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IEEE 802.16 and Passive Optical Network (PON) are two promising broadband access technologies for high-capacity wireless and wired access networks, respectively. In order to better understand the co-existence of both network technologies and to determine whether closer cooperation in the bandwidth provisioning process is advantageous, an access network that utilizes a Gigabit PON (GPON) to backhaul 802.16 network traffic is evaluated. Typical to many network deployments, the equipment is from different manufacturers and has different management and control interfaces. This paper proposes the use of a control bridge that overlooks the operations of both the GPON and 802.16 networks in order to: (1) provide dynamic QoS mapping so as to reduce traffic delivery cost; and (2) to improve overall channel utilization through coordinated dynamic bandwidth allocation. The performance of the converged network under the control of the proposed control bridge is evaluated in terms of cost of data delivery, channel utilization, and service differentiation.