The root locus method: application to linear stability analysis and design of cooperative car-following models

A global framework for linear stability analyses of traffic models, based on the dispersion relation root locus method, is presented and is applied taking the example of a broad class of car-following (CF) models. This approach is able to analyse all aspects of the dynamics: long waves and short wave behaviours, phase velocities and stability features. The methodology is applied to investigate the potential benefits of connected vehicles, i.e. V2V communication enabling a vehicle to send and receive information to and from surrounding vehicles. We choose to focus on the design of the coefficients of cooperation which weights the information from downstream vehicles. The coefficients tuning is performed and different ways of implementing an efficient cooperative strategy are discussed. Hence, this paper brings design methods in order to obtain robust stability of traffic models, with application on cooperative CF models.

[1]  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.

[2]  A. Schadschneider,et al.  Statistical physics of vehicular traffic and some related systems , 2000, cond-mat/0007053.

[3]  Dirk Helbing,et al.  MASTER: macroscopic traffic simulation based on a gas-kinetic, non-local traffic model , 2001 .

[4]  A. C. Avery.  Traffic Flow , 1961 .

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

[6]  Serge P. Hoogendoorn,et al.  Empirics of Multianticipative Car-Following Behavior , 2006 .

[7]  Jing Shi,et al.  Perturbation and Stability Analysis of the Multi-Anticipative Intelligent Driver Model , 2010 .

[8]  孙喜明,et al.  Analysis of Stability for Gas-Kinetic Non-Local Traffic Model , 2006 .

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

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

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

[12]  Dirk Helbing,et al.  Delays, inaccuracies and anticipation in microscopic traffic models , 2006 .

[13]  Romain Billot,et al.  A conditionally linearly stable second-order traffic model derived from a Vlasov kinetic description , 2010 .

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

[15]  Dong Ngoduy,et al.  Platoon-based macroscopic model for intelligent traffic flow , 2013 .

[16]  M. Lighthill,et al.  On kinematic waves I. Flood movement in long rivers , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[17]  Katsuhiro Nishinari,et al.  Multi-value cellular automaton models and metastable states in a congested phase , 2000 .

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

[19]  Mao-Bin Hu,et al.  ENHANCING HIGHWAY CAPACITY BY HOMOGENIZING TRAFFIC FLOW , 2008 .

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

[21]  Naresh K. Sinha,et al.  Modern Control Systems , 1981, IEEE Transactions on Systems, Man, and Cybernetics.

[22]  Carlos F. Daganzo,et al.  THE CELL TRANSMISSION MODEL, PART II: NETWORK TRAFFIC , 1995 .

[23]  Romain Billot,et al.  Distributed and Centralized Approaches for Cooperative Road Traffic Dynamics , 2012 .

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

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

[26]  Ioanna Spyropoulou,et al.  SIMULATION USING GIPPS' CAR-FOLLOWING MODEL—AN IN-DEPTH ANALYSIS , 2007 .

[27]  W. Evans,et al.  Graphical Analysis of Control Systems , 1948, Transactions of the American Institute of Electrical Engineers.

[28]  Julien Monteil,et al.  Investigating the effects of cooperative vehicles on highway traffic flow homogenization: analytical and simulation studies , 2014 .

[29]  R. E. Wilson,et al.  An analysis of Gipps's car-following model of highway traffic , 2001 .

[30]  P. G. Gipps,et al.  A behavioural car-following model for computer simulation , 1981 .

[31]  D. Helbing.  Traffic and related self-driven many-particle systems , 2000, cond-mat/0012229.

[32]  S. Q. Dai,et al.  An extended car-following model based on intelligent transportation system application , 2006 .

[33]  C. Daganzo.  THE CELL TRANSMISSION MODEL.. , 1994 .

[34]  Salima Hassas,et al.  Cooperative Highway Traffic , 2013 .

[35]  R. E. Wilson,et al.  Mechanisms for spatio-temporal pattern formation in highway traffic models , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

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

[37]  R. E. Wilson,et al.  Many-neighbour interaction and non-locality in traffic models , 2004 .