In this paper, we propose an analytic method for dimensioning traffic descriptors at the leaky bucket-based UPC for VBR MPEG video traffic on ATM networks. We analytically derived cell violation probabilities at the UPC by using a proposed scene-based video traffic model, and then we showed that it was possible to select sets of traffic descriptors that produce the required violation probability. In two example video traces, the numerical results showed that our proposed traffic descriptor dimensioning method well approximated the simulation-based traffic control results of the real video traces. In cases where an effective bandwidth allocation method based on the ON/OFF model was used for the call admission control in the networks, we compared the allocated effective bandwidth to each set of traffic descriptors that produced zero UPC losses.