Modern distributed systems rely on consensus protocols to build a fault-tolerant-core upon which they can build applications. Consensus protocols are correct under a specific failure model, where up to f machines can fail. We argue that this f -threshold failure model oversimplifies the real world and limits potential opportunities to optimize for cost or performance. We argue instead for a probabilistic failure model that captures the complex and nuanced nature of faults observed in practice. Probabilistic consensus protocols can explicitly leverage individual machine failure curves and explore side-stepping traditional bottlenecks such as majority quorum intersection, enabling systems that are more reliable, efficient, cost-effective, and sustainable.

We consider the problem of simulating a k-valued register in a wait-free manner using binary registers as building blocks, where k 2. We show that for any simulation using atomic binary base registers to simulate a safe k-valued register in which the read algorithm takes the optimal number of steps (log2 k), the write algorithm must take at least log2 k steps in the worst case. A fortiori, the same lower bound applies when the simulated register should be regular. Previously known algorithms show that both these lower bounds are tight. We also show that in order to simulate an atomic k-valued register for two readers, the optimal number of steps for the read algorithm must be strictly larger than log2 k.

In this paper we show a tight closed-form expression for the optimal clock synchronization in k-ary m-cubes with wraparound, where k is odd. This is done by proving a lower bound of 1/4um (k-1/k), where k is the (odd) number of processes in each of the m dimensions, and u is the uncertainty in delay on every link. Our lower bound matches the previously known upper bound.