Consistency , Availability , and Convergence

We examine the limits of consistency in highly available and fault-tolerant distributed storage systems. We introduce a new property—convergence—to explore the these limits in a useful manner. Like consistency and availability, convergence formalizes a fundamental requirement of a storage system: writes by one correct node must eventually become observable to other connected correct nodes. Using convergence as our driving force, we make two additional contributions. First, we close the gap between what is known to be impossible (i.e. the consistency, availability, and partition-tolerance theorem) and known systems that are highly-available but that provide weaker consistency such as causal. Specifically, in an asynchronous system, we show that natural causal consistency, a strengthening of causal consistency that respects the real-time ordering of operations, provides a tight bound on consistency semantics that can be enforced without compromising availability and convergence. In an asynchronous system with Byzantine-failures, we show that it is impossible to implement many of the recently introduced forking-based consistency semantics without sacrificing either availability or convergence. Finally, we show that it is not necessary to compromise availability or convergence by showing that there exist practically useful semantics that are enforceable by available, convergent, and Byzantine-fault tolerant systems.