The Markov-Gap CA Model for Entering Gaps and Departure Headways at Signalized Intersections

Modeling gaps/headways has many applications in traffic theory and transportation operations. Recently, many researchers begin to show interests in microscopic simulation based interpretations on the formulation of gap and headway distributions. However, there are few cellular automata (CA) model proposed in this area, since most current CA models focus on phase transitions of freeway traffic only. In this paper, a so called Markov-Gap CA models is proposed, aiming on fitting the empirical gap/headway distributions collected. The model treats gap variations between consecutive vehicles approaching or leaving signalized intersections as different Markov processes and provides a concise and uniform method to describe the observed traffic flow phenomena. The agreement between the simulation results and empirical data suggests the soundness of the Markov-Gap CA model.

[1]  Dirk Helbing,et al.  Determination of Interaction Potentials in Freeway Traffic From Steady-State Statistics , 2003, cond-mat/0301484.

[2]  M. Krbálek.  Inter-vehicle gap statistics on signal-controlled crossroads , 2007, 0710.4988.

[3]  A. Abul-Magd.  Modeling highway-traffic headway distributions using superstatistics. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  William J. Stewart,et al.  Introduction to the numerical solution of Markov Chains , 1994 .

[5]  Renfrey B. Potts,et al.  A Theory of the Diffusion of Traffic Platoons , 1964 .

[6]  M. Krbálek.  A O ] 2 6 O ct 2 00 7 Inter-vehicle gap statistics on the signal-controlled crossroad , 2008 .

[7]  Myron Hlynka,et al.  Queueing Networks and Markov Chains (Modeling and Performance Evaluation With Computer Science Applications) , 2007, Technometrics.

[8]  Wei Zheng,et al.  Road user's behavior analyses of urban intersections , 2007 .

[9]  Stephen P. Boyd,et al.  Fastest Mixing Markov Chain on a Graph , 2004, SIAM Rev..

[10]  Zhang Yi,et al.  Departure Headways of Mixed Traffic Flow at Signalized Intersections: Distributions, Simulations and Validations , 2008 .

[11]  Jin Xuexiang.  A Markov-Gap Model for Static Queuing Spacing Distributiont , 2008 .

[12]  Zheng Wei,et al.  Control Strategies for Transit Priority Based on Queue Modeling and Surrogate Testing , 2009, J. Intell. Transp. Syst..

[13]  Weng Xiao-Xiong,et al.  Decouple Analysis on Distributed Architecture of Urban Traffic System , 2006, 2006 9th International Conference on Control, Automation, Robotics and Vision.

[14]  R. Luttinen.  STATISTICAL PROPERTIES OF VEHICLE TIME HEADWAYS , 1992 .

[15]  Fei-Yue Wang,et al.  Approximate Vehicle Waiting Time Estimation Using Adaptive Video-Based Vehicle Tracking , 2006, International Workshop on Intelligent Computing in Pattern Analysis/Synthesis.

[16]  Yi Zhang,et al.  Road user's behavior analyses of urban intersections , 2007, ITSC.

[17]  Hubert Rehborn,et al.  Microscopic features of moving traffic jams. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Bart De Moor,et al.  Cellular automata models of road traffic , 2005, physics/0509082.

[19]  Dirk Helbing,et al.  Understanding interarrival and interdeparture time statistics from interactions in queuing systems , 2006 .

[20]  Li Li,et al.  Modeling of spacing distribution of queuing vehicles at signalized junctions using random-matrix theory , 2008, 0803.2619.

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

[22]  Hesham Rakha,et al.  Issues and Solutions to Macroscopic Traffic Dispersion Modeling , 2006 .