Two main characteristics of VBR MPEG video traffic are different statistics according to different picture types and the periodic traffic pattern due to GOP structure. Especially, the I-pictures at the beginning of each GOP generate $$mu$</TEX>h more traffic than other pictures. When several VBR Mpeg video sources are superposed, the I-picture starting times of these sources may significantly affect the cell loss characteristics of ATM $$mu$</TEX>tiplexers. In this paper, we propse a performance model for ATM $$mu$</TEX>tiplexers with VBR MPEG video sources whose starting times are arbitrary given. For analysis, both single and superposed source traffic are modeled as NDPPs (non-deterministic periodic processes), and the ATM $$mu$</TEX>tiplexer is modeled as a U-state NDPPD/D/1/B queueing system. It is hown that the numerical results are very close to the si$$mu$</TEX>ation results. From the relationships between the starting tiem distributions and the corresponding $$mu$</TEX>tiplexer performances, some considerations for designing a scheduling policy in order to obtain the maxi$$mu$</TEX> $$mu$</TEX>tiplexing gain are presented.