Steady state and scaling limit for a traffic congestion model

Ilie Grigorescu, Min Kang

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


In a general model (AIMD) of transmission control protocol (TCP) used in internet traffic congestion management, the time dependent data flow vector x(t) > 0 undergoes a biased random walk on two distinct scales. The amount of data of each component xi(t) goes up to xi(t)+a with probability 1-ζi(x) on a unit scale or down to γx i(t), 0 < γ < 1 with probability ζi(x) on a logarithmic scale, where ζi depends on the joint state of the system x. We investigate the long time behavior, mean field limit, and the one particle case. According to c = lim inf |X|→∞ ζl(x)1 the process drifts to ∞ in the subcritical c < c+(n, γ) case and has an invariant probability measure in the supercritical case c > c+(n, γ). Additionally, a scaling limit is proved when ζi(x) and a are of order N-1 and t → Nt, in the form of a continuum model with jump rate α(x).

Original languageEnglish (US)
Pages (from-to)271-285
Number of pages15
JournalESAIM - Probability and Statistics
Issue number4
StatePublished - Oct 29 2010


  • AIMD
  • Fluid limit
  • Mean field interaction
  • TCP

ASJC Scopus subject areas

  • Statistics and Probability


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