Probabilistic Analysis of Disagreement in Synchronous Consensus Protocols (Preliminary draft)

This report presents a probabilistic analysis of a family of simple synchronous round-based consensus algorithms aimed at solving the 1-of-n selection problem. In this problem, a set of n nodes are to select one common value among a set of n proposed values. There are two possible outcomes of each node’s selection process: it can decide either to select a value, or to abort. Agreement implies that all nodes select the same value, or all nodes decide to abort. We analyse this problem under the assumption of massive communication failures considering symmetric and asymmetric message losses. Previous research has shown that it is impossible to guarantee agreement among the nodes in a synchronous system subjected to an unbounded number of message losses. Our aim is to find algorithms for which the probability of disagreement is as low as possible. To this end, we study how the probability of disagreement varies for three different decision criteria, the optimistic, pessimistic and the moderately pessimistic. Our results show that that the probability of disagreement varies significantly with the number of nodes, the number of rounds, and the probability of message loss. In general, the optimistic decision criterion performs better (has a lower probability of disagreement) than the pessimistic one when the probability of message loss is less than 30% to 70%. On the other hand, the optimistic decision criterion has in general a higher maximum probability of disagreement compared to the pessimistic decision criterion. Moreover we show that the outcome of the moderately pessimistic decision criterion generally lies in between the two other decision criteria.