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Emerging media overlay networks for wireless applications aim at delivering Variable Bit Rate (VBR) encoded media contents to nomadic end users by exploiting the (fading-impaired and time-varying) access capacity offered by the "last-hop” wireless channel. In this application scenario, a still open question concerns the closed-form design of control policies that maximize the average throughput sent over the wireless last hop, under constraints on the maximum connection bandwidth available at the Application (APP) layer, the queue capacity available at the Data Link (DL) layer, and the average and peak energies sustained by the Physical (PHY) layer. The approach we follow relies on the maximization on a per-slot basis of the throughput averaged over the fading statistic and conditioned on the queue state, without resorting to cumbersome iterative algorithms. The resulting optimal controller operates in a cross-layer fashion that involves the APP, DL, and PHY layers of the underlying protocol stack. Finally, we develop the operating conditions allowing the proposed controller also to maximize the unconditional average throughput (i.e., the throughput averaged over both queue and channel-state statistics). The carried out numerical tests give insight into the connection bandwidth-versus-queue delay trade-off achieved by the optimal controller.