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With DiffServ assured forwarding, a customer contracts a certain bandwidth, which is shared among the flows sent by him. If the customer sends too many flows, the realized throughput for each will be very low, and the corresponding transfer is very likely to be interrupted by its user due to its prolonged completion time. Since the work done in transferring an incomplete document is generally wasted, interrupted transfers constitute a significant source of inefficiency in the utilization of the contracted bandwidth. In order to avoid this inefficiency, we propose the use of admission control to limit the number of flows of a customer to ensure that each receives a minimal acceptable throughput.