Open Multi-Agent Systems with Variable Size: the Case of Gossiping
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We consider open multi-agent systems, which are systems subject to frequent arrivals and departures of agents while the process studied takes place. We study the behavior of all-to-all pairwise gossip interactions in such open systems. Arrivals and departures of agents imply that the composition and size of the system evolve with time, and in particular prevent convergence. We describe the expected behavior of the system by showing that the evolution of scale-independent quantities can be characterized exactly by a fixed size linear dynamical system. We apply this approach to characterize the evolution of the two first moments (and thus also of the variance) for open systems of both fixed and variable size. Our approach is based on the continuous time modelling of random asynchronous events, namely gossip steps, arrivals, departures, and replacements.
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