Past exam of the mathematics course of the University of Cambridge / 2008 / ii / Paper 4 / 26I / e / 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:The clearance time has an atom at zero of mass $e^{-m_t}$, corresponding to an empty room when the window closes.