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A two-node packet-radio network with infinite buffers at the nodes is considered. The two nodes transmit data packets to a common station through a shared radio channel. One of the two nodes is granted full access rights to the channel, while the other node bases its decisions whether to transmit or not on the acknowledgments it receives about its transmissions. For this acknowledgment-based access scheme and for general arrival processes, we derive the joint generating function of the queue contents in steady state, as well as the condition for steady state. From the generating function, any moment can be derived, as well as average time delays. Numerical results are presented for independent Bernoulli arrival processes.