9634681 Bambos This research investigates key dynamical aspect of parallel processing systems, including those pertaining to distributed queueing, synchronization and coordination, and real-time task scheduling and resource allocation. The objective of the research is the development and articulation of a systematic general parallel processing queueing paradigm that goes beyond the current queueing network paradigm, which has had limited success in capturing synchronization and coordination aspects in a dynamic framework. The emphasis of the research is on general canonical models and analysis techniques that will result in systematic design principles and methodologies. Applications will focus on selected parallel processing architectures in manufacturing and computing systems. The research will include an investigation of queueing and synchronization in environments with randomly modulated service as well as systems of "interacting events" that exhibit critical phenomena. While primarily theoretical in nature, this work holds promise for extending our understanding of the complex dynamics inherent in many modern telecommunications and manufacturing systems. To date, no satisfactory mathematical theory has been proposed that comprehends all of the intricacies of material flow in these systems. New mathematical techniques, including those proposed here, are essential in extending the methodological frontiers of research, with the ultimate goal of providing useful modeling and analysis techniques for the design, operation, and optimization of these systems .
