Two main characteristics of VBR MPEG video traffic are the 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 much more traffic than other pictures. Therefore, when several VBR MPEG video sources are superposed, the multiplexing performance can vary according to the variations of their I-picture start times. In this paper, we show how the start time arrangement of the superposed VBR MPEG videos can significantly affect the cell loss ratio characteristics at the multiplexers, by using U-NDPP/D/1/B queueing model. It is also shown that the Lognormal distribution is more suitable for modeling VBR MPEG video traffic than the Normal and Gamma distributions, in the queueing application's view points.