Time-To-Collision Models for Single-File Pedestrian Motion

Cordes, Jakob; Chraibi, Mohcine; Tordeux, Antoine; Schadschneider, Andreas

doi:10.17815/cd.2021.133

Cited by 5 publications

(2 citation statements)

References 16 publications

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“…see also [63][64][65]. The parameters (61) with the second condition (62) give the following condition for stability…”

Section: Proof Of Theorem 32: Matrix a Spectral Boundmentioning

confidence: 99%

Stability analysis of a stochastic port-Hamiltonian car-following model

Rüdiger,

Tordeux,

Ugurcan

2024

J. Phys. A: Math. Theor.

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Port-Hamiltonian systems are pertinent representations of many nonlinear physical systems. In this study, we formulate and analyse a general class of stochastic car-following models with a systematic port-Hamiltonian structure. The model class is a generalisation of classical car-following approaches, including the optimal velocity model of Bando et al (1995 Phys. Rev. E 51 1035), the full velocity difference model of Jiang et al (2001 Phys. Rev. E 64 017101), and recent stochastic following models based on the Ornstein–Uhlenbeck process. In contrast to traditional models where the interaction is totally asymmetric (i.e. depending only on the speed and distance to the predecessor), the port-Hamiltonian car-following model also depends on the distance to the follower. We determine the exact stability condition of the finite system with N vehicles and periodic boundaries. The stable system is ergodic with a unique Gaussian invariant measure. Other properties of the model are studied using numerical simulation. It turns out that the Hamiltonian component improves the flow stability and reduces the total energy in the system. Furthermore, it prevents the problematic formation of stop-and-go waves with oscillatory dynamics, even in the presence of stochastic perturbations.

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“…see also [63][64][65]. The parameters (61) with the second condition (62) give the following condition for stability…”

Section: Proof Of Theorem 32: Matrix a Spectral Boundmentioning

confidence: 99%

Stability analysis of a stochastic port-Hamiltonian car-following model

Rüdiger,

Tordeux,

Ugurcan

2024

J. Phys. A: Math. Theor.

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“…• Chapter 6 examines the dynamics of single-file traffic, which exhibits significant collective effects, such as stop-and-go waves, the latter being a validation benchmark for agent-based modeling approaches to traffic systems [13]. The chapter explores these models with a focus on their interrelationships, building on previous work [16].…”

Section: Plan Of the Chaptermentioning

confidence: 99%

Behavioral Human Crowds and Society

Bellomo,

Gibelli

2023

Modeling and Simulation in Science, Engineering and Technology

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This chapter provides an introduction to the contents of this edited volume. In keeping with the style of the previous edited volumes, we also consider research perspectives. The first part of this chapter contributes to the selection of some key perspectives that take into account not only the technical interest of modeling and simulation, but also the impact that this research activity can have on the well-being of society. The second part provides a brief introduction to the contents of the chapters that follow this editorial introduction. The contents of the chapter refer both to the aforementioned key topics and to the contents of the preceding edited volumes [5,8,15].

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