A technique controls operation of a BRAS device. The technique involves extracting encapsulation information from a communications exchange between a CPE device and an external server device (e.g., a DHCP server). The communications exchange passes through the BRAS device and a DSLAM device. The technique further involves storing the encapsulation information in local memory of the BRAS device, and controlling a flow of a downstream communication passing through the BRAS device and the DSLAM device toward the CPE device based on the encapsulation information stored in the local memory of the BRAS device. Accordingly, the BRAS device is well suited for performing ATM overhead accounting as well as shaping and policing downstream traffic.