A method is provided in one example embodiment and includes predicting a user average data rate for a cable modem; establishing a minimum bandwidth grant size and a maximum bandwidth grant size for the cable modem based on the predicted user average data rate; receiving from the cable modem a request for a particular amount of bandwidth; performing an overgrant if the particular amount of bandwidth is less than the minimum bandwidth grant size, in which the overgrant comprises granting to the cable modem more than the requested particular amount of bandwidth; and performing an undergrant if the particular amount of bandwidth is greater than the maximum bandwidth grant size, in which the undergrant comprises granting to the cable modem less than the requested particular amount of bandwidth.
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