Fluid Limits for Bandwidth-Sharing Networks with Rate Constraints

TL;DR

This paper extends fluid limit models for bandwidth-sharing networks by allowing general distributions for interarrival, flow sizes, and abandonment times, and introduces polynomial-time fixed-point approximations for their stationary distributions.

Contribution

It generalizes previous models by relaxing distributional assumptions and develops efficient methods for approximating stationary behaviors.

Findings

Extended fluid approximation to general distributions.

Developed polynomial-time fixed-point algorithms.

Provided new techniques for stationary distribution analysis.

Abstract

Bandwidth-sharing networks as introduced by Massouli\'e & Roberts (1998) model the dynamic interaction among an evolving population of elastic flows competing for several links. With policies based on optimization procedures, such models are of interest both from a Queueing Theory and Operations Research perspective. In the present paper, we focus on bandwidth-sharing networks with capacities and arrival rates of a large order of magnitude compared to transfer rates of individual flows. This regime is standard in practice. In particular, we extend previous work by Reed & Zwart (2010) on fluid approximations for such networks: we allow interarrival times, flow sizes and patient times (i.e. abandonment times measured from the arrival epochs) to be generally distributed, rather than exponentially distributed. We also develop polynomial-time computable fixed-point approximations for stationary distributions of bandwidth-sharing networks, and suggest new techniques for deriving these types of results.