Near-collision dynamics in a noisy car-following model

We consider a small stochastic perturbation of an optimal velocity car-following model. We give a detailed analysis of behavior near a collision singularity. We show that collision is impossible in a simplified model without noise, and then show that collision is asymptotically unlikely over large time intervals in the presence of small noise, with the large time interval scaling like the square of the reciprocal of the strength of the noise. Our calculations depend on careful boundary-layer analyses.

[1]  Zhichao Li,et al.  Platooning as a service of autonomous vehicles , 2017, 2017 IEEE 18th International Symposium on A World of Wireless, Mobile and Multimedia Networks (WoWMoM).

[2]  YangQuan Chen,et al.  Vehicle Platooning: A Brief Survey and Categorization , 2011 .

[3]  Susan Shaheen,et al.  Automated Vehicles, On-Demand Mobility, and Environmental Impacts , 2015 .

[4]  Benjamin Seibold,et al.  Stabilizing traffic flow via a single autonomous vehicle: Possibilities and limitations , 2017, 2017 IEEE Intelligent Vehicles Symposium (IV).

[5]  Kai Nagel,et al.  Probabilistic Traffic Flow Breakdown in Stochastic Car-Following Models , 2002, cond-mat/0208082.

[6]  Lanhang Ye,et al.  Evaluating the impact of connected and autonomous vehicles on traffic safety , 2019, Physica A: Statistical Mechanics and its Applications.

[7]  D. Ngoduy,et al.  Langevin method for a continuous stochastic car-following model and its stability conditions , 2019, Transportation Research Part C: Emerging Technologies.

[8]  R. Jiang,et al.  Full velocity difference model for a car-following theory. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  M J Willis.  Proportional-Integral-Derivative Control , 1999 .

[10]  Dirk Helbing,et al.  Empirical Features of Congested Traffic States and Their Implications for Traffic Modeling , 2007, Transp. Sci..

[11]  Naomi Zimmerman,et al.  Air quality and greenhouse gas implications of autonomous vehicles in Vancouver, Canada , 2021 .

[12]  M. Freidlin,et al.  Random Perturbations of Dynamical Systems , 1984 .

[13]  Serge P. Hoogendoorn,et al.  A geometric Brownian motion car-following model: towards a better understanding of capacity drop , 2018, Transportmetrica B: Transport Dynamics.

[14]  Maria Laura Delle Monache,et al.  Dissipation of stop-and-go waves via control of autonomous vehicles: Field experiments , 2017, ArXiv.

[15]  L. C. Davis,et al.  Nonlinear dynamics of autonomous vehicles with limits on acceleration , 2014 .

[16]  Ihor Lubashevsky,et al.  Probabilistic Description of Traffic Flow , 2001 .

[17]  Benjamin Seibold,et al.  Quantifying air quality benefits resulting from few autonomous vehicles stabilizing traffic , 2019, Transportation Research Part D: Transport and Environment.

[18]  Walid Saad,et al.  Joint Communication and Control for Wireless Autonomous Vehicular Platoon Systems , 2018, IEEE Transactions on Communications.

[19]  K. Hasebe,et al.  Structure stability of congestion in traffic dynamics , 1994 .

[20]  Hossein Nick Zinat Matin,et al.  Nonlinear Optimal Velocity Car Following Dynamics (II): Rate of Convergence In the Presence of Fast Perturbation , 2020, 2020 American Control Conference (ACC).

[21]  Majid Sarvi,et al.  A State-of-the-Art Review of Car-Following Models with Particular Considerations of Heavy Vehicles , 2015 .

[22]  Maria Laura Delle Monache,et al.  Are Commercially Implemented Adaptive Cruise Control Systems String Stable? , 2019, IEEE Transactions on Intelligent Transportation Systems.

[23]  K. Roberts,et al.  Thesis , 2002 .

[24]  Kai Nagel,et al.  Autonomous Vehicles and their Impact on Parking Search , 2019, IEEE Intelligent Transportation Systems Magazine.

[25]  F. A. Chiarello,et al.  A statistical mechanics approach to macroscopic limits of car-following traffic dynamics , 2021, 2106.15863.

[26]  R. Sowers.  A boundary layer theory for diffusively perturbed transport around a heteroclinic cycle , 2005 .

[27]  Dirk Helbing,et al.  GENERALIZED FORCE MODEL OF TRAFFIC DYNAMICS , 1998 .

[28]  Hani S. Mahmassani,et al.  From Existing Accident-Free Car-Following Models to Colliding Vehicles , 2008 .

[29]  Stefan Krauss,et al.  MICROSCOPIC MODELING OF TRAFFIC FLOW: INVESTIGATION OF COLLISION FREE VEHICLE DYNAMICS. , 1998 .

[30]  Nakayama,et al.  Dynamical model of traffic congestion and numerical simulation. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[31]  Eric Wood,et al.  Quantifying autonomous vehicles national fuel consumption impacts: A data-rich approach , 2017, Transportation Research Part A: Policy and Practice.

[32]  Asis Mazumdar,et al.  Pollution control by reduction of drag on cars and buses through platooning , 2007 .

[33]  R. E. Wilson,et al.  Car-following models: fifty years of linear stability analysis – a mathematical perspective , 2011 .

[34]  Sakinah,et al.  Vol. , 2020, New Medit.

[35]  E. M. de Jager,et al.  The theory of singular perturbations , 1996 .

[36]  D. Gazis,et al.  Nonlinear Follow-the-Leader Models of Traffic Flow , 1961 .

[37]  Anne E. McMills.  Tech , 2021, The Assistant Lighting Designer's Toolkit.

[38]  Martin Treiber,et al.  Traffic Flow Dynamics , 2013 .

[39]  Hossein Nick Zinat Matin,et al.  Nonlinear Optimal Velocity Car Following Dynamics (I): Approximation in Presence of Deterministic and Stochastic Perturbations , 2020, 2020 American Control Conference (ACC).

[40]  L. C. Davis,et al.  Modifications of the optimal velocity traffic model to include delay due to driver reaction time , 2003 .

[41]  Tsuna Sasaki,et al.  ON THE STABIliTY OF TRAFFIC FLOW (REPORT-I) , 1958 .

[42]  Armin Seyfried,et al.  Collision-free nonuniform dynamics within continuous optimal velocity models. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  Jorge A. Laval,et al.  A parsimonious model for the formation of oscillations in car-following models , 2014 .

[44]  Dirk Helbing,et al.  Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts , 2010, 1004.5545.