DASMOD Summer School Lecture Series

Rolf Riedi: "Stochastic Systems and Control in Networking and Finance"

Course Structure

• 3 (4) double lectures on network traffic and multiscale models
• 1 double lecture on financial data
• (1) double lecture on cascade models

Schedule

This lecture series takes place in the second week of the DASMOD Summer School.

Mo 1+2 Communication Networks at Large Scales

• Failure of classical queueing models for communication networks
  • failure of Poisson and Markov [Paxson, Floyd]
• Long-range dependence [Willinger, Taqqu]
• Stochastic modeling of large scale behavior
• ON-OFF-source model ("classical")
  • fractal limit FBM (parsimonious statistical model)
• Physical explanation
  • Long-range dependence and user behavior,
  • Heavy tails on the web [Crovella]

[FBM=Fractional Brownian Motion]

Tu 1+2 Communication Networks at Small Scales

• Non-Gaussian Burstiness and Conspiracy [work with Sarvotham]
  • failure of the classical on-off-model
• multifractal limit: MWM (parsimonious statistical model) [work with Baraniuk, Crouse]
• Physical explanation
  • Burstiness and network heterogeneity,
  • Network-user driven ON-OFF-model [work with Sarvotham]

[MWM=Multiplicative Wavelet Model]

We 1+2 Stochastic Control for Communication Networks

• self-similar traffic: bandwidth-buffer-rule
• Large Deviations: fractal queuing [Norros, Duffield]
• Multiscale Queueing Theory
  • non-asymptotic bounds
  • optimality of exponential time scales [work with Ribeiro]
• bandwidth inference,
  • pathChirp
  • locating bottlenecks in space and time
    • STAB = space-time available bandwidth [work with Ribeiro]
• Optimal sampling of multiscale processes [work with Ribeiro]

Th 1+2 Multiscale Phenomena in Financial Data

• LRD and self-similarity in financial data [Mandelbrot, Evertsz]
• fractal models in finance
  • FBM
  • Cascades, MRW, IDC
  • BM(MFT)
    • trading clock is multifractal

Fr 1+2 Multiscale processes

• Multiplicative cascades
  • beyond powerlaws
• self-similar processes
• Trading in multifractal time

Lecture Notes (pdf)

• Capturing Network Traffic Dynamics I: Large Scales
• Capturing Network Traffic Dynamics II: Small Scales
• Capturing Dynamics III: Trees, Wavelets and Large Deviations
• Capturing Network Traffic Dynamics IV: Using the Tools
• Capturing Market Dynamics