The performance of the leaky bucket, a device for controlling the source traffic parameters of an ATM network is analyzed. The most critical situation, i.e., an on/off bursty source, is assumed. Moreover, the delay jitter introduced by a possible multiplexing of sources inside the customer premises network is not considered. The leaky bucket can be analyzed as a G/D/1/N queue with finite waiting room N and a suitable arrival process. An alternative approach, the fluid flow approximation, in which the bit flow is considered as a continuous variable, is presented. By comparison with the exact model, it is shown that the accuracy of the fluid flow approach is sufficient for practical purposes. An explicit formula for the cell loss probability, in case of exponential distributions for both the burst duration and the inactivity period of the source, is derived. On the basis of that formula, some numerical evaluations are presented with the aim of assessing the effectiveness of the leaky bucket mechanism. It is concluded that while the leaky bucket can easily control the peak rate, difficulties arise in controlling the mean bit rate (because of the long time required) and the burst duration (because of the poor selectivity). >