M-D-1 queue ($M/D/1$)

An M-D-1 queue has a Poisson process of arrivals, a deterministic service time $\tau$, and one work-conserving server. With arrival rate $\lambda$ and $\lambda \tau <1$, its equilibrium idle probability is $1-\lambda \tau$: the stationary completed work per unit time is $\lambda \tau$. Its output generally need not be a Poisson process.