# Steady state and scaling limit for a traffic congestion model

ESAIM: Probability and Statistics (2010)

- Volume: 14, page 271-285
- ISSN: 1292-8100

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topGrigorescu, Ilie, and Kang, Min. "Steady state and scaling limit for a traffic congestion model." ESAIM: Probability and Statistics 14 (2010): 271-285. <http://eudml.org/doc/250828>.

@article{Grigorescu2010,

abstract = {
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 γxi(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|→∞ |x|ζi(x)
, 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).
},

author = {Grigorescu, Ilie, Kang, Min},

journal = {ESAIM: Probability and Statistics},

keywords = {TCP; AIMD; fluid limit; mean field interaction; invariant measures; scaling limit},

language = {eng},

month = {10},

pages = {271-285},

publisher = {EDP Sciences},

title = {Steady state and scaling limit for a traffic congestion model},

url = {http://eudml.org/doc/250828},

volume = {14},

year = {2010},

}

TY - JOUR

AU - Grigorescu, Ilie

AU - Kang, Min

TI - Steady state and scaling limit for a traffic congestion model

JO - ESAIM: Probability and Statistics

DA - 2010/10//

PB - EDP Sciences

VL - 14

SP - 271

EP - 285

AB -
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 γxi(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|→∞ |x|ζi(x)
, 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).

LA - eng

KW - TCP; AIMD; fluid limit; mean field interaction; invariant measures; scaling limit

UR - http://eudml.org/doc/250828

ER -

## References

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