Traffic jams: dynamics and control

This introductory paper reviews the current state-of-the-art scientific methods used for modelling, analysing and controlling the dynamics of vehicular traffic. Possible mechanisms underlying traffic jam formation and propagation are presented from a dynamical viewpoint. Stable and unstable motions are described that may give the skeleton of traffic dynamics, and the effects of driver behaviour are emphasized in determining the emergent state in a vehicular system. At appropriate points, references are provided to the papers published in the corresponding Theme Issue.

[1]  R. Eddie Wilson,et al.  Criteria for convective versus absolute string instability in car-following models , 2011, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[2]  Boris S. Kerner.  A theory of traffic congestion at heavy bottlenecks , 2008 .

[3]  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.

[4]  Carlos F. Daganzo,et al.  A BEHAVIORAL THEORY OF MULTI-LANE TRAFFIC FLOW. PART II, MERGES AND THE ONSET OF CONGESTION , 1999 .

[5]  Martin Treiber,et al.  How Reaction Time, Update Time, and Adaptation Time Influence the Stability of Traffic Flow , 2008, Comput. Aided Civ. Infrastructure Eng..

[6]  Takashi Nagatani.  Traffic behavior in a mixture of different vehicles , 2000 .

[7]  D. Helbing.  Derivation of a fundamental diagram for urban traffic flow , 2008, 0807.1843.

[8]  Kerner,et al.  Structure and parameters of clusters in traffic flow. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  Boris S. Kerner,et al.  Introduction to Modern Traffic Flow Theory and Control: The Long Road to Three-Phase Traffic Theory , 2009 .

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

[11]  E. A. Mueller.  Aspects of the history of traffic signals , 1970 .

[12]  B. Greenshields.  Reaction time in automobile driving. , 1936 .

[13]  Kai Nagel,et al.  Still Flowing: Approaches to Traffic Flow and Traffic Jam Modeling , 2003, Oper. Res..

[14]  C. Daganzo.  Requiem for second-order fluid approximations of traffic flow , 1995 .

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

[16]  E. N. Holland.  A generalised stability criterion for motorway traffic , 1998 .

[17]  Silviu-Iulian Niculescu,et al.  Stability of car following with human memory effects and automatic headway compensation , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

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

[19]  K. Nakanishi,et al.  Bifurcation phenomena in the optimal velocity model for traffic flow. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Serge Hoogendoorn,et al.  Calibration of microscopic traffic-flow models using multiple data sources , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[21]  B. Kerner.  The Physics of Traffic: Empirical Freeway Pattern Features, Engineering Applications, and Theory , 2004 .

[22]  L C Davis,et al.  Multilane simulations of traffic phases. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Pravin Varaiya,et al.  Active traffic management on road networks: a macroscopic approach , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

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

[25]  Shlomo Havlin,et al.  Multifractal chaotic attractors in a system of delay-differential equations modeling road traffic. , 2002, Chaos.

[26]  Michael Schreckenberg,et al.  A cellular automaton model for freeway traffic , 1992 .

[27]  Dirk Helbing,et al.  Criticism of three-phase traffic theory , 2009 .

[28]  Petros A. Ioannou,et al.  Longitudinal control of heavy trucks in mixed traffic: environmental and fuel economy considerations , 2006, IEEE Transactions on Intelligent Transportation Systems.

[29]  Andrew W. Woods,et al.  CAR-FOLLOWING MODEL OF MULTISPECIES SYSTEMS OF ROAD TRAFFIC , 1997 .

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

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

[32]  Freeman Dyson,et al.  A meeting with Enrico Fermi , 2004, Nature.

[33]  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.

[34]  Harold J Payne,et al.  FREFLO: A MACROSCOPIC SIMULATION MODEL OF FREEWAY TRAFFIC , 1979 .

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

[36]  Dirk Helbing,et al.  The spatial variability of vehicle densities as determinant of urban network capacity , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

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

[38]  Dirk Helbing,et al.  Analytical calculation of critical perturbation amplitudes and critical densities by non-linear stability analysis of a simple traffic flow model , 2008, 0807.4006.

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

[40]  Petros A. Ioannou,et al.  Throttle and Brake Control Systems for Automatic Vehicle following , 1994, J. Intell. Transp. Syst..

[41]  József Bokor,et al.  Parameter-dependent modeling of freeway traffic flow , 2010 .

[42]  G. Stépán,et al.  Subcritical Hopf bifurcations in a car-following model with reaction-time delay , 2006, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[43]  L. A. Pipes.  An Operational Analysis of Traffic Dynamics , 1953 .

[44]  I. Gasser,et al.  Bifurcation analysis of a class of ‘car following’ traffic models , 2004 .

[45]  Pravin Varaiya.  Congestion, ramp metering and tolls , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

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

[47]  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.

[48]  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.

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

[50]  Carlos F. Daganzo,et al.  A BEHAVIORAL THEORY OF MULTI-LANE TRAFFIC FLOW. PART I, LONG HOMOGENEOUS FREEWAY SECTIONS , 1999 .

[51]  Dirk Helbing,et al.  THEORETICAL FOUNDATION OF MACROSCOPIC TRAFFIC MODELS , 1995 .

[52]  Jing Zhou,et al.  Range policy of adaptive cruise control vehicles for improved flow stability and string stability , 2005, IEEE Transactions on Intelligent Transportation Systems.

[53]  Petros A. Ioannou,et al.  A Comparision of Spacing and Headway Control Laws for Automatically Controlled Vehicles1 , 1994 .

[54]  D. Roose,et al.  Continuation and Bifurcation Analysis of Delay Differential Equations , 2007 .

[55]  Peter Wagner,et al.  Fluid-dynamical and microscopic description of traffic flow: a data-driven comparison , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[56]  Wolfram Mauser,et al.  On the Fundamental Diagram of Traffic Flow , 2006, SIAM J. Appl. Math..

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

[58]  Dirk Helbing,et al.  General Lane-Changing Model MOBIL for Car-Following Models , 2007 .

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

[60]  I. Gasser,et al.  Dynamical phenomena induced by bottleneck , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[61]  Dirk Helbing,et al.  Enhanced intelligent driver model to access the impact of driving strategies on traffic capacity , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[62]  Rinaldo M. Colombo,et al.  An $n$-populations model for traffic flow , 2003, European Journal of Applied Mathematics.

[63]  P. Wagner,et al.  Metastable states in a microscopic model of traffic flow , 1997 .

[64]  Markos Papageorgiou,et al.  Optimal Motorway Traffic Flow Control Involving Variable Speed Limits and Ramp Metering , 2010, Transp. Sci..

[65]  N. Geroliminis,et al.  An analytical approximation for the macropscopic fundamental diagram of urban traffic , 2008 .

[66]  Berg,et al.  Continuum approach to car-following models , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

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

[69]  H. Lieu.  THE PHYSICS OF TRAFFIC: EMPIRICAL FREEWAY PATTERN FEATURES, ENGINEERING APPLICATIONS, AND THEORY , 2005 .

[70]  Magnus Egerstedt,et al.  Autonomous driving in urban environments: approaches, lessons and challenges , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[71]  H. Lee,et al.  ORIGIN OF SYNCHRONIZED TRAFFIC FLOW ON HIGHWAYS AND ITS DYNAMIC PHASE TRANSITIONS , 1998, cond-mat/9805097.

[72]  Robert Herman,et al.  Kinetic theory of vehicular traffic , 1971 .

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