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In this thesis, we propose the predictive multicast polling scheme for medium access control in wireless networks with multipacket reception capability. We concentrate on the case in which the packet arrival process is general and the maximum queue size is finite but larger than one. We derive both analytical results and simulation results. We use the theory of discrete-time Markov chain to analyze the evolution of the system state. In addition, we propose to use Markov reward processes to calculate the throughput. Furthermore, we obtain the average system size, the packet blocking probability, and the average packet delay. The proposed analysis approach is applicable no matter whether perfect state information is available to the controller or not. We also use simulation results to justify the usage of the proposed approach. Our study shows that the system performance can be significantly improved with a few additional buffers in the queues. The proposed medium access control scheme can be used in the single-hop wireless local area networks and the multi-hop wireless mesh networks.

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.