Large-scale distributed synchronization systems, using a cancel-on-completion redundancy mechanism

TL;DR

This paper analyzes large-scale multi-agent synchronization systems with cancel-on-completion redundancy, extending previous models to include various boundary regulations, and studies their mean-field limits, fixed points, and steady-state behaviors.

Contribution

It generalizes existing particle system models by incorporating flexible boundary regulation and provides a unified analysis of mean-field limits and steady-state properties.

Findings

Existence and uniqueness of mean-field fixed points.

Conditions for steady-state asymptotic independence.

Limits of average velocity in unregulated systems.

Abstract

We consider a class of multi-agent distributed synchronization systems, which are modeled as $n$ particles moving on the real line. This class generalizes the model of a multi-server queueing system, considered in [15], employing so-called cancel-on-completion (c.o.c.) redundancy mechanism, but is motivated by other applications as well. The model in [15] is a particle system, regulated at the left boundary point. The more general model of this paper is such that we allow regulation boundaries on either side, or both sides, or no regulation at all. We consider the mean-field asymptotic regime, when the number of particles $n$ and the job arrival rates go to infinity, while the job arrival rates per particle remain constant. The system state for a given $n$ is the empirical distribution of the particles' locations. The results include: the existence/uniqueness of fixed points of mean-field limits (ML), which describe the limiting dynamics of the system; conditions for the steady-state asymptotic independence (concentration of the stationary distribution on a single ML fixed point); the limits of the average velocity at which unregulated (free) particle system advances. In particular, our results for the left-regulated system unify and generalize the corresponding results in [15]. Our technical approach is such that the systems with different types of regulation are analyzed within a unified framework.