The relationship between car following string instability and traffic oscillations in finite-sized platoons and its use in easing congestion via connected and automated vehicles with IDM based controller

Abstract This paper focuses on two fundamental issues in traffic flow modelling: string stability of car following (CF), and oscillation of traffic flow. Its aim is to explore the complementary use of CF instability analysis and oscillation analysis to compress and ease traffic congestion in a connected environment. Each of these topics has been extensively investigated in the literature. However, each topic has been investigated separately and, despite the inherent conceptual and empirical closeness of the two concepts, little effort has been devoted to untangling their relationship. To address this failing, we first define four types of oscillation – amplitude-decay oscillation, amplitude-ceiling oscillation, speed-deviation ceiling oscillation, and speed-deviation growth oscillation – and reveal their similarities and dissimilarities to CF instability. Based on the stability criterion, we then develop oscillation criteria to identify different types of oscillation by relaxing two unrealistic assumptions used in CF stability analysis (i.e., infinitely-long platoon and long-wavelength perturbation). Finally, to demonstrate how CF instability analysis and oscillation analysis can be combined to influence individual vehicle stability and improve traffic oscillations in a connected environment, a platoon of vehicles that experience an oscillation in the NGSIM data is used in a case study. In this case study, different control factors are used for different vehicle types: connected (but human-driven) vehicles, and automated vehicles. Our analysis shows that a higher stability of some individual vehicles can alleviate the oscillation severity for the platoon. It also shows that desired time gap and maximum acceleration are two promising parameters that can be used to both improve individual vehicle stability and significantly smooth the oscillation of the platoon in a connected and/or automated environment. Of particular note, when considering all of the factors explored in our analysis, adjustment of the desired time gap is the most effective factor in smoothing traffic oscillations.

[1]  C. Daganzo,et al.  Macroscopic Fundamental Diagrams for Freeway Networks: Theory and Observation , 2011 .

[2]  Michael J. Cassidy,et al.  AN OBSERVED TRAFFIC PATTERN IN LONG FREEWAY QUEUES , 2001 .

[3]  Akihiro Nakayama,et al.  Metastability in the formation of an experimental traffic jam , 2009 .

[4]  Y. Ouyang,et al.  Measurement and estimation of traffic oscillation properties , 2010 .

[5]  Thamara Vieira da Rocha,et al.  Does traffic-related calibration of car-following models provide accurate estimations of vehicle emissions? , 2015 .

[6]  Javier Bilbao-Ubillos,et al.  The costs of urban congestion: Estimation of welfare losses arising from congestion on cross-town link roads , 2008 .

[7]  Jorge A. Laval,et al.  Effects of Merging and Diverging on Freeway Traffic Oscillations , 2010 .

[8]  M. Cassidy,et al.  FREEWAY TRAFFIC OSCILLATIONS: OBSERVATIONS AND PREDICTIONS , 2002 .

[9]  Martin Treiber,et al.  Calibrating Car-Following Models by Using Trajectory Data , 2008, 0803.4063.

[10]  G. F. Newell.  Nonlinear Effects in the Dynamics of Car Following , 1961 .

[11]  M. J. D. Powell,et al.  On search directions for minimization algorithms , 1973, Math. Program..

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

[13]  R. Sollacher,et al.  Multi-anticipative car-following model , 1999 .

[14]  S. Dai,et al.  Stabilization analysis and modified Korteweg-de Vries equation in a cooperative driving system. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Soyoung Ahn,et al.  The effects of lane-changing on the immediate follower : anticipation, relaxation, and change in driver characteristics , 2013 .

[16]  J. Hedrick,et al.  String stability of interconnected systems , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[17]  Gábor Stépán,et al.  Traffic jams: dynamics and control , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[18]  Martin Treiber,et al.  Traffic Flow Dynamics: Data, Models and Simulation , 2012 .

[19]  J. M. D. Castillo.  Propagation of perturbations in dense traffic flow: a model and its implications , 2001 .

[20]  Kerner,et al.  Experimental features and characteristics of traffic jams. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[21]  Soyoung Ahn,et al.  Impact of traffic oscillations on freeway crash occurrences. , 2010, Accident; analysis and prevention.

[22]  K. Hasebe,et al.  Analysis of optimal velocity model with explicit delay , 1998, patt-sol/9805002.

[23]  Gábor Orosz,et al.  Delayed car-following dynamics for human and robotic drivers , 2011 .

[24]  Soyoung Ahn,et al.  Applications of wavelet transform for analysis of freeway traffic : bottlenecks, transient traffic, and traffic oscillations , 2011 .

[25]  Martin Treiber,et al.  Comparing Numerical Integration Schemes for Time-Continuous Car-Following Models , 2014, ArXiv.

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

[27]  Romain Billot,et al.  Linear and Weakly Nonlinear Stability Analyses of Cooperative Car-Following Models , 2014, IEEE Transactions on Intelligent Transportation Systems.

[28]  Ludovic Leclercq,et al.  A mechanism to describe the formation and propagation of stop-and-go waves in congested freeway traffic , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[29]  Marcello Montanino,et al.  Speed or spacing? Cumulative variables, and convolution of model errors and time in traffic flow models validation and calibration , 2016 .

[30]  Soyoung Ahn,et al.  Freeway Traffic Oscillations and Vehicle Lane-Change Maneuvers , 2007 .

[31]  Martin Treiber,et al.  The Intelligent Driver Model with Stochasticity -New Insights Into Traffic Flow Oscillations , 2017 .

[32]  Gábor Orosz,et al.  Exciting traffic jams: nonlinear phenomena behind traffic jam formation on highways. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Dong Ngoduy,et al.  Linear stability of a generalized multi-anticipative car following model with time delays , 2015, Commun. Nonlinear Sci. Numer. Simul..

[34]  Xiaopeng Li,et al.  Stop-and-go traffic analysis: Theoretical properties, environmental impacts and oscillation mitigation , 2014 .

[35]  D. Swaroop,et al.  String Stability Of Interconnected Systems: An Application To Platooning In Automated Highway Systems , 1997 .

[36]  Marcello Montanino,et al.  Gaussian Process Metamodels for Sensitivity Analysis of Traffic Simulation Models , 2013 .

[37]  Simon Washington,et al.  Understanding the mechanism of traffic hysteresis and traffic oscillations through the change in task difficulty level , 2017 .

[38]  Helbing,et al.  Congested traffic states in empirical observations and microscopic simulations , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[39]  Robert Herman,et al.  Traffic Dynamics: Analysis of Stability in Car Following , 1959 .

[40]  Marcello Montanino,et al.  Making NGSIM Data Usable for Studies on Traffic Flow Theory , 2013 .

[41]  L. C. Edie.  Car-Following and Steady-State Theory for Noncongested Traffic , 1961 .

[42]  Dirk Helbing,et al.  Adaptive cruise control design for active congestion avoidance , 2008 .

[43]  Jian Sun,et al.  Stability analysis methods and their applicability to car-following models in conventional and connected environments , 2018 .

[44]  Marcello Montanino,et al.  Can Results of car-following Model Calibration Based on Trajectory Data be Trusted? , 2012 .

[45]  Simon Washington,et al.  Revisiting the Task-Capability interface model for incorporating human factors into car-following models , 2015 .

[46]  Martin Treiber,et al.  Microscopic Calibration and Validation of Car-Following Models – A Systematic Approach , 2013, 1403.4990.

[47]  Benjamin Coifman,et al.  A critical evaluation of the Next Generation Simulation (NGSIM) vehicle trajectory dataset , 2017 .

[48]  Soyoung Ahn,et al.  A behavioural car-following model that captures traffic oscillations , 2012 .

[49]  Jie Sun,et al.  Investigating the oscillation characteristics and mitigating its impact with low-penetration connected and automated vehicles , 2018, 2018 21st International Conference on Intelligent Transportation Systems (ITSC).

[50]  Gordon F. Newell,et al.  A simplified car-following theory: a lower order model , 2002 .

[51]  H. M. Zhang,et al.  A stochastic wave propagation model , 2008 .

[52]  E. Montroll,et al.  Traffic Dynamics: Studies in Car Following , 1958 .

[53]  Andrea Goldsmith,et al.  Effects of communication delay on string stability in vehicle platoons , 2001, ITSC 2001. 2001 IEEE Intelligent Transportation Systems. Proceedings (Cat. No.01TH8585).

[54]  Paolo Ferrari,et al.  THE INSTABILITY OF MOTORWAY TRAFFIC , 1994 .

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

[56]  Ashish Bhaskar,et al.  Modelling car-following behaviour of connected vehicles with a focus on driver compliance , 2019, Transportation Research Part B: Methodological.

[57]  Ashish Bhaskar,et al.  Estimating and Comparing Response Times in Traditional and Connected Environments , 2019, Transportation Research Record: Journal of the Transportation Research Board.

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

[59]  Gábor Orosz,et al.  Robotic reactions: delay-induced patterns in autonomous vehicle systems. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[60]  M. Treiber,et al.  Evidence of convective instability in congested traffic flow: A systematic empirical and theoretical investigation , 2011 .

[61]  Romain Billot,et al.  The root locus method: application to linear stability analysis and design of cooperative car-following models , 2014 .

[62]  A. Skabardonis,et al.  Understanding stop-and-go traffic in view of asymmetric traffic theory , 2009 .

[63]  Yanfeng Ouyang,et al.  Characterization of Traffic Oscillation Propagation Under Nonlinear Car-Following Laws , 2011 .

[64]  Soyoung Ahn,et al.  Freeway traffic oscillations : microscopic analysis of formations and propagations using Wavelet Transform , 2011 .

[65]  Y. Sugiyama,et al.  Traffic jams without bottlenecks—experimental evidence for the physical mechanism of the formation of a jam , 2008 .

[66]  Ashish Bhaskar,et al.  Is more always better? The impact of vehicular trajectory completeness on car-following model calibration and validation , 2019, Transportation Research Part B: Methodological.

[67]  Douglas J. Leith,et al.  $\mathcal{L}_2$ and $\mathcal{L}_{\infty}$ Stability Analysis of Heterogeneous Traffic With Application to Parameter Optimization for the Control of Automated Vehicles , 2016, IEEE Transactions on Control Systems Technology.

[68]  Vincenzo Punzo,et al.  On the assessment of vehicle trajectory data accuracy and application to the Next Generation SIMulation (NGSIM) program data , 2011 .

[69]  Julien Monteil,et al.  State-space linear stability analysis of platoons of cooperative vehicles , 2019 .