The paper is concerned with analyzing a time-division multiplexing method with two priority classes. A discrete-time model is established for analyzing the queuing behavior of low priority traffic streams. The motivation came from Dynamic Transfer Mode (DTM) networks, which uses time-division multiplexing of channels, however, the results might also be used for other fast circuit switched networks. The model to be investigated is based on the important observation that from the viewpoint of low priority traffic the system behaves as a queuing system subjected to periodic server interruption. The probability generating function (pgf) of the system time and system content of low priority messages is expressed in closed forms from which the first two moments can be calculated in a straightforward manner. Applying an efficient approximation technique also derives tail probabilities of system content and system time. Finally, we also give numerical examples as simple illustrations.