In this paper, we propose a general cross-layer optimization framework in which we explicitly consider both the heterogeneous and dynamically changing characteristics of delay-sensitive applications and the underlying time-varying network conditions. We consider both the independently decodable data units (DUs, e.g. packets) and the interdependent DUs whose dependencies are captured by a directed acyclic graph (DAG). We first formulate the cross-layer design as a non-linear constrained optimization problem by assuming complete knowledge of the application characteristics and the underlying network conditions. The constrained cross-layer optimization is decomposed into several cross-layer optimization subproblems for each DU and two master problems. The proposed decomposition method determines the necessary message exchanges between layers for achieving the optimal cross-layer solution. However, the attributes (e.g. distortion impact, delay deadline etc) of future DUs as well as the network conditions are often unknown in the considered real-time applications. The impact of current cross-layer actions on the future DUs can be characterized by a state-value function in the Markov decision process (MDP) framework. Based on the dynamic programming solution to the MDP, we develop a low-complexity cross-layer optimization algorithm using online learning for each DU transmission. This online algorithm can be implemented in real-time in order to cope with unknown source characteristics, network dynamics and resource constraints. Our numerical results demonstrate the efficiency of the proposed online algorithm.
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