  In this paper, we analyze a shared access network with a fixed primary node
and randomly distributed secondary nodes whose distribution follows a Poisson
point process (PPP). The secondaries use a random access protocol allowing them
to access the channel with probabilities that depend on the queue size of the
primary. Assuming a system with multipacket reception (MPR) receivers having
bursty packet arrivals at the primary and saturation at the secondaries, our
protocol can be tuned to alleviate congestion at the primary. We study the
throughput of the secondary network and the primary average delay, as well as
the impact of the secondary node access probability and transmit power. We
formulate an optimization problem to maximize the throughput of the secondary
network under delay constraints for the primary node, which in the case that no
congestion control is performed has a closed form expression providing the
optimal access probability. Our numerical results illustrate the impact of
network operating parameters on the performance of the proposed priority-based
shared access protocol.
