Network control by Bayesian broadcast
Ronald L. Rivest · IEEE Transactions on Information Theory · 1987
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 uand further simplifying. Each station keeps a copy of u, transmits a packet with probability1/ u, and then updates uin two steps: For collisions, increment uby(e-2)^{-l}=1.39221 \cdots. For successes and holes, decrement uby1. Set uto\max ( u + \hat{\lambda}, 1), where\hat{\lambda}is an estimate of the arrival rate\lambdaof 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.