Broadband networks are designed to support a wide variety of services with different traffic characteristics and demands for Quality of Services. Bandwidth allocation methods can be classified into two major categories： static and dynamic. In static allocation, bandwidth is allocated only at call setup time and the allocated bandwidth is maintained during a session. In dynamic allocation, the allocated bandwidth is negotiated during a session. The purpose of this paper is to develop policies for deciding and for adjusting the amount of bandwidth requested for a best effort connection over such as ATM networks.. This method is to develop such policies that a good trade off between utilization and latency using cell delay variation to the forecast the incoming traffic in the next period. The performances of the different polices are compared by simulations.