Scalable traffic stability analysis in mixed-autonomy using continuum models

Abstract This paper presents scalable traffic stability analysis for both pure connected and autonomous vehicle (CAV) traffic and mixed traffic based on continuum traffic flow models. Human-drive vehicles (HDVs) are modeled by a non-equilibrium traffic flow model, i.e., Aw-Rascle-Zhang (ARZ) to capture HDV traffic's unstable nature. CAVs are modeled by a mean field game describing their non-cooperative behaviors as rational utility-optimizing agents. Working with continuum models helps avoiding scalability issues in microscopic multi-class traffic models. We demonstrate from linear stability analysis that the mean field game traffic flow model behaves differently from traditional traffic flow models and stability can only be proved when the total density is in a certain regime. We also show from numerical experiments that CAVs help stabilize mixed traffic. Further, we quantify the impact of CAV's penetration rate and controller design on traffic stability. The results may provide qualitative insights on traffic stability in mixed-autonomy for human drivers and city planners. The results also provide suggestions on CAV controller design for CAV manufacturers.

[1]  B. van Arem,et al.  A generic multi-level framework for microscopic traffic simulation with automated vehicles in mixed traffic , 2020, Transportation Research Part C: Emerging Technologies.

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

[3]  Lili Du,et al.  Constrained optimization and distributed computation based car following control of a connected and autonomous vehicle platoon , 2016 .

[4]  Serge P. Hoogendoorn,et al.  Stabilizing mixed vehicular platoons with connected automated vehicles: An H-infinity approach , 2020, Transportation Research Part B: Methodological.

[5]  Meng Wang,et al.  Game theoretic approach for predictive lane-changing and car-following control , 2015 .

[6]  Serge P. Hoogendoorn,et al.  Generic gas-kinetic traffic systems modeling with applications to vehicular traffic flow , 2001 .

[7]  Serge P. Hoogendoorn,et al.  Continuum modeling of cooperative traffic flow dynamics , 2009 .

[8]  B. Kerner.  EXPERIMENTAL FEATURES OF SELF-ORGANIZATION IN TRAFFIC FLOW , 1998 .

[9]  Soyoung Ahn,et al.  Traffic dynamics under speed disturbance in mixed traffic with automated and non-automated vehicles , 2019 .

[10]  Alexandre M. Bayen,et al.  Stabilizing Traffic with Autonomous Vehicles , 2018, 2018 IEEE International Conference on Robotics and Automation (ICRA).

[11]  S. Hoogendoorn,et al.  Continuum modeling of multiclass traffic flow , 2000 .

[12]  Peter E. Caines,et al.  Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle , 2006, Commun. Inf. Syst..

[13]  Natasha Merat,et al.  Risk-based autonomous vehicle motion control with considering human driver’s behaviour , 2019, Transportation Research Part C: Emerging Technologies.

[14]  Michel Rascle,et al.  Resurrection of "Second Order" Models of Traffic Flow , 2000, SIAM J. Appl. Math..

[15]  C. Buisson,et al.  Macroscopic Model and Its Numerical Solution for Two-Flow Mixed Traffic with Different Speeds and Lengths , 2003 .

[16]  Marie-Therese Wolfram,et al.  On a mean field game approach modeling congestion and aversion in pedestrian crowds , 2011 .

[17]  Vicente Milanés,et al.  Mixing V2V- and non-V2V-equipped vehicles in car following , 2019 .

[18]  João Pedro Hespanha,et al.  Mistuning-Based Control Design to Improve Closed-Loop Stability Margin of Vehicular Platoons , 2008, IEEE Transactions on Automatic Control.

[19]  M J Lighthill,et al.  On kinematic waves II. A theory of traffic flow on long crowded roads , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[20]  Meng Wang,et al.  Infrastructure assisted adaptive driving to stabilise heterogeneous vehicle strings , 2018, Transportation Research Part C: Emerging Technologies.

[21]  Dong Ngoduy,et al.  Multiclass first-order simulation model to explain non-linear traffic phenomena , 2007 .

[22]  Dong Ngoduy,et al.  Instability of cooperative adaptive cruise control traffic flow: A macroscopic approach , 2013, Commun. Nonlinear Sci. Numer. Simul..

[23]  Dong Ngoduy,et al.  Analytical studies on the instabilities of heterogeneous intelligent traffic flow , 2013, Commun. Nonlinear Sci. Numer. Simul..

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

[25]  R. LeVeque.  Numerical methods for conservation laws , 1990 .

[26]  Carlos F. Daganzo,et al.  A continuum theory of traffic dynamics for freeways with special lanes , 1997 .

[27]  B. Kerner,et al.  EXPERIMENTAL PROPERTIES OF PHASE TRANSITIONS IN TRAFFIC FLOW , 1997 .

[28]  Axel Klar,et al.  Derivation of Continuum Traffic Flow Models from Microscopic Follow-the-Leader Models , 2002, SIAM J. Appl. Math..

[29]  Swaroop Darbha,et al.  Intelligent Cruise Control Systems And Traffic Flow Stability , 1998 .

[30]  Le Yi Wang,et al.  Stability Margin Improvement of Vehicular Platoon Considering Undirected Topology and Asymmetric Control , 2016, IEEE Transactions on Control Systems Technology.

[31]  Gábor Orosz,et al.  Dynamics of connected vehicle systems with delayed acceleration feedback , 2014 .

[32]  P. Lions,et al.  Mean field games , 2007 .

[33]  H. M. Zhang.  A NON-EQUILIBRIUM TRAFFIC MODEL DEVOID OF GAS-LIKE BEHAVIOR , 2002 .

[34]  Lili Du,et al.  Cooperative platoon control for a mixed traffic flow including human drive vehicles and connected and autonomous vehicles , 2018, Transportation Research Part B: Methodological.

[35]  S. Shankar Sastry,et al.  Inverse Problem for Non-Viscous Mean Field Control: Example From Traffic , 2016, IEEE Transactions on Automatic Control.

[36]  Kuang Huang,et al.  Stabilizing Traffic via Autonomous Vehicles: A Continuum Mean Field Game Approach , 2019, 2019 IEEE Intelligent Transportation Systems Conference (ITSC).

[37]  Alireza Talebpour,et al.  Influence of connected and autonomous vehicles on traffic flow stability and throughput , 2016 .

[38]  Shing Chung Josh Wong,et al.  A multi-class traffic flow model: an extension of LWR model with heterogeneous drivers , 2002 .

[39]  Wang Yi,et al.  Stability analysis and the fundamental diagram for mixed connected automated and human-driven vehicles , 2019, Physica A: Statistical Mechanics and its Applications.

[40]  Daniel B. Work,et al.  A Heterogeneous Multiclass Traffic Flow Model with Creeping , 2015, SIAM J. Appl. Math..

[41]  Markos Papageorgiou,et al.  A Macroscopic Multi-Lane Traffic Flow Model for ACC/CACC Traffic Dynamics , 2018 .

[42]  Jiaqi Ma,et al.  A mixed traffic speed harmonization model with connected autonomous vehicles , 2019, Transportation Research Part C: Emerging Technologies.

[43]  P. I. Richards.  Shock Waves on the Highway , 1956 .

[44]  S Logghe,et al.  Multi-class kinematic wave theory of traffic flow , 2008 .

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

[46]  Roland P. Malhamé,et al.  A micro-macro traffic model based on Mean-Field Games , 2015, 2015 American Control Conference (ACC).

[47]  Stephen D. Boyles,et al.  A multiclass cell transmission model for shared human and autonomous vehicle roads , 2016 .

[48]  Gábor Orosz,et al.  Connected cruise control among human-driven vehicles: Experiment-based parameter estimation and optimal control design , 2018, Transportation Research Part C: Emerging Technologies.