Summary: This paper contains an analysis of a single-server queuing system for which time is treated as a discrete variable. The number of customers arriving within a fixed time interval is assumed to obey a binomial probability distribution. The service times are assumed to be identically distributed and statistically independent but are not otherwise restricted. It is furthermore assumed that customers are served in their order of arrival. Formulas for the mean queue length and the mean waiting time are derived for the general case and it is shown how the previously obtained results for the corresponding continuous-time system may be derived from the results given here by a limiting process. The results are applied to two special cases, (1) a service-time distribution, which has the form of a geometrical progression, and (2) a fixed service-time distribution.