Budget a latency target across a fan-out

NumericalBeginner⏱ 15 minAI Systemsfan-outquantilesbudgeting

Problem

A request fans out to $n = 50$ independent shards and completes when the last one returns. The product target is a p99 of 200 ms for the parent.

What per-shard quantile must sit at 200 ms?
If each shard's latency is exponential with mean 20 ms, what is the parent's p99?
Roughly how many samples are needed to estimate the shard quantile from part 1 with any precision, and what does that imply about measuring it?

Compute the requested quantities and say what they mean. A number without an interpretation is not an answer.

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Opening this before you have a real attempt on paper is the fastest way to feel like you understand something you cannot reproduce.

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