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In this paper, we propose a useful framework for the cross-layer design and analysis of wireless networks where ARQ (automatic repeat reQuest) and AMC (adaptive modulation and coding) schemes are employed. To capture the joint effect of the packet transmission error rate at the PHY layer and the packet loss probability at the MAC layer, we introduce the effective bandwidth function of the packet service process. Base on queueing analysis with this effective bandwidth function, our cross-layer design tries to satisfy the required packet loss probability by each user and minimize the average packet transmission error rate. Numerical examples are provided to show the usefulness and characteristics of our framework.