The IEEE 802.16-based WiMAX technology has great potential for the fourth-generation mobile networks. Some of its service classes use the contention-based broadcast polling mechanism to request resources. In this paper, we investigate the performance experienced by these services when the network is unsaturated. In particular, we model each subscriber station as an M/G/1 queue where the service time is determined by the parameters of the network configuration and the binary exponential backoff contention resolution algorithm. We develop a fixed-point analysis to derive analytical expressions for network throughput and packet access delay. The accuracy of the analytical model is validated by comparing it with simulation over a wide range of operating conditions. The implications of various different parameter configurations on the performance are investigated using the analytical model. Moreover, we show that the model can be degenerated to the saturated condition. The utility of both the unsaturated and saturated models is further demonstrated by finding the optimal set of parameter values that maximize the network throughput.