As part of the IEEE 802.16 protocol, the random access scheme is used for ranging. The ratio between the numbers of periodic ranging slots and data slots in the uplink subframe decides the contention throughput, ranging delay and data throughput, all of which are important parameters of the system performance. However no specific ratio is standardized in the protocol. So, it is necessary to determine the optimal number of periodic ranging slots which is the decisive factor of the ratio. In this paper, the three parameters above are analyzed and the optimal number of the periodic ranging slots is derived. In addition, an estimation method is proposed to predict the number of contention users. The correctness of the analysis is verified by the simulation results, and it is demonstrated that the contention throughput efficiency is high with the derived optimal number.