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To provide heterogeneous quality-of-service (QoS) guarantees to applications, most wireless communications standards combine the error-correcting capability of hybrid automatic repeat request (HARQ) protocols at the data link control layer with the adaptation ability of adaptive modulation and coding (AMC) strategies at the physical layer. In this paper, a novel cross-layer multidimensional discrete-time Markov chain (DTMC)-based queuing model is developed to jointly exploit the capabilities of HARQ and AMC. The analytical DTMC-based model, which generalizes and extends previous results on this topic, stems from a comprehensive consideration of packet multimedia traffic sources modeled as discrete-batch Markovian arrival processes, finite queue-length systems, truncated HARQ protocols, AMC strategies, and a wireless channel first-order 2-D Markov model that relies on the amplitude and rate of change of the fading envelope. Based on the stationary state probability distribution of this multidimensional DTMC, closed-form analytical expressions for performance metrics such as throughput, average packet delay, and packet loss rate, which were caused either by buffer overflow or by exceeding the maximum number of allowed retransmissions, are derived. Furthermore, the proposed analytical framework is used to formulate multidimensional and simplified 2-D constrained optimization problems aiming at maximizing the system throughput under prescribed QoS constraints. Computer simulation results are carried out to verify the validity of the proposed analytical model and to quantify the performance gain due to cross-layer optimization and the use of truncated HARQ protocols.