Stability analysis of a max-min fair Rate Control Protocol (RCP) in a small buffer regime

TL;DR

This paper analyzes the stability of the max-min fair Rate Control Protocol with small buffers, providing conditions for global and local stability in various network configurations and examining bifurcations in simple models.

Contribution

It offers new stability conditions for max-min fair RCP in networks with arbitrary topologies and delays, including bifurcation analysis in simplified models.

Findings

Global stability without delays in arbitrary topologies.

Conditions for local stability with heterogeneous delays.

Identification of Hopf bifurcation in single link, single delay model.

Abstract

In this note we analyse various stability properties of the max-min fair Rate Control Protocol (RCP) operating with small buffers. We first tackle the issue of stability for networks with arbitrary topologies. We prove that the max-min fair RCP fluid model is globally stable in the absence of propagation delays, and also derive a set of conditions for local stability when arbitrary heterogeneous propagation delays are present. The network delay stability result assumes that, at equilibrium, there is only one bottleneck link along each route. Lastly, in the simpler setting of a single link, single delay model, we investigate the impact of the loss of local stability via a Hopf bifurcation.