Single-file motion
Single-file motion refers to the movement of agents, such as pedestrians, vehicles, or bicycles, in a single line without overtaking, focusing on the regulation of speed and spacing between them. This behavior is crucial for deriving fundamental diagrams that express the phenomenological relationship between mean speed, flow, and density in traffic engineering. Single-file traffic flow characteristics can be either smooth (laminar) or exhibit oscillating patterns like stop-and-go waves (accordion traffic, see the experiments by Sugiyama et al., Stern et al. and the simulation modules) which are problematic for traffic safety, performance and the environment and also observed in automated driving system (i.e. adaptive cruise control systems, see the experiments by Gunter et al., OpenACC and the simulation modules) as well as pedestrian and bicycle single-file motions.
Continuous following models, based on ordinary, delayed and stochastic differential equation systems, provide microscopic insights into vehicle and pedestrian behavior, with applications to driving automation and adaptive cruise control (ACC) systems in traffic engineering. We develop isotropic and anisotropic pedestrian and car-following models, including delay, noise, and other heterogeneity mechanisms, analyse their stability and long-term behavior, derive infinite limits and carry out experiment-based simulation and parameter calibration. For instance, the Adaptive Time Gap (ATG) model introduces a safety parameter for time gap regulation that ensure stable uniform dynamics. The Collision-Free Optimal Velocity (CFOV) model is a simplified version of the Optimal Velocity (OV) model by Bando et al. (1995) that mitigates unrealistic collisions and backward movements while describing stop-and-go traffic patterns (see the simulations #1, #2, #3). Derivation of the CFOV microscopic model results in a parabolic convection-diffusion partial differential macroscopic equation while derivation of the ATG models leads to the Lighthill-Whitham-Richards (LWR) macroscopic model.
In the local stability analysis (also called platoon stability), some vehicles follow a leader with assigned speed. The local stability is said to be overdamped when the convergence is oscillation-free. Such a feature allows to ensure, at least partially, the absence of collisions in the dynamics. The global stability analysis (also called string or collective stability) deals with vehicles on an infinite line or with periodic boundary conditions. Both stability properties are expected features of adaptive cruise control systems in traffic engineering. However, string stability conditions, including inductive and convective perturbations that vanish locally, are typically more restrictive than local conditions. Several factors pertubing the stability are identified in our research, including delay and latency in the dynamic, stochastic noise, especially colored and state-dependent noise, as well as individual heterogeneity, and various mechanisms are proposed to offset these effects.
- 2024
- R. Subaih, A. Tordeux and M. Chraibi, "Comprehensive review and new analysis software for single-file pedestrian experiments", Collective Dynamics, vol. 9, pp. 1–47, 2024.
- J. Ackermann, M. Ehrhardt, T. Kruse and A. Tordeux, "Stabilisation of stochastic single-file dynamics using port-Hamiltonian systems", IFAC-PapersOnLine, vol. 58, no. 17, pp. 145-150, 2024.
- B. Rüdiger, A. Tordeux and B. E. Ugurcan, "Stability analysis of a stochastic port-Hamiltonian car-following model", Journal of Physics A: Mathematical and Theoretical, vol. 57, no. 29, pp. 295203, 2024. IOP Publishing.
- M. Ehrhardt, T. Kruse and A. Tordeux, "The collective dynamics of a stochastic Port-Hamiltonian self-driven agent model in one dimension", ESAIM: M2AN, vol. 58, no. 2, pp. 515-544, 2024.
- R. Subaih and A. Tordeux, "Modeling pedestrian single-file movement: Extending the interaction to the follower", Physica A: Statistical Mechanics and its Applications, vol. 633, pp. 129394, 2024.
- 2023
- J. Cordes, M. Chraibi, A. Tordeux and A. Schadschneider, "Single-File Pedestrian Dynamics: A Review of Agent-Following Models", Bellomo, Nicola and Gibelli, Livio, Eds. Cham: Springer International Publishing, 2023, pp. 143-178.
- P. Khound, P. Will, A. Tordeux and F. Gronwald, "The Over-Damped String Stability Condition for a Platooning System", System Theory, Control and Computing Journal, vol. 3, no. 1, pp. 12-19, 2023.
- P. Khound, P. Will, A. Tordeux and F. Gronwald, "Unified framework for over-damped string stable adaptive cruise control systems", Transportation Research Part C: Emerging Technologies, vol. 148, pp. 104039, 2023. Elsevier.
- 2022
- R. Subaih, M. Maree, A. Tordeux and M. Chraibi, "Questioning the anisotropy of pedestrian dynamics: An empirical analysis with artificial neural networks", Applied Sciences, vol. 12, no. 15, pp. 7563, 2022. MDPI.
- P. Khound, P. Will, A. Tordeux and F. Gronwald, "The importance of the over-damped string stability criterion for a platooning control system" in 2022 26th IEEE International Conference on System Theory, Control and Computing (ICSTCC), 2022, pp. 1-6.
- J. Cordes, M. Chraibi, A. Tordeux and A. Schadschneider, "Time-to-collision models for single-file pedestrian motion", Collective Dynamics, vol. 6, pp. 1-10, 2022.
- 2021
- M. Friesen, H. Gottschalk, B. Rüdiger and A. Tordeux, "Spontaneous wave formation in stochastic self-driven particle systems", SIAM Journal on Applied Mathematics, vol. 81, no. 3, pp. 853-870, 2021. SIAM.
- J. Wang, M. Boltes, A. Seyfried, A. Tordeux, J. Zhang and W. Weng, "Experimental study on age and gender differences in microscopic movement characteristics of students", Chinese Physics B, vol. 30, no. 9, pp. 098902, 2021. IOP Publishing.
- P. Khound, P. Will, A. Tordeux and F. Gronwald, "Extending the adaptive time gap car-following model to enhance local and string stability for adaptive cruise control systems", Journal of Intelligent Transportation Systems, vol. 27, pp. 36-56, 2021. Taylor & Francis.
- 2020
- A. Schadschneider and A. Tordeux, "Noise-induced stop-and-go dynamics in pedestrian single-file motion", Collective Dynamics, vol. 5, pp. 356-363, 2020.
- A. Tordeux, J. Lebacque and S. Lassarre, "Robustness analysis of car-following models for full speed range ACC systems" in Traffic and Granular Flow 2019, Springer, 2020, pp. 571-581.
- A. Tordeux, A. Schadschneider and S. Lassarre, "Stop-and-go waves induced by correlated noise in pedestrian models without inertia", Journal of traffic and transportation engineering (English edition), vol. 7, no. 1, pp. 52--60, 2020. Elsevier.
- J. Cordes, A. Schadschneider and A. Tordeux, "The trouble with 2nd order models or how to generate stop-and-go traffic in a 1st order model" in Traffic and Granular Flow 2019, Springer, 2020, pp. 45--51.
- 2019
- J. Wang, M. Boltes, A. Seyfried, A. Tordeux, J. Zhang, V. Ziemer and W. Weng, "Influence of gender on the fundamental diagram and gait characteristics" in International Conference on Traffic and Granular Flow, 2019, pp. 225-234.
- A. Tordeux, A. Schadschneider and S. Lassarre, "Noise-induced stop-and-go dynamics" in International Conference on Traffic and Granular Flow, 2019, pp. 337-345.
- 2018
- A. Tordeux, G. Costeseque, M. Herty and A. Seyfried, "From traffic and pedestrian follow-the-leader models with reaction time to first order convection-diffusion flow models", SIAM Journal on Applied Mathematics, vol. 78, no. 1, pp. 63-79, 2018. SIAM.
- 2017
- A. Tordeux, M. Chraibi, A. Schadschneider and A. Seyfried, "Influence of the number of predecessors in interaction within acceleration-based flow models", Journal of Physics A: Mathematical and Theoretical, vol. 50, no. 34, pp. 345102, 2017. IOP Publishing.