A System Theoretic Approach to Bandwidth Estimation

TL;DR

This paper introduces a system theoretic framework for bandwidth estimation in packet networks using min-plus algebra and network calculus, providing a mathematical basis and experimental validation for existing methods.

Contribution

It formalizes bandwidth estimation within min-plus linear system theory, linking it to network calculus, and demonstrates practical robustness through Emulab experiments.

Findings

Existing methods can be derived using min-plus algebra.

Probing is most informative at the linear to non-linear transition.

Multi-node experiments show effective link-to-path bandwidth estimation.

Abstract

It is shown that bandwidth estimation in packet networks can be viewed in terms of min-plus linear system theory. The available bandwidth of a link or complete path is expressed in terms of a {\em service curve}, which is a function that appears in the network calculus to express the service available to a traffic flow. The service curve is estimated based on measurements of a sequence of probing packets or passive measurements of a sample path of arrivals. It is shown that existing bandwidth estimation methods can be derived in the min-plus algebra of the network calculus, thus providing further mathematical justification for these methods. Principal difficulties of estimating available bandwidth from measurement of network probes are related to potential non-linearities of the underlying network. When networks are viewed as systems that operate either in a linear or in a non-linear regime, it is argued that probing schemes extract the most information at a point when the network crosses from a linear to a non-linear regime. Experiments on the Emulab testbed at the University of Utah evaluate the robustness of the system theoretic interpretation of networks in practice. Multi-node experiments evaluate how well the convolution operation of the min-plus algebra provides estimates for the available bandwidth of a path from estimates of individual links.