A Paxos based algorithm to minimize the overhead of process recovery in consensus

Consensus is a fundamental abstraction in distributed systems and its solvability is widely discussed in the literature. In message passing distributed systems where there is a need to solve sequential instances of consensus, it is possible that some processes become faulty during one instance and recover later in another instance. Though consensus algorithms should be equipped both to handle process failures and process recovery, only a little amount of work has been done in the literature to handle process recovery. Handling process recovery is not trivial because a recovered process may broadcast a new message which could hamper the progress made by other processes towards achieving consensus in their current round, and thereby forcing them to start a new round. Therefore algorithms that are not designed to handle process recovery require \({\text {O}}\bigl (f\bigr )\) rounds or \({\text {O}}\bigl (f\delta \bigr )\) time to achieve consensus, where at most f processes can recover and \(\delta \) is the message delay in the system. But Dutta et al. (in: International conference on dependable systems and networks (DSN’05), pp 22–27), 2005. https://​doi.​org/​10.​1109/​DSN.​2005.​54) showed that the overhead of handling process recovery is constant and their algorithm takes \(17\delta \) time to achieve consensus. In this work, we introduce a new Paxos based algorithm that lowers the upper bound to \(11\delta \). We also show that if all process failures are initial, the upper bound can be further reduced to \(5\delta \). Our algorithm selectively enables processes executing lower rounds to decide irrespective of the presence of higher rounds in the system, minimizing the effect of recovered processes starting a higher round.