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