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In this doctoral thesis we cover the performance evaluation of next generation data plane architectures, comprised of complex software as well as programmable hardware components that allow fine granular configuration. In the scope of the thesis we propose mechanisms to monitor the performance of singular components and model key performance indicators of software based packet processing solutions. We present novel approaches towards network abstraction that allow the integration of heterogeneous data plane technologies into a singular network while maintaining total transparency between control and data plane. Finally, we investigate a full, complex system consisting of multiple software-based solutions and perform a detailed performance analysis. We employ simulative approaches to investigate overload control mechanisms that allow efficient operation under adversary conditions. The contributions of this work build the foundation for future research in the areas of network softwarization and network function virtualization.
We consider a multi-species gas mixture described by a kinetic model. More precisely, we are interested in models with BGK interaction operators. Several extensions to the standard BGK model are studied.
Firstly, we allow the collision frequency to vary not only in time and space but also with the microscopic velocity. In the standard BGK model, the dependence on the microscopic velocity is neglected for reasons of simplicity. We allow for a more physical description by reintroducing this dependence. But even though the structure of the equations remains the same, the so-called target functions in the relaxation term become more sophisticated being defined by a variational procedure.
Secondly, we include quantum effects (for constant collision frequencies). This approach influences again the resulting target functions in the relaxation term depending on the respective type of quantum particles.
In this thesis, we present a numerical method for simulating such models. We use implicit-explicit time discretizations in order to take care of the stiff relaxation part due to possibly large collision frequencies. The key new ingredient is an implicit solver which minimizes a certain potential function. This procedure mimics the theoretical derivation in the models. We prove that theoretical properties of the model are preserved at the discrete level such as conservation of mass, total momentum and total energy, positivity of distribution functions and a proper entropy behavior. We provide an array of numerical tests illustrating the numerical scheme as well as its usefulness and effectiveness.