The stable configuration in acyclic preference-based systems

TL;DR

This paper analyzes the stable configurations of acyclic preference-based systems, providing statistical insights and analytical models for different classes, which helps in understanding their performance in distributed systems.

Contribution

It introduces the statistical properties and analytical models of stable configurations in three classes of acyclic preferences, enhancing understanding of system performance.

Findings

Stable configurations have an asymptotically continuous independent rank distribution.

Analytical solutions match well with simulations.

Results validate performance modeling of unstructured systems.

Abstract

Acyclic preferences recently appeared as an elegant way to model many distributed systems. An acyclic instance admits a unique stable configuration, which can reveal the performance of the system. In this paper, we give the statistical properties of the stable configuration for three classes of acyclic preferences: node-based preferences, distance-based preferences, and random acyclic systems. Using random overlay graphs, we prove using mean-field and fluid-limit techniques that these systems have an asymptotically continuous independent rank distribution for a proper scaling, and the analytical solution is compared to simulations. These results provide a theoretical ground for validating the performance of bandwidth-based or proximity-based unstructured systems.