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Broadband networks based on asynchronous transfer mode (ATM) have to support traffic with widely different traffic characteristics and quality of service requirement. In this paper, we extend our earlier work in and develop a dynamic connection admission controller (CAC) that supports cell loss requirements. The CAC algorithm explicitly computes the equivalent bandwidth required to support each class of connections based on on-line observations of aggregate traffic statistics as well as the declared parameters. We use Gaussian and diffusion approximations to characterize the aggregate traffic stream, and use fuzzy control strategy to combine model and measurement results to derive simple closed-form formulas to estimate the equivalent bandwidth in real time. We validate the proposed algorithms for various variable bit-rate traffic profiles and show that the system utilization can be substantially improved by appropriately tuning the fuzzy logic controller to combine traffic characteristics deduced from the declared parameters and traffic measurements.