Global Stability Analysis for an Internet Congestion Control Model with a Time-Varying Link Capacity

TL;DR

This paper provides a global stability analysis for a rate-based internet congestion control model with a time-varying link capacity, establishing conditions for stability despite delays and capacity fluctuations.

Contribution

It introduces delay-independent stability conditions for a nonlinear delay differential equation model of congestion control with variable link capacity.

Findings

Global asymptotic stability is guaranteed under certain parameter conditions.

The stability conditions are independent of delays.

Numerical simulations confirm the theoretical stability results.

Abstract

In this paper, a global stability analysis is given for a rate-based congestion control system modeled by a nonlinear delayed differential equation. The model determines the dynamics of a single-source single-link network, with a time-varying capacity of link and a fixed communication delay. We obtain a sufficient delay-independent conditions on system parameters under which global asymptotic stability of the system is guarantied. The proof is based on an extension of Lyapunov-Krasovskii theorem for a class of nonlinear time-delay systems. The numerical simulations for a typical scenario justify the theoretical results.