Near-optimum control of multiple access collision channels

A method based on recursive computation of the expected number of attempts and successes during the collision resolution phase of a protocol is introduced for the design of near-optimum protocols for multiple access collision channels with ternary and binary feedback. With this approach it is possible to circumvent the extremely difficult and still unsolved problem of finding the protocol which achieves the highest throughput among all protocols by settling for a near-optimum solution. The key to the design of the protocols is to approximate the originally infinite-dimensional optimization problem by a one-dimensional optimization problem. In the ternary feedback the proposed protocol achieves a throughput virtually identical to the highest throughput reported today. Several forms of binary feedback are considered, and protocols are introduced that achieve the highest throughput of any known protocols