Achieving target throughputs in random-access networks

Random-access algorithms such as CSMA provide a popular mechanism for distributed medium access control in large-scale wireless networks. In recent years, tractable stochastic models have been shown to yield accurate throughput estimates for CSMA networks. We consider a saturated random-access network on a general conflict graph, and prove that for every feasible combination of throughputs, there exists a unique vector of back-off rates that achieves this throughput vector. This result entails proving global invertibility of the non-linear function that describes the throughputs of all nodes in the network. We present several numerical procedures for calculating this inverse, based on fixed-point iteration and Newton’s method. Finally, we provide closed-form results for several special conflict graphs using the theory of Markov random fields.