Corrective consensus with asymmetric wireless links

Consensus algorithms can be used to compute an average value across a multi-hop network in a distributed way. However, their convergence to the right value is not guaranteed in the presence of random packet losses that are common in real life low-power wireless networks. Corrective consensus solves this problem by using a set of auxiliary variables to compensate for the asymmetric state updates caused by packet losses. Nevertheless, one key assumption is that the probability of delivering a packet from node i to a neighboring node j is the same as in the reverse direction, from j to i. This assumption might be violated in real life conditions. Our main contribution is showing that corrective consensus converges to the correct average even when this assumption is removed. In addition, we provide a heuristic for modifying the weights used by corrective consensus that specifically considers the unequal probabilities, and we empirically show that this choice can lead to faster convergence.