IEEE 802.16 standard suite defines the air interface specifications for fixed and mobile broadband access in wireless metropolitan area networks. Although the IEEE 802.16 MAC has been well defined by various bandwidth allocation and scheduling mechanisms to support QoS for different applications, efficient bandwidth allocation still remains as an open issue. We analyze and develop a mathematical model to evaluate the performance of the contention-based and delay-tolerant applications in IEEE 802.16 networks. We focus our attentions on allocating the uplink bandwidth efficiently, the basic goal is to optimize the performance with an optimal bandwidth allocation mechanism. The results of our analysis lay out clearly that a maximum uplink throughput and a minimum number of pending bandwidth request transmission can always be acquired by optimizing the contention period size in a frame. This optimal size is also influenced by the number of terminals in the network, which is also analyzed in the later part of the paper. Our results can be used for providing probabilistic throughput guarantee and determining the optimal contention period.