Quorum systems serve as a basic tool providing a uniform and reliable
way to achieve coordination in a distributed system. They are useful f
or distributed and replicated databases, name servers, mutual exclusio
n, and distributed access control and signatures. The un-availability
of a quorum system is the probability of the event that no live quorum
exists in the system. When such an event occurs the service is comple
tely halted. The un-availability is widely accepted as the measure by
which quorum systems are evaluated. In this paper we characterize the
optimal availability quorum system in the general case, when the failu
re probabilities may take any value in the range 0 < p(i) < 1. Then we
deal with the practical scenario in which the failure probabilities a
re unknown, but can be estimated. We give a robust and efficient algor
ithm that calculates a near optimal quorum system based on the estimat
ed failure probabilities. (C) 1998 Elsevier Science B.V.