Bridging the Gap: From Cellular Automata to Differential Equation Models for Pedestrian Dynamics

Dietrich, Felix; Köster, Gerta; Seitz, Michael; Sivers, Isabella von

doi:10.1007/978-3-642-55195-6_62

Cited by 5 publications

(6 citation statements)

References 19 publications

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“…This so-called overlapping-oscillation duality is discussed in more detail in [25,26]. These problems that often lead to a "complexification" of the original (elegant) Ansatz of force-based models, may explain the paradigm shift observed lately with the emergence of new first-order models or so called "velocity models" [14,17,[27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Jamming transitions in force-based models for pedestrian dynamics

et al. 2015

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Force-based models describe pedestrian dynamics in analogy to classical mechanics by a system of second order ordinary differential equations. By investigating the linear stability of two main classes of forces, parameter regions with unstable homogeneous states are identified. In this unstable regime it is then checked whether phase transitions or stop-and-go waves occur. Results based on numerical simulations show, however, that the investigated models lead to unrealistic behavior in the form of backwards moving pedestrians and overlapping. This is one reason why stop-and-go waves have not been observed in these models. The unrealistic behavior is not related to the numerical treatment of the dynamic equations but rather indicates an intrinsic problem of this model class. Identifying the underlying generic problems gives indications how to define models that do not show such unrealistic behavior. As an example we introduce a force-based model which produces realistic jam dynamics without the appearance of unrealistic negative speeds for empirical desired walking speeds.

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Section: Introductionmentioning

confidence: 99%

Jamming transitions in force-based models for pedestrian dynamics

et al. 2015

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“…The idea of deriving an updating order from the stepping dynamics was even pushed further in the so-called optimal steps model [57,58,59], for which not only the phase but also the duration of the stepping cycle and the length of the steps vary from one individual to another one. Though in the case of a constant step length the optimal steps model can also be applied to cellular automata models, it is more generally defined in a continuous space.…”

Section: Resultsmentioning

confidence: 99%

Two dimensional outflows for cellular automata with shuffle updates

2015

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In this paper, we explore the two-dimensional behavior of cellular automata with shuffle updates. As a test case, we consider the evacuation of a square room by pedestrians modeled by a cellular automaton model with a static floor field. Shuffle updates are characterized by a variable associated to each particle and called phase, that can be interpreted as the phase in the step cycle in the frame of pedestrian flows. Here we also introduce a dynamics for these phases, in order to modify the properties of the model. We investigate in particular the crossover between low-and high-density regimes that occurs when the density of pedestrians increases, the dependency of the outflow in the strength of the floor field, and the shape of the queue in front of the exit. Eventually we discuss the relevance of these results for pedestrians.

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“…age distributions of the group of evacuees). The method of choice for microscopic models is simulation (see, for instance, Dietrich et al 2014).…”

Section: Macroscopic and Microscopic Mathematical Modelsmentioning

confidence: 99%

Optimisation models to enhance resilience in evacuation planning

Goerigk

Hamacher

2015

Civil Engineering and Environmental Systems

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We argue that the concepts of resilience in engineering science and robustness in mathematical optimisation are strongly related. Using evacuation planning as an example application, we demonstrate optimisation techniques to improve solution resilience. These include a direct modelling of the uncertainty for stochastic or robust optimisation as well as taking multiple objective functions into account.

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Bridging the Gap: From Cellular Automata to Differential Equation Models for Pedestrian Dynamics

Cited by 5 publications

References 19 publications

Jamming transitions in force-based models for pedestrian dynamics

Jamming transitions in force-based models for pedestrian dynamics

Two dimensional outflows for cellular automata with shuffle updates

Optimisation models to enhance resilience in evacuation planning

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