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Admission control and bandwidth allocation are important issues in telecommunications networks, especially when there are random uctuating demands for service and variations in the service rates. In the emerging broadband communications environment these services are likely to be o ered via an ATM network. In order to make ATM future safe, methods for controlling the network should not be based on the characteristics of present services. We propose one bandwidth allocation method which has this property. Our proposed approach is based on pricing bandwidth to re ect network utilization, with users competing for resources according to their individual bandwidth valuations. The prices may be components of an actual tari or they may be used as control signals, as in a private network. Simulation results show the improvement possible with our scheme versus a leaky bucket method in terms of cell loss probability, and confirm that a small queue with pricing can be efficient to multiplex heterogeneous sources.