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In this paper, we propose a scalable transport scheme for delivering on-demand video streams over broadband wireless networks in next-generation network/IP multimedia subsystem (NGN/IMS) architecture. The proposed transport scheme makes use of fine-granular-scalability (FGS) encoded videos to accommodate high bandwidth variation of wireless networks. We formulate the bandwidth allocation to FGS-encoded streams as a resource allocation problem and develop a quality-aware bandwidth allocation scheme, called QABA. With QABA, the proposed transport scheme can dynamically adjust the bit rate allocated to different streams to maximize the overall perceptual quality when available network bandwidth varies with time. QABA is theoretically proven to be able to find the optimal bandwidth allocation for all on-demand streams. To validate the effectiveness of QABA, extensive trace-based simulations are performed.