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

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