In this paper we propose a novel model for the capacity analysis on the reservation-based random multiple access system, which can be applied to the medium access control protocol of the emerging WiMax technology. In such a wireless broadband access system, in order to support QoS, the channel time is divided into consecutive frames, where each frame consists of some consequent mini-slots for the transmission of requests, used for the bandwidth reservation, and consequent slots for the actual data packet transmission. Three main outcomes are obtained: first, the upper and lower bounds of the capacity are derived for the considered system. Second, we found through the mathematical analysis that the transmission rate of reservation-based multiple access protocol is maximized, when the ratio between the number of mini-slots and that of the slots per frame is equal to the reciprocal of the random multiple access algorithm's transmission rate. Third, in the case of WiMax networks with a large number of subscribers, our analysis takes into account both the capacity and the mean packet delay criteria and suggests to keep such a ratio constant and independent of application-level data traffic arrival rate.