In this dissertation, we propose using and analytically evaluate the predictive multicast polling scheme and the tree splitting algorithm for medium access control in interference dominating wireless access networks with random traffic and finite nodes. In an interference dominating wireless network, a receiver could simultaneously receive multiple packets from a variety of transmitters, as long as the signal-to-interference-plus-noise ratio exceeds a predetermined threshold. We concentrate on the case of in which the maximum queue size in a node is finite. We use discrete-time Markov chains, reward processes and regenerative processes to derive the throughput, the packet blocking probability, the average packet delay, and the average system size. We show that the system performance of the predictive multicast polling scheme can be significantly improved with a few additional buffers in the queues. Our study also shows that exact performance of the splitting algorithm depends on the total number of nodes in the networks. We verify our numerical results by rigorous mathematical proof and computer simulations.