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An approximate performance analysis of a leaky bucket with Pareto-distributed on/off sources is presented. The aggregate of Pareto-distributed on/off sources is a self-similar traffic. This analysis is applicable to the leaky bucket policing device at the ingresses of (1) a base station in a wireless ATM network, (2) a wireline ATM network, and (3) future generations of IP-based networks with quality of service (QoS) differentiation and with call admission control. The performance metric is packet loss. Numerical results show good agreement between the approximate analysis and simulation results.