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In this paper, an approximated model is proposed to analyze the performance of the contention based services via broadcast polling in unsaturated IEEE 802.16 networks with channel errors. The main idea is that each subscriber station with buffer capacity K can be treated as a M/G/1/K queue with service time determined by the backoff process of broadcast polling. Using this model, the normalized network throughput and the distribution of the packet delay are derived. This proposed analytical model is useful for performance evaluation and optimization of best effort or contention-based non-real time polling services. Our simulator written in C++ verifies the accuracy of the proposed analytical model. Furthermore, we show that the model gives good approximations for network performance with a more realistic bursty arrival process at light load, while providing conservative performance measures at medium and high loads.