Exploiting Omissive Faults in Synchronous Approximate Agreement

ÐIn a fault-tolerant distributed system, it is often necessary for nonfaulty processes to agree on the value of a shared data item. The criterion of Approximate Agreement does not require processes to achieve exact agreement on a value; rather, they need only agree to within a predefined numerical tolerance. Approximate Agreement can be achieved through convergent voting algorithms. Previous research has studied convergent voting algorithms under mixed-mode or hybrid fault models, such as the Thambidurai and Park Hybrid fault model, comprised of three fault modes: asymmetric, symmetric, and benign. This paper makes three major contributions to the state of the art in fault-tolerant convergent voting. 1) We partition both the asymmetric and symmetric fault modes into disjoint omissive and transmissive submodes. The resulting five-mode hybrid fault model is a superset of previous hybrid fault models. 2) We present a new family of voting algorithms, called Omission Mean Subsequence Reduced (OMSR), which implicitly recognize and exploit omissive behavior in malicious faults while still maintaining full Byzantine fault tolerance. 3) We show that OMSR voting algorithms are more fault-tolerant than previous voting algorithms if any of the currently active faults is omissive. Index TermsÐApproximate agreement, clock synchronization, convergent voting algorithms, fault-tolerant distributed systems, hybrid