Network control by bayesian broadcast

A transmission control strategy is described for slotted-ALOHA-type broadcast channels with ternary feedback. At each time slot, each station estimates the probability that n stations are ready to transmit a packet for each n, using Bayes' rule and the observed history of collisions, successful transmissions, and holes (empty slots). A station transmits a packet in a probabilistic manner based on these estimates. This strategy is called Bayesian broadcast. An elegant and very practical strategy--pseudo-Bayesian broadcast--is then derived by approximating the probability estimates with a Poisson distribution with mean nu and further simplifying. Each station keeps a copy of nu, transmits a packet with probability 1/nu, and then updates nu in two steps: For collisions, increment nu by (e-2)^{-l}=1.39221 cdots . For successes and holes, decrement nu by 1 . Set nu to max (nu + hat{lambda}, 1), where hat{lambda} is an estimate of the arrival rate lambda of new packets into the system. Simulation results are presented showing that pseudo-Bayesian broadcast performs well in practice, and methods that can be used to prove that certain versions of pseudo-Bayesian broadcast are stable for lambda < e^{-1} are discussed.