d.f. of Sn is F(x) = 1 − eλx then E[Sn] = 1 λ and E[

  • Sn] =

√π 2

  • 1

λ. Condition does not hold.

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SLIDE 15

Variance evaluation. Examples. Lets p.d.f of Sn is Pierson root square distribution then its moments can be calculated through Γ-function and E[Sn] = 2

1 2Γ(n+1

2 )

Γ(n

2)

and E[

  • Sn] = 2

1 4Γ(2n+1

4 )

Γ(n

2) .

The result depends on parameter n. Condition holds for e.g. n = 10.

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SLIDE 16

Variance evaluation Notice that lim

n→∞ E[X2 n] = lim n→∞ E[X2 n+1]

and lim

n→∞ E[X2 n] = 2bE[Sn]

1 − α2 . Hence there might take place lim

n→∞ E[Xn] =

  • 2b

1 − α2E[

  • Sn].

GetTCP kernel level monitor for OS Linux

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SLIDE 17

Conclusion

  • The Development of Congestion Control schemes is considered
  • The importance of TCP variance evaluation is demonstrated
  • Possible approaches to the problem are analyzed
  • Variance estimation is proposed

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