= General-service infinite-server queue
{title2=$M/G/\infty$}
= M-G-infinity queue
{c}
{synonym}
<Poisson process>[Poisson] arrivals of rate $\lambda$ receive <independent> <service time>[service times] distributed as $S$, with infinitely many servers so service starts on arrival. Starting empty, the <queue population>[occupancy] at time $t$ is <Poisson distribution>[Poisson] with <mean> $\lambda\int_0^t\mathbb P(S>u)\,du$, by <independent> thinning of the marked arrivals. If $\mathbb ES<\infty$, the equilibrium count is <Poisson distribution>[Poisson] with <mean> $\lambda\mathbb ES$. <queue population>[Occupancy] need not be a <Markov process> for a general service law; remaining <service time>[service times] carry additional state information.
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