Evaluations of Stateful NMR with Byzantine Failures

Abstract

NMR (N-Modular Redundancy) is a well-known fault tolerance technique. In NMR, if the majority of modules are normal, failures can be masked. However, if the number of normal modules is less than half, it cannot mask failures. Previously, we proposed Stateful NMR to solve this problem. In Stateful NMR, if at least one normal module exists, it can mask failures. This method operates correctly only if more than one module does not fail simultaneously. To relax this constraint, we proposed Reset table Stateful NMR, where the state of a module is reset manually when possible. As a result, Reset table Stateful NMR always reflects the correct state. However, these evaluations were based on stuck failures, one of two kinds of failures in the real world, with the other being Byzantine failures. In this paper, we evaluate our proposed fault tolerance methods with respect to Byzantine failures. Based on the results of the evaluations, we conclude that the fault tolerance of Reset table Stateful NMR is almost equal to that of NMR, whereas Stateful NMR is not effective with Byzantine failures.