Cutoff points for roll-call protocols in multiple-access systems

This paper is a summary of a longer paper of the same title to appear elsewhere. We consider a communication network which employs a single multiple access channel linked to many users. We assume that the channel has the capability of carrying up to k - 1 successful transmissions (from k - 1 users) simultaneously, but if k or more users transmit simultaneously the transmitted signals interfere with each other to cause a collision and no successful transmission takes place. An algorithm has to be devised to resolve the collision. The k = 2 case is the standard model for multiple-access channel communication. Recently, the general k case has also been studied.