A cellular automata traffic flow model for three-phase theory

This paper presents a newly-modified KKW model including the subdivided vehicles types, and introduces the changes for a driver’s sensitivity into the speed fluctuation. By means of the numerical simulation the following conclusions are obtained herewith: 1. Velocity disturbance propagation in traffic flow is caused by the speed adaptation among vehicles. 2. In free flow phase, very fewer vehicles are affected by the velocity disturbance and the effect can be dissipated quickly thus the time of disturbance in a single vehicle is quite shorter. On the contrary, the impact duration time of the disturbance on a single vehicle is longer in synchronous flow phase, thus, it will affect more vehicles accordingly. 3. Under the free flow phase, the continuous deceleration behavior of a high speed vehicle to adapt the preceding car with slow speed can cause the reduction of the driver’s sensitivity, lead to the vehicle over-deceleration and aggravate the effects of velocity perturbations While in the synchronous flow phase, though the reaction delay caused by the driver’s sensitivity reduction can induce speed wave dissolving in essence, it increases the impact of disturbance on the traffic flow. 4. The large acceleration and deceleration tendency of an aggressive driver in the free flow phase always increase the influence of the velocity disturbance, while a conservative driver often weakens the influence. However, in the synchronized flow, since the high traffic density and the synchronization between vehicles is very strong, also the main factor which affects the driver’s speed choice is the distance among vehicles, therefore the effect of a driver’s behavior tendency to the spread of velocity perturbation is not obvious under this state.

[1]  B. Kerner.  Empirical macroscopic features of spatial-temporal traffic patterns at highway bottlenecks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[3]  B. Kerner,et al.  The physics of empirical nuclei for spontaneous traffic breakdown in free flow at highway bottlenecks , 2015 .

[4]  Tie-Qiao Tang,et al.  An evacuation model accounting for elementary students’ individual properties , 2015 .

[5]  Bastien Chopard,et al.  Cellular Automata Modeling of Physical Systems: Index , 1998 .

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

[7]  Boris S. Kerner,et al.  Cellular automata approach to three-phase traffic theory , 2002, cond-mat/0206370.

[8]  Boris S Kerner,et al.  Microscopic theory of spatial-temporal congested traffic patterns at highway bottlenecks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Boris S. Kerner.  Three-phase traffic theory and highway capacity , 2002 .

[10]  Tie-Qiao Tang,et al.  A car-following model accounting for the driver’s attribution , 2014 .

[11]  A. Schadschneider,et al.  Single-vehicle data of highway traffic: a statistical analysis. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[13]  Liang Tang,et al.  Erratum to: Modeling and simulation for microscopic traffic flow based on multiple headway, velocity and acceleration difference , 2011 .

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

[15]  B. Kerner.  Microscopic theory of traffic-flow instability governing traffic breakdown at highway bottlenecks: Growing wave of increase in speed in synchronized flow. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  A. Sasoh.  Impact of Unsteady Disturbance on Multi-lane Traffic Flow , 2002 .

[17]  Michael Schreckenberg,et al.  Probabilistic physical characteristics of phase transitions at highway bottlenecks: incommensurability of three-phase and two-phase traffic-flow theories. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[19]  N. Pariz,et al.  Synchronization in oscillator networks with time delay and limited non-homogeneous coupling strength , 2015, Nonlinear Dynamics.

[20]  Bin Zhang,et al.  Dynamic Analysis of the High Speed Train and Slab Track Nonlinear Coupling System with the Cross Iteration Algorithm , 2016 .

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

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

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

[24]  Tie-Qiao Tang,et al.  Impacts of the driver’s bounded rationality on the traffic running cost under the car-following model , 2016 .

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

[26]  Bin Yang,et al.  A sliding mode controller for vehicular traffic flow , 2016 .

[27]  Hubert Rehborn,et al.  A study of the influence of severe environmental conditions on common traffic congestion features , 2014 .

[28]  S. Wolfram.  Statistical mechanics of cellular automata , 1983 .

[29]  Kerner,et al.  Experimental properties of complexity in traffic flow. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[30]  B. Kerner.  Criticism of generally accepted fundamentals and methodologies of traffic and transportation theory: A brief review , 2013 .

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

[32]  Boris S. Kerner,et al.  Failure of classical traffic flow theories: a critical review , 2015, Elektrotech. Informationstechnik.

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

[34]  Hubert Rehborn,et al.  Traffic dynamics in empirical probe vehicle data studied with three-phase theory: Spatiotemporal reconstruction of traffic phases and generation of jam warning messages , 2013 .

[35]  B. Kerner,et al.  A microscopic model for phase transitions in traffic flow , 2002 .

[36]  Rui Jiang,et al.  Cellular-automaton model with velocity adaptation in the framework of Kerner's three-phase traffic theory. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Takashi Nagatani,et al.  Kinetic segregation in a multilane highway traffic flow , 1997 .

[38]  Ludger Santen,et al.  Single-vehicle data of highway traffic: microscopic description of traffic phases. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  Rui Jiang,et al.  A new dynamics model for traffic flow , 2001 .

[40]  Xiangdong Hu,et al.  Evaluating the performance of vehicular platoon control under different network topologies of initial states , 2016 .

[41]  Fred L. Mannering,et al.  The effect of speed limits on drivers' choice of speed: A random parameters seemingly unrelated equations approach , 2016 .

[42]  Yu Guizhen,et al.  A Stochastic LWR Model with Consideration of the Driver's Individual Property , 2012 .

[43]  R. Jiang,et al.  A new continuum model for traffic flow and numerical tests , 2002 .

[44]  George A. Bekey,et al.  Mathematical models of public systems , 1971 .

[45]  Wei-Zhen Lu,et al.  A new car-following model with the consideration of incorporating timid and aggressive driving behaviors , 2016 .

[46]  B. Kerner.  Failure of classical traffic flow theories: Stochastic highway capacity and automatic driving , 2016, 1601.02585.

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

[48]  Hai-Jun Huang,et al.  Influences of the driver’s bounded rationality on micro driving behavior, fuel consumption and emissions , 2015 .

[49]  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.

[50]  Avishai Ceder.  Transportation and Traffic Theory , 1999 .

[51]  Hubert Rehborn,et al.  An empirical study of common traffic congestion features based on traffic data measured in the USA, the UK, and Germany , 2011 .

[52]  Hubert Rehborn,et al.  Game-Theoretic Context and Interpretation of Kerner’s Three-Phase Traffic Theory , 2015 .

[53]  Laura Eboli,et al.  Combining speed and acceleration to define car users’ safe or unsafe driving behaviour , 2016 .

[54]  B. Kerner.  Congested Traffic Flow: Observations and Theory , 1999 .

[55]  Hai-Jun Huang,et al.  A new pedestrian-following model for aircraft boarding and numerical tests , 2012 .

[56]  Michael Schreckenberg,et al.  Effect of driver over-acceleration on traffic breakdown in three-phase cellular automaton traffic flow models , 2013 .

[57]  Y. Sugiyama,et al.  Coupled Map Traffic Flow Simulator Based on Optimal Velocity Functions , 1998 .

[58]  Rui Jiang,et al.  Cellular automata models for synchronized traffic flow , 2003 .

[59]  Dirk Helbing.  Modeling and simulation of multilane traffic flow , 1997 .

[60]  Srinivas Peeta,et al.  Non-lane-discipline-based car-following model considering the effects of two-sided lateral gaps , 2018, 2018 Chinese Automation Congress (CAC).

[61]  Li Zhang,et al.  A car-following model considering the effect of electronic throttle opening angle under connected environment , 2016 .

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

[63]  Ludger Santen,et al.  Human behavior as origin of traffic phases. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[64]  Rui Jiang,et al.  First order phase transition from free flow to synchronized flow in a cellular automata model , 2005 .

[65]  R. Jiang,et al.  Spatial–temporal patterns at an isolated on-ramp in a new cellular automata model based on three-phase traffic theory , 2004 .

[66]  Dihua Sun,et al.  On the stability analysis of microscopic traffic car-following model: a case study , 2013 .

[67]  M Cremer,et al.  A fast simulation model for traffic flow on the basis of Boolean operations , 1986 .

[68]  Dirk Helbing,et al.  Coherent moving states in highway traffic , 1998, Nature.

[69]  Tadaki Shin-ichi,et al.  Dynamical Phase Transition in One Dimensional Traffic Flow Model with Blockage , 1994 .

[70]  S. L. Paveri-Fontana,et al.  On Boltzmann-like treatments for traffic flow: A critical review of the basic model and an alternative proposal for dilute traffic analysis , 1975 .