English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we analyze some local stability and local bifurcationproperties of the Proportionally fair, TCP fair, and the Delay-based dualalgorithms in the presence of two distinct time delays. In particular, ourfocus is on the interplay between different notions of fairness, stability, andbifurcation theoretic properties. Different notions of fairness give rise todifferent non-linear models for the class of Dual algorithms. One can deviseconditions for local stability, for each of these models, but such conditionsdo not offer clear design recommendations on which fairness criteria isdesirable. With a bifurcation-theoretic analysis, we have to take non-linearterms into consideration, which helps to learn additional dynamical propertiesof the various systems. In the case of TCP fair and Delay dual algorithms, withtwo delays, we present evidence that they can undergo a sub-critical Hopfbifurcation, which has not been previously revealed through analysis of thesingle delay variants of these algorithms. A sub-critical Hopf bifurcation canresult in either large amplitude limit cycles or unstable limit cycles, andhence should be avoided in engineering applications. In the case of theProportionally fair algorithm, we provide strong evidence to suggest that allone should expect is the occurrence of a super-critical Hopf bifurcation, whichleads to stable limit cycles with small amplitude. Thus, from a designperspective, our analysis favors the use of Proportional fairness in the classof dual congestion control algorithms. To best of our knowledge, this is thefirst study that presents evidence to suggest that fluid models representingInternet congestion control algorithms may undergo a sub-critical Hopfbifurcation.

Stability and non-linear dynamics of Dual congestion control schemes with two delays