Uplink traffic channel allocation is realized by utilizing a dedicated control channel in which a prescribed portion of the control channel resource, for example, frequency, time slot or the like, is reserved for transporting the uplink traffic channel requests. Both the base station and the particular mobile unit know the prescribed portion of the control channel resource a priori. Consequently, when the particular mobile unit transmits an uplink traffic channel request via the prescribed portion of the control channel resource there is no need for adding any control header information, thereby minimizing overhead. Furthermore, the length of the uplink traffic channel requests can be optimally chosen without constraints imposed by other control message schemes. Reduced overhead coupled with the prescribed portion of the control channel resource arriving quite frequently reduces latency in the particular mobile unit acquiring an uplink traffic channel. In one example, delivery of adequate uplink traffic channel request information to the base station, while minimizing the adverse impact of losing requests, is ensured by persistently transmitting the requests. Specifically, after the mobile unit transmits a first request, it transmits a second or even a third request instead of waiting to receive a response message from the base station and/or waiting for a timer to time out. By the mobile unit using such a persistent request transmission scheme, the base station can readily determine the true value of the received request by eliminating the transmission loop delay effect, thereby allowing a sensible assignment decision to be made.