Considering that the application of the direct-sequence slotted spread ALOHA communications system to access/control channel is effective in communications systems with traffic channels operating at CDMA mode, the spread ALOHA communications system is discussed in terms of the system configuration and transmission efficiency. The transmission efficiency of the spread ALOHA communications system using a unified spread code is derived by means of two methods. One is based on the simulation of demodulation algorithm, and the other is based on the approximation by modeling. It becomes obvious from quantitative evaluation in terms of the probability of packet success and the throughput performance that the approximated results coincide with the simulated results, and that the modeling is very effective to estimate the transmission efficiency of the spread ALOHA communications system.