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CHAPTER 4. QUORUM INTERSECTION REVISED 87 e = 0 e ∈ [1, k] e = k + 1 e ∈ [k + 2, ∞] Phase one quorums, Qe1 = {{}} {{a1}, {a2}, {a3}} {{a1}, {a2}, {a3}} Phase two quorums, Qe2 = {{a1, a2, a3}} {{a1, a2, a3}} {{a1, a2}, {a2, a3}, {a1, a3}} {{a1, a2}, {a2, a3}, {a1, a3}} {{a1, a2}, {a2, a3}, {a1, a3}} Table 4.1: Example quorums for All aboard Paxos with three acceptors U = {a1, a2, a3}. than or equal to 1 can be chosen for k. An example set of phase two quorums is shown in the third column of Table 4.1. Without revision B, we would require majority quorums for all phase ones, regardless of the epoch, to ensure quorum intersection across phases. However, using the weakened quorum intersection requirements for revision B, we can reduce the phase one quorums. As we have already discussed, there is no phase one quorum intersection requirement for epoch 0. For proposals numbers 1 to k + 1, any acceptor is a valid phase one quorum. For epochs k + 2 onward, any majority of acceptors is a valid phase one quorum. The result is that proposers can fall back to Classic Paxos if they do not receive responses from all acceptors. An example set of phase one quorums is shown in the second column of Table 4.1. A decision can be reached in one round trip if all acceptors are available (and provided no proposer has tried to propose in epoch > k) or two round trips if only a majority of acceptors are available. Example: Singleton Paxos Alternatively, we could instead require that all acceptors promise in phase one thus allowing any acceptor to accept a value in phase two. For example, in a system of 3 acceptors A = {a1, a2, a3}, the following are also valid quorum sets: Q1 ={{a1,a2,a3}} Q2 ={{a1},{a2},{a3}} The phase two could also include a phase three to store the decided value, as described in §3.3. Example: Majority quorums for co-location The idea of using different quorums for different epochs, as proposed in §4.2 may seen unusual, however this is already common place. Consider a Classic Paxos system of 5 par- ticipants U = {u1, u2, u3, u4, u5}, where each participant is both an acceptor and proposer.PDF Image | Distributed consensus
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