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For wireless caching networks, the scheme design for content delivery is non-trivial in the face of the following tradeoff. On one hand, to optimize overall throughput, users can associate their nearby APs with great channel capacities; however, this may lead to unstable queue backlogs on APs and prolong request delays. On the other hand, to ensure queue stability, some users may have to associate APs with inferior channel states, which would incur throughput loss. Moreover, for such systems, how to conduct predictive scheduling to reduce delays and the fundamental limits of its benefits remain unexplored. In this paper, we formulate the problem of online user-AP association and resource allocation for content delivery with predictive scheduling under a fixed content placement as a stochastic network optimization problem. By exploiting its unique structure, we transform the problem into a series of modular maximization sub-problems with matroid constraints. Then we devise PUARA, a Predictive User-AP Association and Resource Allocation scheme which achieves a provably near-optimal throughput with queue stability. Our theoretical analysis and simulation results show that PUARA can not only perform a tunable control between throughput maximization and queue stability but also incur a notable delay reduction with predicted information.