This paper considers the problem of performance analysis for the multiplexer, when homogeneous periodic on-off sources are statistically multiplexed. Periodic on-off source model is defined that on-period and off-period are repeated by once in a deterministic periodic time and in on-period, cell arrives with deterministic time interval. In order to reflect periodicity of source model, we consider two multiplexing situation, such as random multiplexing and synchronized multiplexing. In both case, we obtain the overload-period distribution in the multiplexer, and an approximate method using the overload period distribution is suggested for obtaining the CLP(Cell Loss Probability) in the buffer of the multiplexer. A numerical example using MPEG-I real traffic samples and the results are also presented.