An approach is presented to describe traffic processes in asynchronous transfer mode (ATM) environments. Using a discrete-time Markov chain to describe the cell process dynamics, an algorithm is derived to calculate the correlation function of the traffic process. As an example, the correlation properties of a two-state process are investigated. A hierarchical characterization of discrete-time traffic processes is used to capture the short-term and the long-term dependencies of process segments as well as different time scales according to cell, burst, dialog, and call layers of traffic streams in ATM systems. It is shown by comparison of the process description techniques using the index of dispersion of count (IDC) and using the correlation function (CF), that the CF gives significant additional insight in understanding the short- and long-term dependencies of traffic processes in ATM environments.>