We consider, in this paper, channel allocation and rate adaptation scheme for relayed transmission over correlated fading channels via cross-layer design. Specifically, jointly considering the data link layer buffer occupancy and channel quality at both the source and relay nodes, we develop an optimal channel allocation and rate adaptation policy for a dual-hop relayed transmission. As such the overall transmit power for the relayed system is minimized while a target packet dropping rate (PDR) due to buffer over flows is guaranteed. In order to find such an optimal policy, the channel allocation and rate adaptation transmission framework is formulated as a constraint Markov decision process (CMDP). The PDR performance of the optimal policy is compared with that of two conventional suboptimal schemes, namely the channel quality based and the buffer occupancy based channel allocation schemes. Numerical results show that for a given power budget, the optimal scheme requires significantly less power than the conventional schemes in order to maintain a target PDR.