On the flow-level stability of data networks without congestion control: the case of linear networks and upstream trees

TL;DR

This paper analyzes the stability of data networks without congestion control, focusing on linear networks and upstream trees, using fluid limits and monotonic properties to derive stability bounds and asymptotic behavior.

Contribution

It provides new stability bounds for linear networks and demonstrates asymptotic maximization of stability regions in upstream trees as user access rates diminish.

Findings

Bounds on the stability region of linear networks.

Asymptotic maximization of stability in upstream trees.

Use of fluid limits and monotonic properties for analysis.

Abstract

In this paper, flow models of networks without congestion control are considered. Users generate data transfers according to some Poisson processes and transmit corresponding packet at a fixed rate equal to their access rate until the entire document is received at the destination; some erasure codes are used to make the transmission robust to packet losses. We study the stability of the stochastic process representing the number of active flows in two particular cases: linear networks and upstream trees. For the case of linear networks, we notably use fluid limits and an interesting phenomenon of "time scale separation" occurs. Bounds on the stability region of linear networks are given. For the case of upstream trees, underlying monotonic properties are used. Finally, the asymptotic stability of those processes is analyzed when the access rate of the users decreases to 0. An appropriate scaling is introduced and used to prove that the stability region of those networks is asymptotically maximized.