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In this paper, we consider the problem of real-time transmission scheduling over time-varying channels. We first formulate this transmission scheduling problem as a Markov decision process and systematically unravel the structural properties (e.g., concavity in the state-value function and monotonicity in the optimal scheduling policy) exhibited by the optimal solutions. We then propose an online learning algorithm that preserves these structural properties and achieves \varepsilon-optimal solutions for an arbitrarily small \varepsilon. The advantages of the proposed online method are given as follows: 1) It does not require a priori knowledge of the traffic arrival and channel statistics, and 2) it adaptively approximates the state-value functions using piecewise linear functions and has low storage and computation complexity. We also extend the proposed low-complexity online learning solution to enable prioritized data transmission. The simulation results demonstrate that the proposed method achieves significantly better utility (or delay)–energy tradeoffs compared to existing state-of-the-art online optimization methods. [ABSTRACT FROM PUBLISHER]