The Slow Tail of an Inference Server

A deployed model's inference latency $T$ (measured in tens of milliseconds) has probability density

$f(t) = c\,t(4 - t) \quad \text{for } 0 \le t \le 4, \qquad f(t) = 0 \text{ everywhere else,}$

with $c$ chosen so that $f$ is a valid density.

Your service-level target counts a request as slow when $T \ge 3$.

What fraction of requests are slow?