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Broadband wireless access network based on the IEEE 802.16e is one of the most promising solutions to provide broadband services. This paper proposes an efficient bandwidth request scheme for non real-time polling service and best effort service. In order to reduce the delay for bandwidth request, the proposed scheme makes BR code indicate the UIUC and the number of subchannels required by mobile station. Accordingly, it can omit the transmission procedure of bandwidth request message. We perform the mathematical analysis. The results show that the proposed scheme can reduce the delay and the signaling overhead compared to the IEEE 802.16e scheme.