The enormous bandwidth potential of optical fiber has resulted in a worldwide effort to develop high-speed ATM networks, also called broadband integrated services digital networks (BISDN). Many of the applications that ATM networks will support will have a strong video component to them. Hence, it is important to understand the behavior of video traffic as it travels through these networks. To that end, we develop the generalized histogram model (GHM) to characterize "highly correlated" traffic, such as motion JPEG or "smoothed" MPEG traffic over ATM networks end-to-end. Using our GHM model we show how to determine the loss rate at any node in an ATM network. We find that, for highly correlated video sources, increasing the buffer size beyond a certain region called the "cell region" only marginally decreases the probability of loss. This implies that large buffers cannot be used to control the loss for such sources. The analytical model provided in this paper can be used for admission control, and network dimensioning and design in ATM networks. We have validated our results using simulations of real traces of video sources.