Lorenz and Little: How Much Does Your Tail Cost?

Lorenz and Little: How Much Does Your Tail Cost? Lorenz and Little sounds like hipster burger bar from 2015. It’s time for Marc’s Amateur Statistics Corner! Today: why I pay a lot of attention to tail latency when optimizing cost. I’ve written before on the importance of tail latency for customer experience (e.g. in 2026, 2021, and 2021, and 2017). Today, I want to talk about tail latency from the perspective of cost and capacity. Like many system operators, I think about tail latency using percentiles. Here’s a question: how much does each of my latency percentiles contributed to the mean latency? Intuitively, the answer is “quite a lot”, but can we quantify that? We can! The thing we’re looking for is the empirical Lorenz Curve. It directly calculates the answer to the question: given a latency percentile $P$ (e.g. p99=100ms), how much do requests taking shorter than $P$ contribute to the mean latency? (Let’s call it $L(P)$ , so the real answer to our question is $1 - L(P)$).…