Evacuation dynamics influenced by spreading hazardous material
Simone Göttlich Sebastian Kühn Jan Peter Ohst Stefan Ruzika Markus Thiemann
Networks & Heterogeneous Media 2011, 6(3): 443-464 doi: 10.3934/nhm.2011.6.443
In this article, an evacuation model describing the egress in case of danger is considered. The underlying evacuation model is based on continuous network flows, while the spread of some gaseous hazardous material relies on an advection-diffusion equation. The contribution of this work is twofold. First, we introduce a continuous model coupled to the propagation of hazardous material where special cost functions allow for incorporating the predicted spread into an optimal planning of the egress. Optimality can thereby be understood with respect to two different measures: fastest egress and safest evacuation. Since this modeling approach leads to a pde/ode-restricted optimization problem, the continuous model is transferred into a discrete network flow model under some linearity assumptions. Second, it is demonstrated that this reformulation results in an efficient algorithm always leading to the global optimum. A computational case study shows benefits and drawbacks of the models for different evacuation scenarios.
keywords: Evacuation dynamic network flows optimization.
Optimization for a special class of traffic flow models: Combinatorial and continuous approaches
Simone Göttlich Oliver Kolb Sebastian Kühn
Networks & Heterogeneous Media 2014, 9(2): 315-334 doi: 10.3934/nhm.2014.9.315
In this article, we discuss the optimization of a linearized traffic flow network model based on conservation laws. We present two solution approaches. One relies on the classical Lagrangian formalism (or adjoint calculus), whereas another one uses a discrete mixed-integer framework. We show how both approaches are related to each other. Numerical experiments are accompanied to show the quality of solutions.
keywords: Traffic networks conservation laws combinatorial optimization. control of discretized PDEs adjoint calculus

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