Asymptotic behavior of internet congestion controllers in a many-flows regime

Supratim Deb, Sanjay Shakkottai, R. Srikant

Research output: Contribution to journalReview article

Abstract

Congestion controllers for the Internet are typically designed based on deterministic delay differential equation models. In this paper, we consider the case of a single link accessed by many TCP-like congestion-controlled flows and uncontrolled flows that are modeled as stochastic disturbances. We show that if the number of flows is large and the link capacity is scaled in proportion to the number of users, then under appropriate conditions, the trajectory of the stochastic system is eventually well approximated by the trajectory of a delay-differential equation. Our analysis also throws light on the choice of various parameters that ensure global asymptotic stability of the limiting deterministic system in the presence of feedback delay. Numerical examples with some popular congestion feedback mechanisms validate the parameter choices from the analysis. The results indicate that a system with multiple TCP-like flows is globally stable (and thus, that a deterministic model is reasonable if the number of flows is large) as long as the product of the throughput and feedback delay per flow is not very small.

Original languageEnglish (US)
Pages (from-to)420-440
Number of pages21
JournalMathematics of Operations Research
Volume30
Issue number2
DOIs
StatePublished - May 1 2005

Fingerprint

Congestion
Asymptotic Behavior
Internet
Feedback
Controller
Controllers
Differential equations
Trajectories
Feedback Delay
Stochastic systems
Asymptotic stability
Delay Differential Equations
Throughput
Trajectory
Global Asymptotic Stability
Deterministic Model
Stochastic Systems
World Wide Web
Asymptotic behavior
Proportion

Keywords

  • Congestion controller
  • Delay-differential equations
  • Mean-flow behavior

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

Cite this

Asymptotic behavior of internet congestion controllers in a many-flows regime. / Deb, Supratim; Shakkottai, Sanjay; Srikant, R.

In: Mathematics of Operations Research, Vol. 30, No. 2, 01.05.2005, p. 420-440.

Research output: Contribution to journalReview article

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