In this paper, we consider a ranging procedure occurred in the fixed and mobile broadband wireless access systems based on the Wireless MAN-OFDMA (Metropolitan Area Network -Orthogonal Frequency Division Multiple Access). A ranging procedure is a collection of processes for a Mobile Subscriber Station (MSS) and a Base Station (BS) to maintain the quality of the radio frequency communication link between them. When multiple subscribers select the same ranging codes from the given ranging code pool and range the BS by transmitting those identical ranging codes at the same time frame, the ranging collision may be occurred at BS because the BS can not differentiate two different MSSs since they selected the same ranging code. We propose a mathematical performance model to analyze the probability of ranging collision affected by both the capacity of the ranging code pool and the rate of the MSS arriving to the system and investigate the numerical results of the proposed model. By the proposed model and its numerical results, we can calculate the minimum number of the required ranging codes to be implemented in BS(Base Station). We compare the analytical results with the simulated results to validate the proposed mathematical model is correct.