Particle methods for multi-group pedestrian flow

Mahato, Naveen Kumar; Klar, Axel; Tiwari, Sudarshan

doi:10.1016/j.apm.2017.08.024

Cited by 25 publications

(14 citation statements)

References 44 publications

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“…Walking is a natural and basic form of human movement, and one of the basic aspects of personal freedom, so in some countries it is even regulated and protected by law [2,6].…”

Section: Pedestrian and Cyclist Flows Interactionmentioning

confidence: 99%

Pedestrian and cyclist flows interaction in the urban street and road network

Sotnikova¹,

Francke²

2020

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Due to the active popularization of sustainable urban mobility principles, there is an increase in the share of bicycle traffic in the overall modal split. The pedestrians are getting used to the fact that the cyclist is a full member of the traffic and has his/her own separate space. The concequence of this is cyclist and pedestrian flows conflicts.The article analyses the results of field research of cycling and pedestrian traffic volume. The permissible number of conflicts between them is defined, which makes it possible to understand the principles of combination or separation of flows in space. Based on the results obtained, recommendations for the design and arrangement of cycling and pedestrian infrastructure are provided.

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“…Walking is a natural and basic form of human movement, and one of the basic aspects of personal freedom, so in some countries it is even regulated and protected by law [2,6].…”

Section: Pedestrian and Cyclist Flows Interactionmentioning

confidence: 99%

Pedestrian and cyclist flows interaction in the urban street and road network

Sotnikova¹,

Francke²

2020

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“…Interacting particle systems and, more generally interacting multiagent models, appear frequently in the natural and social sciences. In addition to the well known applications, e.g., plasma physics [22] and stellar dynamics [7], new applications include, e.g., the modeling of chemotaxis [40], pedestrian dynamics [24,30], crowd dynamics [32], urban modeling [14], models for opinion formation [18,21], collective behavior [11], and models for systemic risk [20]. In many of these applications, the phenomenological models involve unknown parameters that need to be estimated from data.…”

Section: Introductionmentioning

confidence: 99%

Eigenfunction martingale estimators for interacting particle systems and their mean field limit

Pavliotis¹,

Zanoni²

2021

Preprint

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We study the problem of parameter estimation for large exchangeable interacting particle systems when a sample of discrete observations from a single particle is known. We propose a novel method based on martingale estimating functions constructed by employing the eigenvalues and eigenfunctions of the generator of the mean field limit, linearized around the (unique) invariant measure of the mean field dynamics. We then prove that our estimator is asymptotically unbiased and asymptotically normal when the number of observations and the number of particles tend to infinity, and we provide a rate of convergence towards the exact value of the parameters. Finally, we present several numerical experiments which show the accuracy of our estimator and corroborate our theoretical findings, even in the case the mean field dynamics exhibit more than one steady states.

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“…Of course, we lose the explicit information of each particle, but have the advantage of saving a lot of storage in the simulation of the dynamics. Despite the lower accuracy many studies Albi and Pareschi 2013;Mahato et al 2018 indicate that the evolution of the density yields a good approximation of the original particle system, see also Weissen et al (2021), which proposed a limiting procedure that is considered in more detail below.…”

Section: Introductionmentioning

confidence: 99%

Space mapping-based optimization with the macroscopic limit of interacting particle systems

2021

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We propose a space mapping-based optimization algorithm for microscopic interacting particle dynamics which are infeasible for direct optimization. This is of relevance for example in applications with bounded domains for which the microscopic optimization is difficult. The space mapping algorithm exploits the relationship of the microscopic description of the interacting particle system and a corresponding macroscopic description as partial differential equation in the “many particle limit”. We validate the approach with the help of a toy problem that allows for direct optimization. Then we study the performance of the algorithm in two applications. A pedestrian flow is considered and the transportation of goods on a conveyor belt is optimized. The numerical results underline the feasibility of the proposed algorithm.

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Particle methods for multi-group pedestrian flow

Cited by 25 publications

References 44 publications

Pedestrian and cyclist flows interaction in the urban street and road network

Pedestrian and cyclist flows interaction in the urban street and road network

Eigenfunction martingale estimators for interacting particle systems and their mean field limit

Space mapping-based optimization with the macroscopic limit of interacting particle systems

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