This paper presents a fuzzy control-based intelligent medium access controller (FiMAC), which optimizes random access control between heterogeneous traffic aiming at more efficient voice/data integrated services in dynamic reservation TDMA-based broadband radio access networks. In order to achieve the design objective, viz. a differentiated quality-of-service (QoS) guarantee for individual service plus maximal system resource utilization, the FiMAC intelligently and independently controls the random access parameters such as the lengths of random access regions dedicated to respective service traffic and the corresponding permission probabilities, frame-by-frame basis. In addition, we have adopted a mobile-assisted random access mechanism where the voice terminal readjusts a global permission probability from the FiMAC, to handle the 'fair access' issue resulting from distributed queueing problems inherent in the access network. Our extensive simulation results indicate that the FiMAC is well coordinated with a mobile-assisted mechanism such that significant improvements are achieved in terms of voice capacity, delay, and fairness over most of the existing MAC schemes for the integrated services.