A Three-Node Packet Radio Network

A two-hop packet radio network consisting of three nodes is considered. The three nodes have infinite buffers and share a common radio channel for transmitting their packets. Two of the nodes forward their packets to a third node that acts as a source of data as well as a relay that forwards all the packets entering the network to a main station. We assume that two of the nodes are granted full rights in accessing the channel while the third node uses a random access scheme. For this network we derive the condition for steady state and the generating function of the joint queue length distribution at the nodes in steady state. We also give several numerical examples and compare the performance of the network with and without a relay node.