Sponsor: NSF
The main motivation for this research is the need for effective methods for the study of the asymptotic behavior and fundamental limits that occur in networking. In this proposal we restrict our interest to stability problems in a multidimensional environment. Our definition of stability 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 stable 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, sudden changes in network behavior, and so forth. The variability inherent in most distributed systems is such that to make meaningful performance predictions, it is necessary to study the evolution of a stochastic model. Such a stochastic approach is assumed throughout this project. Our past experiences led us to the conclusion that Markovian techniques applied to multidimensional stability provide only a partial solution. In this project we propose several new approaches to the stability analysis of networking that are based on a non-Markovian philosophy. We 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. The proposed research is in part a continuation and extension of the work carried out by the PI under previous NSF/NCR sponsorship.