Analytical Theory of Traffic Flows, Empirical Facts and Scientific Controversies Related to Them

1. Micro-Macro Link: Theoretical Derivation of "Macroscopic" Fluid-Dynamic Traffic Equations from "Microscopic" Car-Following Models

• D. Helbing (2009) Derivation of non-local macroscopic traffic equations and consistent traffic pressures from microscopic car-following models. European Physical Journal B 69(4), 539-548.
  
• V. Shvetsov and D. Helbing (1999) Macroscopic dynamics of multilane traffic. Physical Review E 59, 6328-6339.
  
• M. Treiber, A. Hennecke, and D. Helbing (1999) Derivation, properties, and simulation of a gas-kinetic-based, non-local traffic model. Physical Review E 59, 239-253.
  
• D. Helbing and M. Treiber (1998) Gas-kinetic-based traffic model explaining observed hysteretic phase transition. Physical Review Letters 81, 3042-3045.
  
• D. Helbing (1996) Gas-kinetic derivation of Navier-Stokes-like traffic equations. Physical Review E 53, 2366-2381.

2. Linear Instability Analysis, Requiem of Second-Order Traffic Flow Models, and Controversy on Characteristic Speeds

• D. Helbing and A. Johansson (2009) On the controversy around Daganzo's requiem for and Aw-Rascle's resurrection of second-order traffic flow models, European Physical Journal B 69(4), 549-562.
• D. Helbing (2009) Reply to "What faster-than-traffic characteristic speeds mean for vehicular traffic flow'', European Physical Journal B 69(4), 569-570.
• D. Helbing (1996) Derivation and empirical validation of a refined traffic flow model. Physica A 233, 253-282.

3. Non-Linear Instability Analysis, Metastable Traffic Flows, Critical Perturbation Amplitudes, and Characteristic Constants

• D. Helbing and M. Moussaid (2009) Analytical calculation of critical perturbation amplitudes and critical densities by non-linear stability analysis of a simple traffic flow model. European Physical Journal B 69(4), 571-581.
• D. Helbing and M. Schreckenberg (1999) Cellular automata simulating experimental properties of traffic flows. Physical Review E 59, R2505-R2508.

4. Effects of Bottlenecks, Classification of Spatio-Temporal Traffic Patterns and Conditions for their Occurence

• M. Treiber, A. Kesting, and D. Helbing (2010) Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts. Transportation Research Part B 44(8-9), 983-1000.
• D. Helbing, M. Treiber, A. Kesting, and M. Schönhof (2009) Theoretical vs. empirical classification and prediction of congested traffic states. European Physical Journal B 69(4), 583-598.
• D. Helbing, A. Hennecke, and M. Treiber (1999) Phase diagram of traffic states in the presence of inhomogeneities. Physical Review Letters 82, 4360-4363.

5. Effects of Heterogeneous Driver-Vehicle Units and Multi-Lane Interactions

• D. Helbing and B. Tilch (2009) A power law for the duration of high-flow states and its interpretation from a heterogeneous traffic flow perspective. European Physical Journal B 68(4), 577-586.
• D. Helbing and B. A. Huberman (1998) Coherent moving states in highway traffic. Nature 396, 738-740.

6. Effects of Fluctuations/Noise/Stochasticity

• M. Treiber and D. Helbing (2009) Hamilton-like statistics in onedimensional driven dissipative many-particle systems. European Physical Journal B 68(4), 607-618.
• D. Helbing, M. Treiber, and A. Kesting (2006) Understandinginterarrival and interdeparture time statistics from interactions in queuing systems.Physica A 363(1), 62-72.

7. Network Flows with Merges, Diverges, and Intersections; Urban Fundamental Diagram

• D. Helbing (2009) Derivation of a fundamental diagram for urban traffic flow. European Physical Journal B 70(2), 257-274.
• D. Helbing, J. Siegmeier, and S. Lämmer (2007) Self-organized network flows. Networks and Heterogeneous Media 2(2), 193-210.
  
• D. Helbing, R. Jiang, and M. Treiber (2005) Analytical investigation of oscillations in intersecting flows of pedestrian and vehicle traffic. Physical Review E 72, 046130.
  
• D. Helbing (2003) A section-based queueing-theoretical traffic model for congestion and travel time analysis in networks. Journal of Physics A: Mathematical and General 36, L593-L598.

8. Traffic Optimization and Control

• A. Kesting, M. Treiber, and D. Helbing (2010) Enhanced intelligent driver model to access the impact of driving strategies on traffic capacity. Phil. Trans. R. Soc. A 368(1928), 4585-4605.
• D. Helbing, A. Deutsch, S. Diez, K. Peters, Y. Kalaidzidis, K. Padberg-Gehle, S. Lämmer, A. Johansson, G. Breier, F. Schulze,and M Zerial (2009)Biologistics and the struggle for efficiency: Concepts and perspectives. Advances in Complex Systems12(6), 533-548.
• D. Helbing and A. Mazloumian (2009) Operation regimes and slower-is-faster-effect in the control of traffic intersections. European Physical Journal B 70(2), 229-241.
• S. Lämmer and D. Helbing (2008) Self-control of traffic lights and vehicle flows in urban road networks. JSTAT, P04019.
  
• A. Kesting, M. Treiber, M. Schönhof, and D. Helbing (2008) Adaptive cruise control design for active congestion avoidance. Transportation Research C 16(6), 668-683.
  
• M. Schönhof, M. Treiber, A. Kesting, and D. Helbing (2007) Autonomous detection and anticipation of jam fronts from messages propagated by intervehicle communication. Transportation Research Record 1999, 3-12.
  
• S. Lämmer, H. Kori, K. Peters, and D. Helbing (2006) Decentralised control of material or traffic flows in networks using phase-synchronisation. Physica A 363, 39-47.
  
• D. Helbing, S. Lämmer, and J.-P. Lebacque (2005) Self-organized control of irregular or perturbed network traffic. Pages 239-274 in: C. Deissenberg and R. F. Hartl (eds.) Optimal Control and Dynamic Games (Springer, Dordrecht).

9. Empirical Facts and Controversy regarding "Synchronized Traffic", "Pinch Effect", and "Three Phase Traffic Theory"

• M. Treiber, A. Kesting, and D. Helbing (2010) Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts. Transportation Research Part B 44(8-9), 983-1000.
• M. Schönhof and D. Helbing (2009) Criticism of three-phase traffic theory. Transportation Research B 43, 784-797.
• M. Schönhof and D. Helbing (2007) Empirical features of congested traffic states and their implications for traffic modeling. Transportation Science 41(2), 135-166.
  
• K. Nishinari, M. Treiber, and D. Helbing (2003) Interpreting the wide scattering of synchronized traffic data by time gap statistics. Physical Review E 68, 067101.
  
• S. Lämmer, B. Gehlsen, and D. Helbing (2006) Scaling laws in the spatial structure of urban road networks. Physica A 363, 89-95.
• R. Kölbl and D. Helbing (2003) Energy laws in human travel behaviour. New Journal of Physics 5, 48.1-48.12.
  
• D. Helbing and M. Treiber (2002) Critical discussion of "synchronized flow". Cooper@tive Tr@nsport@tion Dyn@mics 1, 2.1-2.24.
  
• M. Treiber, A. Hennecke, and D. Helbing (2000) Congested traffic states in empirical observations and microscopic simulations. Physical Review E 62, 1805-1824.
  
• M. Treiber and D. Helbing (1999) Macroscopic simulation of widely scattered synchronized traffic states. Journal of Physics A: Mathematical and General 32, L17-L23.

10. Reviews

• D. Helbing (2005) Traffic flow. In: Alwyn Scott (ed.) Encyclopedia of Nonlinear Science (Routledge, New York).
• D. Helbing and K. Nagel (2004) The physics of traffic and regional development. Contemporary Physics 45(5), 405-426.
  
• D. Helbing, A. Hennecke, V. Shvetsov, and M. Treiber (2002) Micro- and macro-simulation of freeway traffic. Mathematical and Computer Modelling 35(5/6), 517-547.
• D. Helbing, A. Hennecke, V. Shvetsov, and M. Treiber (2001) MASTER: Macroscopic traffic simulation based on a gas-kinetic, non-local traffic model. Transportation Research B 35, 183-211.
  
• D. Helbing (2001) Traffic and related self-driven many-particle systems. Reviews of Modern Physics 73, 1067-1141.
• D. Helbing and M. Treiber (1998) Jams, waves, and clusters. Science 282, 2001-2003.

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