An innovating PDE model based on fluid flow paradigm for multithread systems

We propose traffic flow models of multithread systems. 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 computation of the service times. A numerical stable and efficient method of discretization is then proposed. To illustrate the usefulness of such models, we numerically solve a problem of optimal control of quality of service (QoS) management and demonstrate the efficiency of the method.