Decentralized control of a multiple access broadcast channel: performance bounds

Optimal decentralized control of the multiple access broadcast channel is considered. A technique is presented for upper bounding the throughput of a slotted multiple access system with a finite number of users, immediate ternary feedback, retransmission of collisions, and no buffering. The upper bound is calculated for the two- and three-user cases, and it is shown that Hluchyj and Gallager's (1981) optimized window protocol is effectively optimal for these cases.