Flow-level models for multipath routing

TL;DR

This paper analyzes flow-level models for multipath routing in networks with route length one, exploring static and dynamic cases, identifying clustering patterns, and studying equilibrium and diffusion limits to understand network behavior.

Contribution

It introduces a clustering pattern in rate allocation, provides an explicit algorithm for static cases, and analyzes equilibrium and diffusion limits in dynamic models with stochastic flows.

Findings

Clustering pattern in rate allocation identified.

Explicit algorithm for static rate allocation.

Uniqueness of equilibrium point established.

Abstract

In this paper we study coordinated multipath routing at the flow-level in networks with routes of length one. As a first step the static case is considered, in which the number of flows is fixed. A clustering pattern in the rate allocation is identified, and we describe a finite algorithm to find this rate allocation and the clustering explicitly. Then we consider the dynamic model, in which there are stochastic arrivals and departures; we do so for models with both streaming and elastic traffic, and where a peak-rate is imposed on the elastic flows (to be thought of as an access rate). Lacking explicit expressions for the equilibrium distribution of the Markov process under consideration, we study its fluid and diffusion limits; in particular, we prove uniqueness of the equilibrium point. We demonstrate through a specific example how the diffusion limit can be identified; it also reveals structural results about the clustering pattern when the minimal rate is very small and the network grows large.