A new technique for the analysis of a buffered two-node packet radio network

The authors consider a packet radio network with two nodes both of which access a single channel using the slotted-Aloha protocol. This model results in a network of two interfering queues. Such networks seldom have closed-form expressions for the equilibrium probabilities. However, if fixed arrival probabilities are assumed and it is also assumed that one node uses a constant transmission probability, a product-form-solution control (PFS-control) can be found which controls the other node´s transmission probability. This is done using the consistency graph method. Under PFS-control, the transmission probabilities approach asymptotic values as the packet backlog increases. It is noted that the PFS-control is intuitively satisfying; the network under PFS-control tends to adjust its transmission probabilities to reduce large unequal packet backlogs. Using the asymptotic values for the transmission probabilities, they also find a set of necessary conditions for network stability