Structured first order conservation models for pedestrian dynamics

Hartmann, Dirk; Sivers, Isabella von

doi:10.3934/nhm.2013.8.985

Cited by 15 publications

(9 citation statements)

References 38 publications

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“…In this sense, we refer to some important contributions related to flux limiters, 22,40 while dependence of pedestrians' speed on the local density is an important way to control overcrowding. 12,13,24,39 We assume that the maximal reachable dimensionless velocity modulus v m = v m (α) depends linearly on the quality of the environment, in such a way that v m (0) = 0 -any movement is hindered -and v m (1) = 1 -the maximal speed can be reached. The dependence of the velocity modulus on the local density proposed in this paper is motivated by the fundamental diagrams for crowd flow, critically analyzed in Ref.…”

Section: Modeling the Velocity Modulusmentioning

confidence: 99%

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A kinetic theory approach to the dynamics of crowd evacuation from bounded domains

Agnelli

Colasuonno

Knopoff

2014

Math. Models Methods Appl. Sci.

106

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A mathematical model of the evacuation of a crowd from bounded domains is derived by a hybrid approach with kinetic and macro-features. Interactions at the micro-scale, which modify the velocity direction, are modeled by using tools of game theory and are transferred to the dynamics of collective behaviors. The velocity modulus is assumed to depend on the local density. The modeling approach considers dynamics caused by interactions of pedestrians not only with all the other pedestrians, but also with the geometry of the domain, such as walls and exits. Interactions with the boundary of the domain are non-local and described by games. Numerical simulations are developed to study evacuation time depending on the size of the exit zone, on the initial distribution of the crowd and on a parameter which weighs the unconscious attraction of the stream and the search for less crowded walking directions.

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Section: Modeling the Velocity Modulusmentioning

confidence: 99%

“…15, while Ref. 24 offers an interesting comparison between them. In the middle of these two scales, the kinetic theory approach was initiated in Ref.…”

Section: Introductionmentioning

confidence: 97%

A kinetic theory approach to the dynamics of crowd evacuation from bounded domains

Agnelli

Colasuonno

Knopoff

2014

Math. Models Methods Appl. Sci.

106

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“…Pedestrian dynamics simulations support successful crowd management by helping organizers of public events to foresee and prevent dangerous situations. Macroscopic pedestrian dynamic models like the Hartmann & Sivers mode (HARTMANN and VON SIVERS, 2013) are most suitable for simulating large numbers of people . The same macroscopic model can be applied to simulate the motion of cars.…”

Section: Hartmann-sivers Modelmentioning

confidence: 99%

“…Therefore, we introduce an interface which links human and vehicular flow. The movement behavior of cars and pedestrians is based on the macroscopic Hartmann and Sivers model (HARTMANN and VON SIVERS, 2013) and is calculated on a discrete network. Roads for cars and walking paths for pedestrians are represented by the edges of this network.…”

Section: The Hybrid Approachmentioning

confidence: 99%

Liquid Humans - Pedestrian Simulator based on the LWR-model

Aumann,

Osorio,

Lai

2016

Preprint

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Dense human flow has been a concern for the safety of public events for a long time. Macroscopic pedestrian models, which are mainly based on fluid dynamics, are often used to simulate huge crowds due to their low computational costs (COLOMBO and ROSINI, 2005). Similar approaches are used in the field of traffic simulations (LIGHTHILL and WHITHAM, 1955). A combined macroscopic simulation of vehicles and pedestrians is extremely helpful for all-encompassing traffic control. Therefore, we developed a hybrid model that contains networks for vehicular traffic and human flow. This comprehensive model supports concurrent multi-modal simulations of traffic and pedestrians (BIEDER-MANN, KIELAR, AUMANN, LAI and OSORIO, 2015).

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“…Models on the macroscopic scale ensure fast simulations but have a low spatial resolution. These approaches reduce the simulation scenario to a graph-network and describe pedestrians as cumulated and flowing densities [13,14]. In contrast, mesoscopic approaches model pedestrians as singular and discrete simulation objects.…”

Section: Related Workmentioning

confidence: 99%

Oppilatio+ - A data and cognitive science based approach to analyze pedestrian flows in networks

et al. 2017

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Public transport services are a widespread and environmentally friendly option for mobility. In the majority of cases, passengers of public transport services will have to walk from a subway, train, or bus station to their desired travel destination. In an urban environment with a network of narrow streets, this can lead to crowd congestions during rush hour, due to the fact that passengers tend to arrive in waves. In order to monitor and analyze such crowding behavior, city planners, crowd managers, and organizers of public events must ascertain which routes these pedestrians will take from the respective station to their destination. The Oppilatio + approach is suitable for solving this problem. It is an easy-to-apply approach to predict way-finding behavior with a minimal set of information. The necessary data includes the schedule of incoming transport vehicles at the stations and the time-stamped count of pedestrians at the respective destinations. Under these conditions, the Oppilatio + approach is suitable for estimating the distribution of pedestrians on all possible walkways between stations and destinations. This information helps crowd control experts to recognize weak spots in the infrastructure and help event organizers to ensure an undisturbed arrival at their event. We validated our approach using two field experiments. The first one was a field study on a public event, and the second one was a case study for a large Swiss train station.

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Structured first order conservation models for pedestrian dynamics

Cited by 15 publications

References 38 publications

A kinetic theory approach to the dynamics of crowd evacuation from bounded domains

A kinetic theory approach to the dynamics of crowd evacuation from bounded domains

Liquid Humans - Pedestrian Simulator based on the LWR-model

Oppilatio+ - A data and cognitive science based approach to analyze pedestrian flows in networks

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