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Partial quorum systems are widely used in distributed key-value stores due to
their latency benefits at the expense of providing weaker consistency
guarantees. The probabilistically bounded staleness framework (PBS) studied the
latency-consistency trade-off of Dynamo-style partial quorum systems through
Monte Carlo event-based simulations. In this paper, we study the
latency-consistency trade-off for such systems analytically and derive a
closed-form expression for the inconsistency probability. Our approach allows
fine-tuning of latency and consistency guarantees in key-value stores, which is
intractable using Monte Carlo event-based simulations.

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