There are three main results in this dissertation. They are PLS-completeness of discrete Hopfield network convergence with eight different restrictions, (degree 3, bipartite and degree 3, 8-neighbor mesh, dual of the knight's graph, hypercube, butterfly, cube-connected cycles and shuffle-exchange), exponential convergence behavior of discrete Hopfield network, and simulation of Turing machines by discrete Hopfield Network.

In this thesis, a framework for Quality of Service provisioning in next generation wireless access networks is proposed. The framework aims at providing a differentiated service treatment to real-time (delay-sensitive) and non-real-time (delay-tolerant) multimedia traffic flows at the link layer. Novel techniques such as bandwidth compaction, channel reservation, and channel degradation are proposed. Using these techniques, we develop a call admission control algorithm and a call control block as part of the QoS framework. The performance of the framework is captured through analytical modeling and simulation experiments. By analytical modeling, the average carried traffic and the worst case buffer requirements for real-time and non-real-time calls are estimated. Simulation results show a 21% improvement in call admission probability of real-time calls, and a 17% improvement for non-real-time calls, when bandwidth compaction is employed. The channel reservation technique shows a 12% improvement in call admission probability in comparison with another proposed scheme in the literature.