Recurrence Analysis Applications to Short-Term Macroscopic and Microscopic Road Traffic

The applicability of the theory of Recurrence Plots and Recurrence Quantification Analysis to short-term traffic flow is demonstrated through three distinct road traffic case studies. The first focuses on short-term traffic patterns of volume and speed in urban freeway sections. The second case study examines urban traffic flow dynamics under different traffic conditions and associates them to specific short-term statistical characteristics. The third case study discusses the use of the Recurrence Analysis for modeling the dynamics of the microscopic car following behavior on freeways. The applicability is discussed at a conceptual level and each case study is then presented. Finally, the modeling implications of the results on traffic flow prediction are discussed.

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

[2]  Eleni I. Vlahogianni,et al.  Temporal Evolution of Short‐Term Urban Traffic Flow: A Nonlinear Dynamics Approach , 2008, Comput. Aided Civ. Infrastructure Eng..

[3]  Takashi Nagatani,et al.  Effect of irregularity on vehicular traffic through a sequence of traffic lights , 2008 .

[4]  Fraser,et al.  Independent coordinates for strange attractors from mutual information. , 1986, Physical review. A, General physics.

[5]  Eleni I. Vlahogianni,et al.  Spatio‐Temporal Short‐Term Urban Traffic Volume Forecasting Using Genetically Optimized Modular Networks , 2007, Comput. Aided Civ. Infrastructure Eng..

[6]  H. M. Zhang.  A mathematical theory of traffic hysteresis , 1999 .

[7]  G. F. Newell.  A simplified theory of kinematic waves in highway traffic, part I: General theory , 1993 .

[8]  Havlin,et al.  Presence of many stable nonhomogeneous states in an inertial car-following model , 2000, Physical review letters.

[9]  Eleni I. Vlahogianni,et al.  Memory properties and fractional integration in transportation time-series , 2009 .

[10]  Jürgen Kurths,et al.  Recurrence plots for the analysis of complex systems , 2009 .

[11]  J. Zbilut,et al.  Embeddings and delays as derived from quantification of recurrence plots , 1992 .

[12]  H. Abarbanel,et al.  Determining embedding dimension for phase-space reconstruction using a geometrical construction. , 1992, Physical review. A, Atomic, molecular, and optical physics.

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

[14]  C L Webber,et al.  Dynamical assessment of physiological systems and states using recurrence plot strategies. , 1994, Journal of applied physiology.

[15]  C. Daganzo,et al.  Possible explanations of phase transitions in highway traffic , 1999 .

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

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

[18]  D. Helbing,et al.  Cellular Automata Simulating Experimental Properties of Traffic Flow , 1998, cond-mat/9812300.

[19]  B. Kerner,et al.  EXPERIMENTAL PROPERTIES OF PHASE TRANSITIONS IN TRAFFIC FLOW , 1997 .

[20]  G. F. Newell.  A simplified theory of kinematic waves in highway traffic, part II: Queueing at freeway bottlenecks , 1993 .

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

[22]  Gábor Stépán,et al.  Traffic jams: dynamics and control , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

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

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

[25]  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.

[26]  A. Schadschneider.  Statistical Physics of Traffic Flow , 2000, cond-mat/0007418.

[27]  Jianbo Gao,et al.  On the structures and quantification of recurrence plots , 2000 .

[28]  M. Casdagli.  Recurrence plots revisited , 1997 .

[29]  Howell Tong,et al.  Non-linear time series analysis , 2005 .

[30]  Alexander Skabardonis,et al.  Statistical characteristics of transitional queue conditions in signalized arterials , 2007 .

[31]  Gordon F. Newell,et al.  INSTABILITY IN DENSE HIGHWAY TRAFFIC: A REVIEW. , 1965 .

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

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

[34]  J. Kurths,et al.  Recurrence-plot-based measures of complexity and their application to heart-rate-variability data. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  A. Giuliani,et al.  Recurrence Quantification Analysis and Principal Components in the Detection of Short Complex Signals , 1997, chao-dyn/9712017.

[36]  D. Ruelle,et al.  Recurrence Plots of Dynamical Systems , 1987 .