PDE FLUID MODELING OF MULTITHREAD SYSTEMS AND OPTIMAL CONTROL Florian De Vuyst Ecole Centrale Paris, laboratoire de Math´ ematiques Appliqu´ ees aux Syst` emes Grande Voie des Vignes, 92 295 Chˆ atenay-Malabry cedex FRANCE devuyst@mas.ecp.fr Pascal Jaisson Ecole Centrale Paris, laboratoire de Math´ ematiques Appliqu´ ees aux Syst` emes Grande Voie des Vignes, 92 295 Chˆ atenay-Malabry cedex FRANCE jaisson@mas.ecp.fr Abstract We here propose fluid models of a multithread/multitask system. This can be straighforwardly extended to a network of such components. The leading equations form a system of hyperbolic equations coupled by a nonlocal term of current total load. PDEs are also used for the compu- tation of the service times. A numerical stable and efficient method of discretisation is then proposed. To illustrate the usefulness of such mod- els, we numerically solve a problem of optimal control of quality of ser- vice (QoS) management and demonstrate the efficiency of the method. Keywords: System modeling, fluid modeling, buffer system, multithread system, partial differential equation (PDE), optimal control, quality of service, genetic algorithms Introduction It is of interest to try to mimic principles of Fluid Mechanics to other fields and disciplines, especially for process and flux management. About pioneer works in this direction, let us mention Whitham’s book [8]; the author proposes conservation laws for modeling roadway traffic flows. Those PDEs are shown to be able to capture traffic bottlenecks with formation of nonlinear shock waves. The idea to find high level mean flow equations is particularly interesting