The optimal strategy for the average long-lived consensus

Abstract

Consider a system composed of n sensors operating in synchronous rounds. In each round an input vector of sensor readings x is produced, where the r-th entry of x is a value, selected in a finite set of potential values, produced by the r-th sensor. The sequence of input vectors is assumed to be smooth: exactly one entry of the vector changes from one round to the next one. The system implements a fault-tolerant averaging consensus function f. This function returns, in each round, a representative output value v of the sensor readings x. Assuming there are a + 1 equal entries of the vector, f is required to return a value that appears at least a + 1 times in x. We study strategies that minimize the instability of a fault-tolerant consensus system. More precisely, we find the strategy that minimizes, in average, the frequency of output changes over a random walk sequence on input vectors (where each component of the vector corresponds to a particular sensor reading). © 2011 Springer-Verlag Berlin Heidelberg.