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This paper proposes a novel framework for the cross-layer analysis and design of wireless networks combining adaptive modulation and coding (AMC) at the physical layer with an automatic repeat request (ARQ) protocol at the data-link layer. Most previous works rely on first-order amplitude-based finite-state Markov chains (AFSMCs) to model the physical layer. It is shown that these models present several deficiencies that could compromise the design of higher layer protocols. Thus, a physical-layer first-order 2-D Markov model using both the amplitude and the rate of change of the fading envelope is presented. Based on this multidimensional physical-layer Markov model, the quality-of-service (QoS) performance at the data-link layer is investigated through the use of two different approaches. The first one relies on an analytical framework based on a discrete-time Markov chain (DTMC) that jointly describes the statistical behavior of the arrival process, the queueing system, and the physical layer. The second one is based on the effective-bandwidth and effective-capacity theories. Both the DTMC-based and the effective-bandwidth/capacity-based approaches are analyzed and compared in combination with our proposed physical-layer first-order 2-D Markov model in a cross-layer design aiming to satisfy the required average packet loss probability constraint by maximizing the average throughput of the system. Numerical results show that our proposed framework represents a significant improvement over previous models.