This paper investigates mean delays in a single-server queueing model with cyclic service. An approximate analysis is performed for an arbitrary number of queues, constant switch-over time, exhaustive service discipline, Poisson arrival processes, and general service-time distributions. Neither inter-arrival nor service-time distributions have to be identical for the different queues. A major value of our approximation lies in the simplicity of its numerical evaluation for an arbitrary number of queues and any traffic pattern. Extensive comparisons with simulation results show the high accuracy of the approximation over a wide range of parameters. © 1983.