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Linearizability and quorums

Intuitively, it seems as though strict quorum reads and writes should be linearizable in a Dynamo-style model. However, when we have variable network delays, it is possible to have race conditions, as demonstrated in Figure 9-6.

A nonlinearizable execution, despite using a strict quorum

Figure 9-6. A nonlinearizable execution, despite using a strict quorum.

In Figure 9-6, the initial value of x is 0, and a writer client is updating x to 1 by sending the write to all three replicas (n = 3, w = 3). Concurrently, client A reads from a quorum of two nodes (r = 2) and sees the new value 1 on one of the nodes. Also concurrently with the write, client B reads from a different quorum of two nodes, and gets back the old value 0 from both.

The quorum condition is met (w + r > n), but this execution is nevertheless not linearizable: B’s request begins after A’s request completes, but B returns the old value while A returns the new value. (It’s once again the Alice and Bob situation from Figure 9-1.)

Interestingly, it is possible to make Dynamo-style quorums linearizable at the cost of reduced performance: a reader must perform read repair (see “Read repair and antientropy” on page 178) synchronously, before returning results to the application [23], and a writer must read the latest state of a quorum of nodes before sending its writes [24, 25]. However, Riak does not perform synchronous read repair due to the performance penalty [26]. Cassandra does wait for read repair to complete on quorum reads [27], but it loses linearizability if there are multiple concurrent writes to the same key, due to its use of last-write-wins conflict resolution.

Moreover, only linearizable read and write operations can be implemented in this way; a linearizable compare-and-set operation cannot, because it requires a consensus algorithm [28].

In summary, it is safest to assume that a leaderless system with Dynamo-style replication does not provide linearizability.

 
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