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A recent class of approaches for enhancing the performance of cellular wireless data networks has focused on improving the underlying network model. It has been shown that using the peer-to-peer network model, a mode of communication typically seen in ad hoc wireless networks, can result in performance improvements such as increased data rate, reduced transmission power, better load balancing, and enhanced network coverage. However, the true impact of adopting the peer-to-peer network model in such an environment is yet to be fully understood. In this paper, we investigate the performance benefits and drawbacks of using the peer-to-peer network model for Internet access in cellular wireless data networks. We find that, although the peer-to-peer network model has significantly better spatial reuse characteristics, the improved spatial reuse does not translate into better throughput performance. Instead, we observe that using the peer-to-peer network model as-is might actually degrade the throughput performance of the network. We identify and discuss the reasons behind these observations. Using the insights gained through the performance evaluations, we then propose two categories of approaches to improve the performance of the peer-to-peer network model: approaches that leverage assistance from the base station and approaches that leverage the relaying capability of multihomed hosts. Through simulation results, we show that using the peer-to-peer network model in cellular wireless data networks is a promising approach when the network model is complemented with appropriate mechanisms.