Critical scale for a continuous AIMD model

Ilie Grigorescu, Min Kang

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

A scaled version of the general AIMD model of transmission control protocol (TCP) used in Internet traffic congestion management leads to a Markov process x(t) representing the time dependent data flow that moves forward with constant speed on the positive axis and jumps backward to γx(t), 0 <γ <1 according to a Poisson clock whose rate α(x) depends on the interval swept in between jumps. We give sharp conditions for Harris recurrence and analyze the convergence to equilibrium on multiple scales (polynomial, fractional exponential, exponential) identifying the critical case xα(x) ∼ β. Criticality has different behavior according to whether it occurs at the origin or infinity. In each case, we determine the transient (possibly explosive), null-and positive-recurrent regimes by comparing β to (-ln γ)-1.

Original languageEnglish (US)
Pages (from-to)319-343
Number of pages25
JournalStochastic Models
Volume30
Issue number3
DOIs
StatePublished - Jul 3 2014

Fingerprint

Transmission control protocol
Traffic congestion
Markov processes
Clocks
Harris Recurrence
Jump
Fractional Polynomials
Polynomials
Internet
Convergence to Equilibrium
Internet Traffic
Traffic Congestion
Multiple Scales
Critical Case
Dependent Data
Criticality
Sweep
Data Flow
Markov Process
Null

Keywords

  • AIMD
  • Criticality
  • Geometric ergodicity
  • Harris recurrence
  • Local Doeblin condition
  • TCP

ASJC Scopus subject areas

  • Modeling and Simulation
  • Statistics and Probability
  • Applied Mathematics

Cite this

Critical scale for a continuous AIMD model. / Grigorescu, Ilie; Kang, Min.

In: Stochastic Models, Vol. 30, No. 3, 03.07.2014, p. 319-343.

Research output: Contribution to journalArticle

Grigorescu, Ilie ; Kang, Min. / Critical scale for a continuous AIMD model. In: Stochastic Models. 2014 ; Vol. 30, No. 3. pp. 319-343.
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