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A hybrid wireless-optical broadband access network (WOBAN) is a promising architecture for future access networks. Recently, the WOBAN has been gaining increasing attention, and early versions are being deployed as municipal access solutions. This architecture saves on network deployment cost because fiber need not penetrate to each end user. However, a major research opportunity exists in developing an efficient routing algorithm for the wireless front-end of the WOBAN. We propose and investigate the characteristics of the delay-aware routing algorithm (DARA) that minimizes the average packet delay in the wireless front-end of a WOBAN. In DARA we model wireless routers as queues and predict wireless link states periodically. Our performance studies show that DARA achieves less delay and congestion, and improved load balancing compared to traditional approaches such as the minimum-hop routing algorithm, shortest-path routing algorithm, and predictive throughput routing algorithm.