What Leaves Must Promise

The leaf's $p_{99.9}$ must be 10 ms, which puts about 9 percent of root requests over budget.

The leaf's $p_{99.99}$ must be 10 ms: solving $p^{100} \ge 0.99$ gives $p \ge 0.99^{1/100} \approx 0.99990$. A leaf whose $p_{99}$ is 10 ms leaves $1 - 0.99^{100} \approx 63$ of root requests over budget.

The leaf's $p_{99}$ must be 10 ms, because with independent identically distributed leaves the root inherits the leaf's percentile unchanged.

The leaf's $p_{99}$ must be 0.1 ms, because the 10 ms budget is divided across the 100 leaves.