9403742 Meyn This proposal concerns development and application of new methodologies for analysis of complex systems, most of which can be seen as special cases of general multiclass network systems with feedback. Perhaps the most important examples is the design of semiconductor manufacturing systems, where one impact of the analysis would include the construction of stable and efficient routing and scheduling policies; but the applications of understanding the general systems is far more widespread. Specifically we propose to carry out research into three aspects of system analysis: (i) Methods of evaluating system stability and instability, which will include not only discrete and continuous time representations of systems, but also fluid and diffusion approximations for such systems; (ii) Performance measures on stable systems, and specifically comparison of rates at which such systems achieve a stable regime; (iii) Robustness of system design against perturbations in assumptions. The specific types of applications envisaged include manufacturing systems, and more general queuing systems with feedback, for which the stability and performance results to be developed are well suited. We will also consider in detail scheduling algorithms for such systems, and develop simulation methods for modeling and performance validation. Overall this project can be expected to deliver new methodologies which will unify the current work in all of (i)- (iii); and to provide a number of significant applications to manufacturing and engineering systems which, of themselves, will be a major importance in improving design guidelines. ***
