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We derive fundamental limitations on the performances of intrinsic averagingalgorithms in open multi-agent systems, which are systems subject to randomarrivals and departures of agents. Each agent holds a value, and their goal isto estimate the average of the values of the agents presently in the system. Weprovide a lower bound on the expected Mean Square Error for any estimationalgorithm, assuming that the number of agents remains constant and thatcommunications are random and pairwise. Our derivation is based on the expectederror obtained with an optimal algorithm under conditions more favorable thanthose the actual problem allows, and relies on an analysis of the constraintson the information spreading mechanisms in the system, and relaxations ofthese.

Lower bound performances for average consensus in open multi-agent systems (extended version)