Communication to the Editor—An Equilibrium Property of Finite-Population Queues

The purpose of this note is to extend, by means of a somewhat simpler derivation, a result of Sherbrooke [Sherbrooke, C. C. 1966. Generalization of a queueing theorem of palm to finite populations. Management Sci.12(11, July) 907–908.] to the case of arbitrary arrival distributions, arbitrary in the sense that customers are distinguishable and may have different density functions of holding time and interarrival time.