POINT PROCESS MODELS OF 1f NOISE AND INTERNET TRAFFIC V' Gontis, B' Kaulakys and J' Ruseckas, Instit

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POINT PROCESS MODELS OF 1/f NOISE AND INTERNET
TRAFFIC V. Gontis, B. Kaulakys and J.
Ruseckas, Institute of Theoretical Physics and
Astronomy,Vilnius University,gontis_at_ktl.mii.lt
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Complexity, 1/f noise, fractals and computer
networks

• 1/f noise - characteristic signature of
  complexity in computer networks ?
• Point process as natural approach modeling
  network traffics
• Stochastic point process models exhibiting 1/f
  noise and fractality
• Power-law requests explain self similar
  statistics of computer networks

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The power spectrum of the router network traffic,
measurement data http//www.doc.ic.ac.uk/uh/QUA
INT/data/A.J. Field, Uli Harder, P.G. Harrison,
Network Traffic Behaviour in Switched Ethernet
Systems, AESOP.
S(f)1/f ß ß1
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Signal as stochastic sequence of pulses
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Pulses with variable duration
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Power spectral density
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Fractal (power-law) stochastic processes
Physics resistors, semiconductors, vacuum
tubes, photon-counting .. Biomedicine
neurotransmitters, heartbeat dynamics, Social
systems financial markets, traffics, network
models .. Geophysics earthquakes . Elsewhere
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Stochastic models of interevent time

• Poisson processes
• Fractal renewal processes
• Autoregressive conditional duration (ACD)
  processes
• Recurrent stochastic point processes

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Stochastic point processes with autoregressive
interevent time
B. Kaulakys and T. Meskauskas, Phys. Rev. E 58
(1998) 7013-7019

.
B. Kaulakys, J. Ruseckas, PHYSICAL REVIEW E 70,
020101(R) (2004)
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Multiplicative point process
V. Gontis, B. Kaulakys, PHYSICA A, (2004)
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Numerical power spectral density of the
multiplicative point process
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Sequence of pulses with stochastic duration
Uncorrelated pulses
J.Ruseckas, B. Kaulakys, M. Alaburda, Lithuanian
Journal of Physics, Vol. 43, No.4, pp. 223-228
(2003)
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Modeling computer network traffic
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Comparison with empirical data
http//www.doc.ic.ac.uk/uh/QUAINT/data/
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Conclusions

• We introduced few stochastic point processes
  with non Poisson interevent time statistics
• Analytical and numerical results confirm power
  law behavior in several statistics and serve as a
  generic models of 1/f noise
• Our modeling confirm that power-law distribution
  of Web requests is responsible for the self
  similar statistics of computer network traffics