A random access system with a finite number of buffered terminals is considered. The problem of how to decompose this system into a number of interconnected subsystems in order to maximize its throughput is studied. Two different interconnection topologies are considered, a directional ring topology and a fully connected network of subsystems. For each of these two topologies the problem of maximizing the throughput is reduced to a simple maximization problem. We apply the attained results to a slotted ALOHA and a CSMA/CD system. For the former a significant improvement in the throughput performance is reported, while simulation analysis shows an expected deterioration in the delay performance, for low intensity traffic.