A system that includes one or more priority failure detectors may be included that detect node or process failures in the distributed computer network. The system has a fault-tolerant, client-server architecture where a client process presents a particular consensus problem to one or more server processes to solve such a consensus based problem. The system assigns priority levels to processes involved in a consensus session and controls the frequencies of their heartbeat status messages based on their respective priority levels. By controlling the frequencies, the reliability of the network is enhanced and the overall message load on the even bus is reduced to a minimum number. The system also discloses a name service that assigns unique logical identities to all processes in a consensus session. Further, by tagging all involved processes appropriately, multiple consensus based problems can be dealt with on a set of consensus server processes simultaneously.