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This is Part II of a two-part paper series that studies the use of the proportional fairness (PF) utility function as the basis for resource allocation and scheduling in multichannel multi-rate wireless networks. The contributions of Part II are twofold, (i) First, we extend the problem formulation, theoretical results, and algorithms to the case of time-varying channels, where opportunistic resource allocation and scheduling can be exploited to improve system performance. We lay down the theoretical foundation for optimization that "couples" the time-varying characteristic of channels with the requirements of the underlying applications into one consideration. In particular, the extent to which opportunistic optimization is possible is not just a function of how fast the channel characteristics vary, but also a function of the elasticity of the underlying applications for delayed resource allocation, (ii) Second, building upon our theoretical framework and results, we study subcarrier allocation and scheduling in orthogonal frequency division multiplexing (OFDM) cellular wireless networks. We introduce the concept of a W-normalized Doppler frequency to capture the extent to which opportunistic scheduling can be exploited to achieve throughput-fairness performance gain. We show that a "lookback PF" scheduling can strike a good balance between system throughput and fairness while taking the underlying application requirements into account.