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I've read Lamport's paper on Paxos. I've also heard that it isn't used much in practice, for reasons of performance. What algorithms are commonly used for consensus in distributed systems?
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Paxos is an algorithm that enables a distributed set of computers (for example, a cluster of distributed database nodes) to achieve consensus over an asynchronous network. To achieve agreement, one or more of the computers proposes a value to Paxos.
Although Multi-Paxos might compromise the efficiency, it can restore services quicker when the leader fails. Therefore, Multi-Paxos has better availability than Raft.
A consensus algorithm is a process in computer science used to achieve agreement on a single data value among distributed processes or systems. These algorithms are designed to achieve reliability in a network involving multiple users or nodes.
Keeping in mind the above facts, Both Paxos and Raft belongs to the partial synchronous models. The Byzantine Generals' Problem is a classic problem faced by any distributed computer system network.
Not sure if this is helpful (since this is not from actual production information), but in our "distributed systems" course we've studied, along with Paxos, the Chandra-Toueg and Mostefaoui-Raynal algorithms (of the latter our professor was especially fond).
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Check out the Raft algorithm for a consensus algorithm that is optimized for ease of understanding and clarity of implementation. Oh... it is pretty fast as well.
https://ramcloud.stanford.edu/wiki/display/logcabin/LogCabin
https://ramcloud.stanford.edu/wiki/download/attachments/11370504/raft.pdf
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