Stability Properties of Networks with Interacting TCP Flows

TL;DR

This paper analyzes the equilibrium distributions of a Markovian network model with interacting TCP flows, focusing on fixed point equations for different network topologies like rings, trees, and linear networks.

Contribution

It studies specific fixed point equations for various network topologies, extending understanding of TCP flow interactions in complex networks.

Findings

Invariant distributions are determined by fixed point solutions.

Examples include rings, trees, and linear network topologies.

The model captures self-adaptive TCP behavior based on congestion levels.

Abstract

The equilibrium distributions of a Markovian model describing the interaction of several classes of permanent connections in a network are analyzed. It has been introduced by Graham and Robert. For this model each of the connections has a self-adaptive behavior in that its transmission rate along its route depends on the level of congestion of the nodes on its route. It has been shown that the invariant distributions are determined by the solutions of a fixed point equation in a finite dimensional space. In this paper, several examples of these fixed point equations are studied. The topologies investigated are rings, trees and a linear network, with various sets of routes through the nodes.