A parsimonious model for the formation of oscillations in car-following models

This paper shows that the formation and propagation of traffic oscillations in the absence of lane changes can be explained by the stochastic nature of drivers’ acceleration processes. By adding a white noise to drivers’ desired acceleration in free-flow, oscillations are produced that accord well with observation. This theory suggests that driver error is a function of roadway geometry, that it determines the average speed at the bottleneck, as well as oscillation period and amplitude. The model has been implemented with a single additional parameter compared to the kinematic wave model with bounded accelerations.

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

[2]  Dong Ngoduy.  OPERATIONAL EFFECTS OF ACCELERATION LANE ON MAIN TRAFFIC FLOW AT DISCONTINUITIES , 2008 .

[3]  Soyoung Ahn,et al.  Evolution of Oscillations in Congested Traffic , 2009 .

[4]  A. Schadschneider,et al.  Metastable states in cellular automata for traffic flow , 1998, cond-mat/9804170.

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

[6]  B. Øksendal.  Stochastic differential equations : an introduction with applications , 1987 .

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

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

[9]  Dong Ngoduy,et al.  Multiclass first-order traffic model using stochastic fundamental diagrams , 2011 .

[10]  Jorge A. Laval.  Effects of geometric design on freeway capacity: Impacts of truck lane restrictions , 2009 .

[11]  Soyoung Ahn,et al.  Microscopic traffic hysteresis in traffic oscillations : a behavioral perspective , 2012 .

[12]  P. Protter.  Stochastic integration and differential equations , 1990 .

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

[14]  Carlos F. Daganzo,et al.  In Traffic Flow, Cellular Automata = Kinematic Waves , 2004 .

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

[16]  Jorge A. Laval,et al.  Microscopic modeling of the relaxation phenomenon using a macroscopic lane-changing model , 2008 .

[17]  D. Helbing,et al.  DERIVATION, PROPERTIES, AND SIMULATION OF A GAS-KINETIC-BASED, NONLOCAL TRAFFIC MODEL , 1999, cond-mat/9901240.

[18]  Soyoung Ahn,et al.  Verification of a simplified car-following theory , 2004 .

[19]  Ludovic Leclercq,et al.  Capacity drops at merges: An endogenous model , 2011 .

[20]  Ludovic Leclercq,et al.  Relaxation Phenomenon After Changing Lanes: Experimental Validation with NGSIM Data Set , 2007 .

[21]  C. Daganzo.  A variational formulation of kinematic waves: basic theory and complex boundary conditions , 2005 .

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

[23]  Victor L. Knoop,et al.  Number of Lane Changes Determined by Splashover Effects in Loop Detector Counts , 2012, IEEE Transactions on Intelligent Transportation Systems.

[24]  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.

[25]  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.

[26]  H. J. Van Zuylen,et al.  Part 2: Car-Following Models: Continuum Traffic Model for Freeway with On- and Off-Ramp to Explain Different Traffic-Congested States , 2006 .

[27]  M Koshi,et al.  CAPACITY OF SAGS AND TUNNELS ON JAPANESE MOTORWAYS , 1992 .

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

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

[30]  V Shvetsov,et al.  Macroscopic dynamics of multilane traffic. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[31]  E Lerner-Lam,et al.  Neo-traditional neighborhood design and its implications for traffic engineering , 1991 .

[32]  Ludovic Leclercq,et al.  Relaxation Phenomenon after Lane Changing , 2007 .

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

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

[35]  Xin-Gang Li,et al.  Cellular automaton model with time gap dependent randomisation under Kerner's three-phase traffic theory , 2011 .

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

[37]  Jean-Patrick Lebacque,et al.  A Stochastic Macroscopic Traffic Model Devoid of Diffusion , 2009 .

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

[39]  Soyoung Ahn,et al.  A method to account for non-steady state conditions in measuring traffic hysteresis , 2013 .

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

[41]  Andreas Deutsch,et al.  Cellular Automaton Modeling , 2009, Encyclopedia of Complexity and Systems Science.

[42]  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.

[43]  Carlos F. Daganzo,et al.  Impacts of Lane Changes at Merge Bottlenecks: A Theory and Strategies to Maximize Capacity , 2007 .

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

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

[46]  Jorge A. Laval.  Stochastic Processes of Moving Bottlenecks: Approximate Formulas for Highway Capacity , 2006 .

[47]  A. Schadschneider,et al.  Open boundaries in a cellular automaton model for traffic flow with metastable states. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  Ludovic Leclercq,et al.  The Hamilton-Jacobi Partial Differential Equation and the Three Representations of Traffic Flow , 2013 .

[49]  D. Helbing,et al.  Gas-Kinetic-Based Traffic Model Explaining Observed Hysteretic Phase Transition , 1998, cond-mat/9810277.

[50]  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.

[51]  Jorge A. Laval.  Hysteresis in traffic flow revisited: An improved measurement method , 2011 .

[52]  Carlos F. Daganzo,et al.  Lane-changing in traffic streams , 2006 .

[53]  B. Kerner.  THE PHYSICS OF TRAFFIC , 1999 .

[54]  Martin Treiber,et al.  Validation of traffic flow models with respect to the spatiotemporal evolution of congested traffic patterns , 2012 .

[55]  Serge P. Hoogendoorn,et al.  Continuum Traffic Model for Freeway with On- and Off-Ramp to Explain Different Traffic-Congested States , 2006 .

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

[57]  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.