A buffered two-node packet radio network with product form solution

A packet radio network with two nodes, both of which access a single radio channel using the slotted ALOHA protocol, is discussed. This model results in a network of two interfering queues. Networks of interfering nodes normally do not have partial balance and thus seldom have product-form solution (PFSs). However, when certain assumptions are made on the network parameters, PFS-controls can be found that yield a PFS for the interfering two-node network. Three such cases are described. In the first two cases, PFS controls are found that control the new packet arrival rate. When operating under these PFS controls, the two-mode network has a simple, closed-form solution of the equilibrium probabilities, the expected throughput, and the expected packet delay. The throughput-delay performance closely approximates that of an exact two-node packet radio model. In the third case, a PFS control is found on one node's transmission probabilities. When operating under this PFS control, the transmission probabilities approach asymptotic values as the packet backlog increases. The network tends to adjust its transmission probabilities to reduce large unequal packet backlogs.<
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