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 eachn, 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 further simplifying. Each station keeps a copy ofν, transmits a packet with probability1/ν, and then updates two steps: For collisions, increment(e-2)⁻ˡ=1.39221 ⋯. For successes and holes, decrement1. Setmax (ν + λ̂, 1), whereλ̂is an estimate of the arrival rate 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 forλ < e⁻¹are discussed.