An M/M/s queueing system with a simple cost structure is considered, under the assumption that the system will close in a finite time after which any remaining customers will require extra overtime service costs. We determine the optimal policy for admitting customers to the queue, as a function of the time, t, to closing and the current queue length, i. It is shown to have the form: admit if and only if f1(t) ≦ i ≦ f2(t). The bounds f1(t) and f2(t) are specified, and it is shown under what conditions f1(t) = 0 (a control limit rule) or f2(t) = ∞ (an inverse control limit rule).
