Solution
= Solution
After closing, the count can only decrease. Thus $V(t)>v$ is the event that at least one mosquito remains at $t+v$. The zero probability of a Poisson count yields the <clearance time after closing an infinite-server queue>:
$$
\boxed{\mathbb P(V(t)>v)
=1-\exp\left[-\lambda\int_v^{t+v}\mathbb P(S>s)\,ds\right],\qquad v\geq0.}
$$
The clearance time has an atom at zero of mass $e^{-m_t}$, corresponding to an empty room when the window closes.