This paper studies a stochastic system where the performance of the server changes stochastically and cyclically. We first investigate the performance measures of the system, including the queue length and the overall cost. In particular, we derive an exact expression for the expected length of the renewal cycle, and present closed matrix forms for the mean and variance of the queue length. We then develop an explicit method to tackle a workload control problem, based on an M/G/1 queue approximation. Numerical examples are presented to illustrate the effectiveness of the method.