Enforced idle time occurs in any queuing system in which it is possible for the server to be idle and the queue length to be nonzero simultaneously. This paper examines queuing systems in which the server is constrained to start service only at fixed intervals of time, with arrivals of customers and service completions occurring continuously. The GI/M/N, GI/D/N, M/D/N, and GI/G/1 queuing systems with enforced idle time are studied and some closed form steady-state results are presented. An application to railroad car pool systems is suggested.