Device-to-device (D2D) communication is envisioned as a promising technology in future cellular networks. In this paper, we investigate the delay-aware resource allocation and power control algorithm for delay-sensitive D2D communications underlaying cellular networks. With the objective to minimize the average delay and average drop rate, we formulate the optimization problem as an infinite horizon average cost Markov Decision Process (MDP). To address the curse of dimensionality, we propose a low complexity two-stage scheme. In the first stage, a heuristic resource allocation algorithm is proposed, which considers the imbalance of queue lengths between different queues. In the second stage, we derive the transition probability of the system state and obtain the optimal power control policy by solving the Bellman equation. Simulation results show that our proposed scheme outperforms all the baselines, and thus can effectively improve the delay performance.
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