Distributed averaging is among the most relevant cooperative control problems, with applications in sensor and robotic networks, distributed signal processing, data fusion, and load balancing. Consensus and gossip algorithms have been investigated and successfully deployed in multi-agent systems to perform distributed averaging in synchronous and asynchronous settings. This study proposes a heuristic approach to estimate the convergence rate of averaging algorithms in a distributed manner, relying on the computation and propagation of local graph metrics while entailing simple data elaboration and small message passing. The protocol enables nodes to predict the time (or the number of interactions) needed to estimate the global average with the desired accuracy. Consequently, nodes can make informed decisions on their use of measured and estimated data while gaining awareness of the global structure of the network, as well as their role in it. The study presents relevant applications to outliers identification and performance evaluation in switching topologies.

翻译：分布式平均是最重要的协同控制问题之一，其在传感器网络、机器人网络、分布式信号处理、数据融合及负载均衡等领域具有广泛应用。一致性与闲聊算法已在多智能体系统中得到深入研究并成功部署，可在同步和异步场景下实现分布式平均。本研究提出一种启发式方法，通过计算和传播局部图度量指标，以分布式方式估计平均算法的收敛速度，同时仅需简单的数据处理和少量消息传递。该协议使节点能够预测达到所需精度全局平均值所需的时间（或交互次数）。因此，节点可在利用测量与估计数据时做出明智决策，同时获知网络的全局结构及其在其中的角色。本研究将相关方法应用于切换拓扑下的异常值识别与性能评估。