The authors discuss some basic issues relevant to the policing function in asynchronous transfer mode (ATM) networks. The problem of controlling the source peak rate in the presence of the cell delay variation introduced in the customer premises network is considered. A model for analyzing the cell delay variation is presented, under the assumption of a constant bit rate source multiplexed with a Poisson stream. On the basis of the distribution obtained, the relevant parameters of two policing devices (the jumping window and the leaky bucket) are dimensioned. The numerical results lead to the conclusion that the leaky bucket allows a tighter source control then the jumping window.>