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The IEEE 802.16 standard is a promising technology for the fourth-generation mobile networks and is being actively promoted by the Worldwide Interoperability for Microwave Access (WiMAX) Forum: an industry-led consortium. Among the various service classes supported in the standard, best-effort service is expected to be the major service class subscribed to by users due to its operational simplicity and lower charging rate compared with other service classes. In this paper, we investigate the throughput and packet-access-delay performance of best-effort service using the contention-based bandwidth request mechanism in a saturated IEEE 802.16 network. In particular, we develop a simple fixed-point analysis to approximate the failure probability of a bandwidth request and derive analytical expressions for network throughput and packet access delay. Furthermore, the uniqueness of the fixed point is established. The accuracy of the analytical model is validated by comparison with simulation over a wide range of operating conditions. The implications of various different parameter configurations on the system performance are investigated using the analytical model. The utility of the model is further demonstrated by finding the maximum achievable throughput and obtaining its corresponding optimal initial contention window.