Open Multi-Agent Systems: Gossiping with Random Arrivals and Departures

TL;DR

This paper studies open multi-agent systems where agents randomly join or leave, analyzing how their interactions lead to evolving average states, modeled through a linear dynamical system, with applications to fixed and growing system sizes.

Contribution

It introduces a novel framework for analyzing open multi-agent systems with random arrivals and departures using scaled moments and linear dynamical systems.

Findings

Expected system behavior characterized by a 2D linear dynamical system

Applicable to systems with fixed size and unbounded growth

Provides insights into non-convergent dynamics of open systems

Abstract

We consider open multi-agent systems. Unlike the systems usually studied in the literature, here agents may join or leave while the process studied takes place. The system composition and size evolve thus with time. We focus here on systems where the interactions between agents lead to pairwise gossip averages, and where agents either arrive or are replaced at random times. These events prevent any convergence of the system. Instead, we describe the expected system behavior by showing that the evolution of scaled moments of the state can be characterized by a 2-dimensional (possibly time-varying) linear dynamical system. We apply this technique to two cases : (i) systems with fixed size where leaving agents are immediately replaced, and (ii) systems where new agents keep arriving without ever leaving, and whose size grows thus unbounded.