The introduction of Quality of Service in high-speed networks requires the use of more complex policy than the simple FIFO policy commonly used on servers today. Among these policies, GPS is the paradigm of a large set of policies aiming at sharing the bandwidth among sources in a very efficient way. Moreover, tight end-to-end delay bounds results are provided in the deterministic and statistical frameworks. However, the weight assignment process commonly used, RPPS, appears to perform poorly and the resulting admission procedure is cumbersome. To fill this gap, we propose a new weight assignment policy, called EBBPS, which captures the QoS requirement of sources. Moreover, the corresponding admission procedure is shown to be scalable, and provides an efficient use of resource capacity.