The IEEE 802.16 standard is a promising technology for 4G mobile networks. Though supporting versatile service classes, best effort (BE) service class is expected to dominate WiMAX networks, due to operational simplicity. One of bandwidth request mechanisms that subscriber stations (SS) can utilize to issue bandwidth requests (BW-REQ) for BE connections is contention-based random access. An SS starts a timer T16 when transmitting a BW-REQ. If getting a grant before timer expiration, the SS transmits data packets at the allocated time slots; otherwise it performs truncated binary exponential backoff process for BW-REQ retransmission. The default value of T16 is one frame time. However, T16 impacts on contention and request collision significantly. In the paper, we develop an analytical model for T16 timer setting. Besides, we derive analytical expressions for the average number of tries per BW-REQ and the average packet delay. We compare the theoretical results of fixed and adjustable timers. The results show that adjusting timer reduces both the number of collision and the average packet delay.