In this letter, the probability of reaching consensus in wireless multi-agent systems (WMASs) is introduced. Starting with the connectivity probability of random graphs, and considering link outages between agents, we obtain the probability expression that a WMAS with ${N}$ agents reaches consensus. We validate the obtained exact expression via simulation results. Furthermore, we show that the corresponding diversity order is N −1, hence increasing the number of agents will contribute towards the likelihood of consensus, despite the increased communication need between each agent. Finally, we observe that the consensus speed is highly dependent on the signal-to-noise ratio (SNR) level and the number of agents in a WMAS.

中文翻译：

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衰落信道上无线多代理系统的共识分析

在这封信中，介绍了在无线多代理系统 (WMAS) 中达成共识的概率。从随机图的连通性概率开始，并考虑代理之间的链接中断，我们获得了 WMAS 的概率表达式 ${N}$ 代理达成共识。我们通过仿真结果验证了获得的精确表达式。此外，我们表明相应的分集顺序是N-1，因此增加代理的数量将有助于达成共识的可能性，尽管每个代理之间的通信需求增加。最后，我们观察到共识速度高度依赖于信噪比 (SNR) 水平和 WMAS 中的代理数量。