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130 7.3. EPOCHS BY RECOVERY na k |QP| 221 322-3 31 432-3 41 533-5 4 2-3 51 643-5 5 2-3 61 744-7 5 3-5 6 2-3 71 Table 7.1: Examples of the counting quorums for epochs by recovery (na), the number of acceptors for phase two (k) and the number of acceptors for phase one (|QP |). We will now consider four possible executions of Algorithm 29. In each example, the system is comprised of 3 acceptors (na = 3), 2 proposers (np = 2) and strict majority quorums are used (k = 2). As before, epochs are used by proposers in sequence, starting from epoch 0. Since emin = 0 then any proposer using it can skip phase one and proceed directly to phase two. Firstly, we will examine Figures 7.2, 7.3 and 7.4 where the two proposers execute serially, proposer p1 followed by proposer p2. All three executions begin after the proposer p1 has proposed and decided the proposal (0, A). In Figure 7.2, the proposal (0, A) is accepted by all acceptors. However, in Figures 7.3 and 7.4 the acceptor a3 has not accepted the proposal (0, A), due to delay/loss of the message or a slow/failed acceptor. All three cases begin with proposer p2 proposing (0, B) but p2 does not receive the two accepts necessary to complete phase two as the value A has already been decided. In Figure 7.2, the acceptor a3 does not accept the proposal (0, B) as it has already accepted (0, A). In Figure 7.3, the acceptor a3 is able to accept the proposal (0, B) since it has not yet accepted any proposals but does not do so due to loss/failure. In Figure 7.4, the acceptor a3 accepts the proposal (0, B). At this point in time, the three examples differ only by the state of acceptor a3. In Figure bypass phase one for epoch 0.PDF Image | Distributed consensus
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