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88 4.3. IMPLICATIONS Epochs are pre-allocated in a round robin fashion such that participant u1 may use epochs E = {0,5,10,...}, participant u2 may use epoch E = {1,6,11,...} and so on. We assume our system is using majority quorums, therefore regardless of phase or epoch, our quorums are as follows: Q = {{u1, u2, u3}, {u1, u2, u4}, {u1, u2, u5}, {u1, u3, u4}, {u1, u3, u5}, {u1, u4, u5}, {u2, u3, u4}, {u2, u3, u5}, {u2, u4, u5}, {u3, u4, u5}} In practice, however each participant will include itself in its quorums. Therefore the phase two quorums will be of the form: Q02 ={{u1,u2,u3},{u1,u2,u4},{u1,u2,u5},{u1,u3,u4},{u1,u3,u5},{u1,u4,u5}} Q12 ={{u1,u2,u3},{u1,u2,u4},{u1,u2,u5},{u2,u3,u4},{u2,u3,u5},{u2,u4,u5}} The insight from revision B is that the phase one quorums need only intersect with the phase two quorums of smaller epochs. We are therefore able to refine the first few phase one quorums as follows: Q01 = {{}} Q1 ={{u1},{u2,u3,u4},{u2,u3,u5},{u2,u4,u5},{u3,u4,u5}} Q21 ={{u1,u2},{u1,u3,u4},{u1,u3,u5},{u1,u4,u5}, {u2, u3, u4}, {u2, u3, u5}, {u2, u4, u5}, {u3, u4, u5}} We could generalise this example across any quorum system to say that the set of all participants associated with previous epochs < e is a valid phase one quorum for epoch e. In this specific example, the phase one quorums of the first three epochs have been improved, however, this insight it not helpful for epochs > 3 since any set of 3 or more participants is already a valid quorum. We address this in the next section. 4.3.3 Multi-Paxos In Multi-Paxos (§3.6), the steady state of the algorithm is a proposer executing phase two with a majority of acceptors. If we assume that failures occur rarely, then phase one of Classic Paxos would be seldom executed compared to phase two. From Paxos revision A, we learned that quorum intersection is required only between phase one and phase two quorums. As a result, we can tradeoff between quorums sets for the phase one and phasePDF Image | Distributed consensus
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