To enhance the throughput of a slotted ALOHA control channel in a radio com
munication system, we present and analyze a method for estimating the numbe
r of remote stations that are attempting to transmit to a central base stat
ion. Each of the contending remote stations randomly chooses to transmit wi
th probability p. Our novel contribution is the use of information concerni
ng the number of successful packet transmissions that arrive without retran
smission (i.e., that are successfully received on their first transmission
attempt), as a metric for accurately and robustly estimating the number of
contending remote stations. This estimate is determined at the base station
and then used to compute the optimal transmission probability p that is us
ed as feedback to the remote stations for their use. The proposed estimatio
n method is analyzed and shown to provide good steady-state performance for
a variety of system models, including situations with noise and idling rem
ote stations. The scheme is also shown to provide good tracking capabilitie
s.