  In this paper, the area swept under the workload graph is analyzed: with
$\{Q(t) : t\ge0\}$ denoting the stationary workload process, the asymptotic
behavior of \[\pi_{T(u)}(u):={\mathbb{P}}\biggl(\int_0^
{T(u)}Q(r)\,\mathrm{d}r>u\biggr)\] is analyzed. Focusing on regulated Brownian
motion, first the exact asymptotics of $\pi_{T(u)}(u)$ are given for the case
that $T(u)$ grows slower than $\sqrt{u}$, and then logarithmic asymptotics for
(i) $T(u)=T\sqrt{u}$ (relying on sample-path large deviations), and (ii)
$\sqrt{u}=\mathrm{o}(T(u))$ but $T(u)=\mathrm{o}(u)$. Finally, the Laplace
transform of the residual busy period are given in terms of the Airy function.
