Equation 28 · The Network Is the Computer Again
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The reason this matters more for collectives than for ordinary traffic is synchronisation. A collective is a barrier. Every participant waits for the operation to complete, so the operation completes when the last contribution arrives. Tail latency therefore stops being a tail statistic and becomes the mean cost of every step. Dean and Barroso’s analysis of latency variability in large fan-out services is the canonical statement of the mechanism: background activity, queueing at multiple layers including network switches, and shared-resource contention produce occasional slow responses, and a request that must wait on many servers is very likely to encounter one [ 18 ] . The arithmetic is…
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The reason this matters more for collectives than for ordinary traffic is synchronisation. A collective is a barrier. Every participant waits for the operation to complete, so the operation completes when the last contribution arrives. Tail latency therefore stops being a tail statistic and becomes the mean cost of every step. Dean and Barroso’s analysis of latency variability in large fan-out services is the canonical statement of the mechanism: background activity, queueing at multiple layers including network switches, and shared-resource contention produce occasional slow responses, and a request that must wait on many servers is very likely to encounter one [ 18 ] . The arithmetic is unforgiving. If each participant independently exceeds its budget with probability q , the probability that at least one of p participants does so is
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