In this paper, we analyze a shared access network with a fixed primary node and randomly distributed secondary nodes whose spatial distribution follows a poisson point process. The secondary nodes use a random access protocol allowing them to access the channel with probabilities that depend on the queue size of the primary node. Assuming a system with multipacket reception receivers, having bursty packet arrivals at the primary and saturated traffic at the secondary nodes, our protocol can be tuned to alleviate congestion at the primary. We analyze 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; in the case of no congestion control, the optimal access probability can be provided in closed form. Our numerical results illustrate the effect of network operating parameters on the performance of the proposed priority-based shared access protocol.