-The MMPP/D/2/K System

1
-The MMPP/D/2/K System

• Steven Pilarski

2
Contents

• Introduction
• Examples for source modelling with Petri Nets
• The MMPP/D/2/K system
• How it works
• Token game with Danamics
• Important performance results
• Own results of the MMPP system computed with
  Sharpe
• Conclusion
• References

3
Source Models with Petri Nets

• Some examples
• Poisson source
• (Markov)1
• ON/OFF source
• (IPP)2

1,2 Stochastische Netze 1, Prof.Dr.
Müller-Clostermann (http//www.informatik.uni-esse
n.de/SysMod/lehre/SN/)
4
MMPP/D/2/K Model as a DSPN
Source
Buffer/Mux
Operators
http//www.dspnexpress.de/
5
Values

• Given
• Duration of bursty mode and normal mode are
• Average arrival rate
• Searched
• With these values and a burst factor B we can
  compute the necessary ?s (Bursty_Arrival and
  Normal_Arrival)

6
Some Performance Results

• It is interesting to see how the loss probability
  behaves when the buffer size or/and burst factor
  are increasing/decreasing

3,4 Thümler, Axel Stochastic Modeling and
Analysis of 3G Mobile Communication Systems
(http//eldorado.uni-dortmund.de8080/FB4/ls4/fors
chung/2003/Thuemmler/Thuemmlerunt.pdf
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Some Sharpe results (1)

• Restrictions
• With Sharpe it is not possible to model
  deterministic SPNs (only GSPNs), beause of that
  the service rates are neg.ex. distributed

Burst_Factor Loss_Probability bei K100 Loss_Probability K200 Loss_Probability K300 Loss_Probability K500
B1 0 0 0 0
B10 0 0 0 0
B25 1,36E-09 0 0 0
B50 0,00000061 3,6E-11 0 0
B100 0,0000338 0,000000152 6E-10 0
B200 0,000276 0,00000845 0,00000026 2,45E-10
B300 0,00052 0,0000301 0,00000185 6,7E-09
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Some Sharpe results (2)-Burst Factor vs. Buffer
Size

Loss Probability
Burst Factor
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Conclusion

• Burst traffic influences loss probability
  enormously
• Big buffers can help to avoid these problems, but
  they (can) offer other problems too
• Increasing of Jitter and End-to-End delay
  (important for VoIP e.g.)
• Buffers are expensive
• Fast memory is necessary
• Queuing algorithms are complex, particularly if
  priorities have to be implemented (e.g. Fair
  Queuing, Loss Priorities)
• But without or too little buffer, packet loss can
  grow about all limits and service level
  agreements are hard to keep
• E.g. Typical values for cell loss in ATM are in
  the range of 10-8 to 10-10!!

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References

• MMPP/D/2/K System
• http//mobicom.cs.uni-dortmund.de/gsmp/DSPN/mmppd2
  k/mmppd2k.html
• Thümmler, Axel
• Stochastic Modeling and Analysis of 3G Mobile
  Communication Systems (http//eldorado.uni-dortmu
  nd.de8080/FB4/ls4/forschung/2003/Thuemmler/Thuemm
  lerunt.pdf)
• Müller-Clostermann, Bruno
• Stochstische Netze 1, Modelle der Informatik
  (http//www.informatik.uni-essen.de/SysMod/lehre/i
  ndex.html)
• Rathgeb, Erwin
• Hochgeschwindigkeitsnetze (http//tdrwww.exp-math.
  uni-essen.de/index2.php)
• Sharpe
• http//www.ee.duke.edu/chirel/IRISA/sharpeGui.htm
  l
• Danamics
• http//www.cs.uct.ac.za/Research/DNA/DaNAMiCS/