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 to- day. 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 de- terministic and statistical frameworks. However， the weight assignment process commonly used，RPPS, appears to perform poorly and the re- sulting 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 proce- dure is shown to be scalable， and provides an efficient use of resource capacity。