Optimal Throughput Allocation in Random Access Networks of General Topology

We consider a model of the random access (Slotted Aloha-type) network of general topology. We characterize efficient (Pareto) boundary of the network throughput region as the family of solutions optimizing weighted proportional fairness objective, parameterized by link weights. Using this characterization we propose a generic distributed scheme, which uses dynamic link weights to "move" link throughput allocation within the Pareto boundary to a desired point optimizing a specific objective. As an example of application of the general scheme, we propose an algorithm seeking to optimize weighted proportional fairness objective subject to minimum link throughput constraints. We study asymptotic behavior of the algorithm and show that link throughputs converge to optimal values as long as link dynamic weights converge. Finally, we present simulation experiments that show good performance of the algorithm.