In ATM networks, bursty sources can be described as the Interrupted Bernoulli Pro-cess(IBP). With the use of the thin process theory, the Probability Generating Function(PGF) of the IBP is obtained. An iterative algorithm, which can be used to calculate the IBP probability distribution, is presented. The bursty source's equivalent description is discussed. It is proposed that the leaky bucket output process can be approximately described as the IBP. The accuracy of the analytical results has been largely validated by means of the simulation approach. Moreover, how to improve its accuracy is discussed. The smoothing function of the leaky bucket algorithm is quantitatively analyzed.