The research will address the need for effective methods for the study of the asymptotic behavior and fundamental limits that occur in networking. The work will be restricted to stability problems in a multidimensional environment. The definition of stability as used here is broad enough to cover many aspects of networking behavior such as boundness in probability (i.e. substability), limiting distributions, geometric ergodicity, strong stability, rate of convergence to table modes, finite moments and tails of the queue lengths and waiting time distributions, partial stability, robustness, cut-off phenomena, shape of distributions, bistability, structural properties (e.g. monotonicity of some parameters of interest), asymptotic performance, no-starvation regime for real time systems, practical stability, and sudden changes in network behavior. A stochastic approach is assumed through the project. The research will use new approaches to the stability analysis of networking that are based on a non-Markovian philosophy. The research will demonstrate that such an approach can rigorously provide stability criteria for such open problems as stability of multiaccess systems, token passing rings, FDDI, ATM networks, general network of queues, and so forth.
