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.

中文翻译：

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可变大小的开放多代理系统：八卦案例

我们考虑开放的多代理系统，这些系统在所研究的过程发生时会受到代理频繁到达和离开的影响。我们研究了这种开放系统中多对多成对八卦交互的行为。代理的到达和离开意味着系统的组成和大小随时间演变，特别是防止收敛。我们通过展示与尺度无关的量的演化可以通过固定大小的线性动力系统精确表征来描述系统的预期行为。我们应用这种方法来表征固定和可变大小的开放系统的两个第一矩（以及方差）的演变。我们的方法基于随机异步事件的连续时间建模，即八卦步骤、到达、离开、