Best-effort networks: modeling and performance analysis via large networks asymptotics

TL;DR

This paper models best-effort data networks using Markov models and analyzes their performance through mean field techniques, providing insights into how traffic and topology affect transfer times in large symmetrical networks.

Contribution

It introduces the best-effort network class and the min bandwidth sharing policy, deriving ergodicity conditions and fixed point equations for large network performance analysis.

Findings

Derived conditions for network stability.

Established fixed point equations for large networks.

Analyzed impact of traffic and topology on transfer times.

Abstract

In this paper we introduce a class of Markov models, termed best-effort networks, designed to capture performance indices such as mean transfer times in data networks with best-effort service. We introduce the so-called min bandwidth sharing policy as a conservative approximation to the classical max-min policy. We establish necessary and sufficient ergodicity conditions for best-effort networks under the min policy. We then resort to the mean field technique of statistical physics to analyze network performance deriving fixed point equations for the stationary distribution of large symmetrical best-effort networks. A specific instance of such net- works is the star-shaped network which constitutes a plausible model of a network with an overprovisioned backbone. Numerical and analytical study of the equations allows us to state a number of qualitative conclusions on the impact of traffic parameters (link loads) and topology parameters (route lengths) on mean document transfer time.