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arxiv: 2605.31095 · v2 · pith:QZLWCKTZnew · submitted 2026-05-29 · ⚛️ physics.soc-ph

Vehicle Overacceleration -- A Fundamental Microscopic Mechanism for Traffic Breakdown Control Using Automated Vehicles and AI

Boris S. Kerner This is my paper

Pith reviewed 2026-06-28 20:05 UTC · model grok-4.3

classification ⚛️ physics.soc-ph
keywords traffic breakdownvehicle overaccelerationoverdecelerationautomated vehiclestraffic flow theorybottlenecksnucleation
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0 comments X

The pith

Traffic breakdown at bottlenecks is governed by vehicle overacceleration rather than overdeceleration in both human-driven and automated traffic.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper addresses whether the nucleation of traffic breakdown at bottlenecks stems from vehicle overdeceleration through overbraking or from discontinuous vehicle acceleration called overacceleration. It establishes that overacceleration governs breakdown in both human-driven and automated traffic flows. Microscopic modeling is used to isolate the overacceleration effect from braking-related instabilities. This matters because it points to specific dynamic behaviors that automated vehicles could adjust to prevent breakdowns.

Core claim

In both human-driven and automated traffic flow, traffic breakdown is governed by vehicle overacceleration rather than vehicle overdeceleration. This conclusion follows from microscopic modeling that separates traffic breakdown caused by overacceleration from traffic instabilities caused by overdeceleration due to braking behavior.

What carries the argument

Microscopic modeling separation of traffic breakdown caused by overacceleration from instabilities caused by overdeceleration due to braking behavior.

If this is right

  • Automated vehicle control algorithms can target prevention of overacceleration to suppress breakdown nucleation.
  • The same overacceleration mechanism applies to human-driven traffic, so driver assistance systems should address acceleration discontinuities.
  • AI-managed traffic at bottlenecks can use individual vehicle dynamics to maintain flow stability.
  • Mixed fleets of human and automated vehicles remain subject to the same breakdown trigger.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Traffic management could monitor acceleration profiles in real time to predict and avert breakdowns before they nucleate.
  • Vehicle design standards might shift emphasis toward smooth acceleration limits rather than only braking response.
  • The distinction between the two mechanisms could be tested in other congested flow systems such as pedestrian movement or supply chains.

Load-bearing premise

Microscopic modeling can reliably separate traffic breakdown caused by overacceleration from traffic instabilities caused by overdeceleration due to braking behavior.

What would settle it

A simulation or field observation in which traffic breakdown occurs at a bottleneck solely through sequences of overdeceleration with no overacceleration present would falsify the central claim.

Figures

Figures reproduced from arXiv: 2605.31095 by Boris S. Kerner.

Figure 1
Figure 1. Figure 1: FIG. 1: Empirical nucleation nature of traffic breakdown (F [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Qualitative presentation of indifferent zone for car [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Qualitative explanations of the origin of the indif [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Hypothesis of three-phase traffic theory about the [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Qualitative explanation of the range of highway ca [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Steady states of ACC-model (10) (a) and TPACC [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Overacceleration through safely acceleration in AC [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Characteristics of highway capacity of traffic con [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Induced traffic breakdown in traffic of 100% of [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Steady states of model (21)–(23) in space-gap–spee [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: Continuation of Fig. 14(b). (a), (b) Location [PITH_FULL_IMAGE:figures/full_fig_p017_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: Effect of cooperation of different mechanisms of over [PITH_FULL_IMAGE:figures/full_fig_p018_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17: Simulations of the metastability of free flow with re [PITH_FULL_IMAGE:figures/full_fig_p019_17.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20: Continuation of Fig. 17. Induced traffic breakdown [PITH_FULL_IMAGE:figures/full_fig_p020_20.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19: Continuation of Fig. 17. (a, b) Simulated vehicle [PITH_FULL_IMAGE:figures/full_fig_p020_19.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22: Simulations of spatiotemporal competition betwee [PITH_FULL_IMAGE:figures/full_fig_p021_22.png] view at source ↗
Figure 24
Figure 24. Figure 24: FIG. 24: Continuation of Fig. 23. Simulations of automated [PITH_FULL_IMAGE:figures/full_fig_p022_24.png] view at source ↗
Figure 23
Figure 23. Figure 23: FIG. 23: Simulations of induced F [PITH_FULL_IMAGE:figures/full_fig_p022_23.png] view at source ↗
Figure 25
Figure 25. Figure 25: FIG. 25: Vehicle overacceleration versus vehicle overdece [PITH_FULL_IMAGE:figures/full_fig_p024_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: FIG. 26: Explanation of a possible confusion by simulations [PITH_FULL_IMAGE:figures/full_fig_p024_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: FIG. 27: Nucleation character of S [PITH_FULL_IMAGE:figures/full_fig_p026_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: FIG. 28: Nucleation character of S [PITH_FULL_IMAGE:figures/full_fig_p027_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: FIG. 29: Qualitative explanation of jam absorption effect in [PITH_FULL_IMAGE:figures/full_fig_p028_29.png] view at source ↗
read the original abstract

This review article addresses a fundamental controversial question in traffic theory: Is the nucleation character of traffic breakdown at a bottleneck governed by vehicle overdeceleration (overbraking) or by discontinuous vehicle acceleration, referred to as vehicle overacceleration. This question is of particular importance in the context of automated vehicles and AI, whose individual dynamic behavior can enable reliable strategies for traffic breakdown control in the future. We show that, in both human-driven and automated traffic flow, traffic breakdown is governed by vehicle overacceleration rather than vehicle overdeceleration. With this objective, in microscopic modeling we separate traffic breakdown caused by overacceleration from traffic instabilities caused by overdeceleration due to braking behavior, while following recent papers [Phys. Rev. E 108, 014302 (2023); 108, 064305 (2023); 112, 034309 (2025)].

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. This review article claims that traffic breakdown at bottlenecks is governed by vehicle overacceleration (discontinuous acceleration) rather than overdeceleration (overbraking) in both human-driven and automated traffic. The conclusion is reached via microscopic modeling that separates overacceleration-induced breakdown from overdeceleration instabilities, following the separation procedure in the author's cited Phys. Rev. E papers from 2023 and 2025.

Significance. If the modeling separation is robust, the result would reframe the nucleation mechanism of traffic breakdown and open pathways for AV and AI-based control strategies that target overacceleration behavior to suppress breakdowns, with potential benefits for traffic flow stability.

major comments (2)
  1. [Abstract] Abstract: the claim that microscopic modeling separates traffic breakdown caused by overacceleration from instabilities caused by overdeceleration is asserted without any description of the data, simulation setup, error handling, or validation metrics used to achieve the separation.
  2. [Abstract] Abstract (and referenced modeling): the separation procedure is stated to follow Phys. Rev. E 108, 014302 (2023), 108, 064305 (2023), and 112, 034309 (2025), yet the manuscript contains no robustness checks against variations in braking parameters, reaction times, or alternative deceleration rules that could couple the two mechanisms.
minor comments (1)
  1. Clarify in the text which results are new to this review versus direct summaries of the cited prior works.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed review and valuable feedback on our manuscript. The paper is a review article that builds upon our previous Phys. Rev. E publications to argue that vehicle overacceleration governs traffic breakdown. We address each major comment below and indicate the revisions we will make to enhance the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that microscopic modeling separates traffic breakdown caused by overacceleration from instabilities caused by overdeceleration is asserted without any description of the data, simulation setup, error handling, or validation metrics used to achieve the separation.

    Authors: We agree that the abstract, being concise, does not provide details on the simulation data, setup, error handling, or validation metrics. As this is a review summarizing results from our cited works, these elements are fully described in Phys. Rev. E 108, 014302 (2023), 108, 064305 (2023), and 112, 034309 (2025), including comparisons with empirical data and validation procedures. We will revise the abstract to include a brief statement referencing the modeling framework and validation in those papers, improving transparency for readers. revision: yes

  2. Referee: [Abstract] Abstract (and referenced modeling): the separation procedure is stated to follow Phys. Rev. E 108, 014302 (2023), 108, 064305 (2023), and 112, 034309 (2025), yet the manuscript contains no robustness checks against variations in braking parameters, reaction times, or alternative deceleration rules that could couple the two mechanisms.

    Authors: The referee correctly notes that the current manuscript does not explicitly present robustness checks. However, such checks, including variations in braking parameters, reaction times, and alternative deceleration rules, were performed in the referenced Phys. Rev. E papers to confirm that overacceleration and overdeceleration mechanisms can be separated without coupling. We will add a concise summary of these robustness analyses in the main text of the review, directing readers to the specific sections in the cited papers where the parameter studies are detailed. revision: yes

Circularity Check

1 steps flagged

Central separation of overacceleration vs. overdeceleration effects is achieved only by following author's prior self-cited papers

specific steps
  1. self citation load bearing [Abstract]
    "in microscopic modeling we separate traffic breakdown caused by overacceleration from traffic instabilities caused by overdeceleration due to braking behavior, while following recent papers [Phys. Rev. E 108, 014302 (2023); 108, 064305 (2023); 112, 034309 (2025)]."

    The separation procedure that allows attribution of breakdown to overacceleration (rather than overdeceleration) is not re-derived or validated here; it is imported wholesale from the author's own prior publications. The central controversial claim therefore depends on the validity and uniqueness of those self-citations without new external benchmarks.

full rationale

The paper's core claim—that breakdown is governed by overacceleration rather than overdeceleration—rests on the ability to separate the two mechanisms in microscopic modeling. This separation is explicitly performed 'while following' three papers by the same author (Kerner). No independent derivation, machine-checked proof, or external falsifiability test for the separation procedure is supplied in the present manuscript. This matches the self_citation_load_bearing pattern exactly: the load-bearing modeling step reduces to the cited self-work by the paper's own wording.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

With only the abstract available, no specific free parameters, axioms, or invented entities can be identified from the text.

pith-pipeline@v0.9.1-grok · 5681 in / 960 out tokens · 32160 ms · 2026-06-28T20:05:19.139638+00:00 · methodology

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Reference graph

Works this paper leans on

224 extracted references · 7 canonical work pages · 1 internal anchor

  1. [1]

    The control of vehicle overacceleration can be realized through the individual control of vehicle motion

    The essential contribution of this review article is that, by employing microscopic deterministic three-phase traffic flow models, we are able to demonstrate that the key element in controlling traffic breakdown lies in the control of vehicle overacceleration – and not, as assumed in standard traffic theories and models, in the control of traffic instability. The ...

  2. [2]

    We have shown that the empirical nucleation nature of traffic breakdown is indeed caused by the competition of discontinous overacceleration with speed adaptation, not by vehicle overdeceleration, i.e., not by traffic insta- bility

  3. [3]

    To confirm this statement, we have considered sev- eral microscopic three-phase traffic flow models for auto- mated and human-driving vehicles, in which traffic break- down (F → S transition) at the bottleneck is realized ex- clusively through vehicle overacceleration: In the models, neither classical traffic instability nor string instability can occur

  4. [4]

    The nucleation nature of traffic breakdown (F → S transition) at the bottleneck is qualitatively the same in traffic with human-driving vehicles or in traffic with au- tomated vehicles: The nucleation nature of traffic break- down is caused by the interplay of discontinuous vehicle overacceleration and vehicle speed adaptation

  5. [5]

    1(a)), in simulations of automated vehicles no moving jams have been observed during the MSP prop- agation as well as during and after the traffic breakdown (Figs

    Simulations of traffic consisting of automated vehi- cles can reproduce empirical data of traffic with human- driving vehicles, in which the MSP while propagating upstream has induced the F → S transition at the bottle- neck with the LSP emergence: As found in the empirical data (Fig. 1(a)), in simulations of automated vehicles no moving jams have been observ...

  6. [6]

    1(a) can be simulated with none of the standard traffic flow models in which either classical traffic instability or string instability results in traffic breakdown at the bottleneck

    Contrary to three-phase traffic flow models, the empirical data shown in Fig. 1(a) can be simulated with none of the standard traffic flow models in which either classical traffic instability or string instability results in traffic breakdown at the bottleneck. This means that approaches such as jam absorption driving (also referred to as dissipation of stop-and-go...

  7. [7]

    This proposal for the recovering of free flow could represent very interesting tasks for future traffic research

    Nevertheless, we can assume that overacceleration management in cooperation with jam absorption driving could be useful for the dissolution of traffic congestion at the bottleneck. This proposal for the recovering of free flow could represent very interesting tasks for future traffic research

  8. [8]

    Individual control of the competition between dis- continuous overacceleration and speed adaptation of au- tomated vehicles with the use of AI, which (as we know) has not yet been carried out, could be a very important subject of future development of microscopic theory of mixed traffic. Appendix A: Choice of Dynamic Coefficient in Helly’s Model of ACC-Vehicl...

  9. [9]

    We have found that at cho- sen model parameters no moving jams occur in synchro- nized flow and the term vτd/g in (A2) does not influence results noticeably

    9 s− 1 as those in [200] at which condition for string stability (11) is satisfied. We have found that at cho- sen model parameters no moving jams occur in synchro- nized flow and the term vτd/g in (A2) does not influence results noticeably. For this reason, simulations of the ACC-model (10), (A2) presented in the paper can be ap- plied for a comparison with...

  10. [10]

    May, Traffic Flow Fundamentals, Prentice-Hall, Inc., New Jersey, 1990

    A.D. May, Traffic Flow Fundamentals, Prentice-Hall, Inc., New Jersey, 1990

    1990

  11. [11]

    Highway Capacity Manual, Sixth Edition, National Re- search Council, Transportation Research Board, Wash- ington, DC, 2016

    2016

  12. [12]

    Gartner, C.J

    N.H. Gartner, C.J. Messer, A. Rathi (Eds.), Traffic Flow Theory: A State-of-the-Art Report, Transportation Re- search Board, Washington DC, 2001

    2001

  13. [13]

    Elefteriadou, An introduction to traffic flow theory , in Springer Optimization and its Applications, Vol

    L. Elefteriadou, An introduction to traffic flow theory , in Springer Optimization and its Applications, Vol. 84 (Springer, Berlin, 2014)

    2014

  14. [14]

    Daganzo, Fundamentals of Transportation and Traffic Operations, Elsevier Science Inc., New York, 1997

    C.F. Daganzo, Fundamentals of Transportation and Traffic Operations, Elsevier Science Inc., New York, 1997

    1997

  15. [15]

    Chowdhury, L

    D. Chowdhury, L. Santen, A. Schadschneider, Physics Reports 329 (2000) 199–329

    2000

  16. [16]

    Brockfeld, R.D

    E. Brockfeld, R.D. K¨ uhne, A. Skabardonis, P, Wagner, Trans. Res. Rec. 1852 (2003) 124–129

    2003

  17. [17]

    Bellomo, V

    N. Bellomo, V. Coscia, M. Delitala, Math. Mod. Meth. App. Sc. 12 (2002) 1801–1843

    2002

  18. [18]

    Ferrara, S

    A. Ferrara, S. Sacone, S. Siri, Freeway Traffic Modelling and Control, Springer, Berlin, 2018

    2018

  19. [19]

    Leutzbach, Introduction to the Theory of Traffic Flow, Springer, Berlin, 1988

    W. Leutzbach, Introduction to the Theory of Traffic Flow, Springer, Berlin, 1988

    1988

  20. [20]

    Mahnke, J

    R. Mahnke, J. Kaupuˇ zs, I. Lubashevsky, Phys. Rep. 408 (2005) 1–130

    2005

  21. [21]

    Mahnke, J

    R. Mahnke, J. Kaupuˇ zs, I. Lubashevsky, Physics of Stochastic Processes: How Randomness Acts in Time, Wiley-VCH, Weinheim, 2009

    2009

  22. [22]

    Whitham, Linear and Nonlinear Waves, Wiley, New York, 1974

    G.B. Whitham, Linear and Nonlinear Waves, Wiley, New York, 1974

    1974

  23. [23]

    Schadschneider, D

    A. Schadschneider, D. Chowdhury, K. Nishinari, Stochastic Transport in Complex Systems, Elsevier Sci- ence Inc., New York, 2011

    2011

  24. [24]

    Saifuzzaman, Z

    M. Saifuzzaman, Z. Zheng, Transp. Res. C 48 (2014) 379–403

    2014

  25. [25]

    Papageorgiou, Application of Automatic Con- trol Concepts in Traffic Flow Modeling and Control, Springer, Berlin, New York, 1983

    M. Papageorgiou, Application of Automatic Con- trol Concepts in Traffic Flow Modeling and Control, Springer, Berlin, New York, 1983

    1983

  26. [26]

    Newell, Instability in dense highway traffic, a re- view, in: Proceedings of the second international sym- posium on traffic road traffic flow, OECD, London, 1963, pp 73–83

    G.F. Newell, Instability in dense highway traffic, a re- view, in: Proceedings of the second international sym- posium on traffic road traffic flow, OECD, London, 1963, pp 73–83

    1963

  27. [27]

    Prigogine, R

    I. Prigogine, R. Herman, Kinetic theory of vehicular traffic, American Elsevier, New York, 1971

    1971

  28. [28]

    Newell, Applications of Queuing Theory, Chapman Hall, London, 1982

    G.F. Newell, Applications of Queuing Theory, Chapman Hall, London, 1982

    1982

  29. [29]

    Nagel, P

    K. Nagel, P. Wagner, R. Woesler, Oper. Res. 51 (2003) 681–716

    2003

  30. [30]

    Nagatani, Rep

    T. Nagatani, Rep. Prog. Phys. 65 (2002) 1331–1386

    2002

  31. [31]

    W. D. Ashton, The theory of traffic flow (Methuen & Co. London, John Wiley & Sons, New York, 1966)

    1966

  32. [32]

    D. R. Drew, Traffic Flow Theory and Control (McGraw Hill, New York, 1968)

    1968

  33. [33]

    D. L. Gerlough, M. J. Huber, Traffic Flow Theory Spe- cial Report 165 (Transp. Res. Board, Washington D.C., 1975)

    1975

  34. [34]

    D. C. Gazis, Traffic Theory (Springer, Berlin, 2002)

    2002

  35. [35]

    Barcel´ o (Ed.), Fundamentals of Traffic Simulation, International Series in Operations Research and Man- agement Science, Vol

    J. Barcel´ o (Ed.), Fundamentals of Traffic Simulation, International Series in Operations Research and Man- agement Science, Vol. 145, Springer, Berlin, 2010

    2010

  36. [36]

    Treiber and A

    M. Treiber and A. Kesting, Traffic Flow Dynamics: Data, Models and Simulation , Second Edition (Springer, Cham, 2025)

    2025

  37. [37]

    Daiheng Ni, Traffic Flow Theory , Edition 2 (Elsevier, Amsterdam, 2026)

    2026

  38. [38]

    Michail Makridis and Yifan Zhang, Autonomous Driv- ing and Mixed Traffic Dynamics: Modeling, Simulation, and Control , (Elsevier, Amsterdam, 2026)

    2026

  39. [39]

    Kessels, Traffic flow modelling (Springer, Berlin, 2019)

    F. Kessels, Traffic flow modelling (Springer, Berlin, 2019)

    2019

  40. [40]

    Schadschneider, D

    A. Schadschneider, D. Chowdhury, K. Nishinari, Stochastic Transport in Complex Systems (Elsevier Sci- ence Inc., New York, 2011)

    2011

  41. [41]

    Chowdhury, L

    D. Chowdhury, L. Santen, and A. Schadschneider, Phys. Rep. 329, 199 (2000)

    2000

  42. [42]

    Helbing, Rev

    D. Helbing, Rev. Mod. Phys. 73, 1067 (2001)

    2001

  43. [43]

    Mannering, W.P

    F.L. Mannering, W.P. Kilareski, Principles of Highway Engineering and Traffic Analysis, 2nd ed., John Wiley & Sons, New York, 1998

    1998

  44. [44]

    Brackstone, M

    M. Brackstone, M. McDonaldm, Transp. Res. F 2 (1999) 181–196

    1999

  45. [45]

    Shvetsov, Automation and Remote Control 64 (2003) 1651–1689

    V.I. Shvetsov, Automation and Remote Control 64 (2003) 1651–1689

    2003

  46. [46]

    Maerivoet, B

    S. Maerivoet, B. De Moor, , Phys. Rep. 419 (2005) 1–64

    2005

  47. [47]

    Rakha, A

    H. Rakha, A. Tawfik, in: B.S. Kerner (Ed.), Com- plex Dynamics of Traffic Management, Encyclopedia of Complexity and Systems Science Series, Springer, New York, NY, 2019, pp 79–129

    2019

  48. [48]

    Piccoli, A

    B. Piccoli, A. Tosin Vehicular traffic: a review of contin - uum mathematical models, in: R.A. Meyers (Ed.), En- cyclopedia of Complexity and System Science, Springer, Berlin, 2009, pp. 9727–9749

    2009

  49. [49]

    Roess, E.S

    R.P. Roess, E.S. Prassas, The Highway Capacity Man- ual: A Conceptual and Research History, Springer, Berlin, 2014

    2014

  50. [50]

    Hegyi, T

    A. Hegyi, T. Bellemans, B. De Schutter, in: B.S. Kerner (Ed.), Complex Dynamics of Traffic Management, En- cyclopedia of Complexity and Systems Science Series, Springer, New York, NY, 2019, pp. 167–193

    2019

  51. [51]

    Seo, A.M

    T. Seo, A.M. Bayen, T. Kusakabe, Y. Asakura, Annual. Rev. in Control 43 (2017) 128–151. 32

    2017

  52. [52]

    doi:10.5334/baw

    A. Horni, K. Nagel, K.W. Axhausen (Eds.), The Multi-Agent Transport Simulation MATSim, Ubiquity, London, 2016, URL: http://matsim.org/the-book. doi: 10.5334/baw

    work page doi:10.5334/baw 2016

  53. [53]

    Kerner, The Physics of Traffic , Springer, Berlin, New York, 2004

    B.S. Kerner, The Physics of Traffic , Springer, Berlin, New York, 2004

    2004

  54. [54]

    Papageorgiou, I

    M. Papageorgiou, I. Papamichail, Transp. Res. Rec. 2047 (2008) 28–36

    2047

  55. [55]

    Papageorgiou, J.-M

    M. Papageorgiou, J.-M. Blosseville, H. Hadj-Salem, Transp. Res. A 24 (1990) 361–370; M. Papageorgiou, H. Hadj-Salem, J.-M. Blosseville, Transp. Res. Rec. 1320 (1991) 58–64; M. Papageorgiou, H. Hadj-Salem, F. Mid- dleham, Transp. Res. Rec. 1603 (1997) 99–98

    1990

  56. [56]

    Kerner, Physica A, 355, 565–601 (2005); IEEE Trans

    B.S. Kerner, Physica A, 355, 565–601 (2005); IEEE Trans. ITS 8, 308 (2007)

    2005

  57. [57]

    Kerner, Introduction to Modern Traffic Flow The- ory and Control , (Springer, Berlin, New York, 2009)

    B.S. Kerner, Introduction to Modern Traffic Flow The- ory and Control , (Springer, Berlin, New York, 2009)

    2009

  58. [58]

    Kerner, Transp

    B.S. Kerner, Transp. Res. Rec. 1999, 30–39, 2007

    1999

  59. [59]

    Yizhi Wang, Yi Zhang, Jianming Hu, and Li Li, Inter. J. . Modern Phys. C 23, 1250060, 2012

    2012

  60. [60]

    Yang H, Zhai X, Zheng C, Physica A 509, 567–577 (2018)

    2018

  61. [61]

    Y. Han, A. Hegyi, L. Zhang, Z. He, E. Chung, and P. Liu, Transportation Research C 144, 103900, (2022)

    2022

  62. [62]

    Hegyi and S

    A. Hegyi and S. P. Hoogendoorn, in IEEE Conf. on ITS, Proceedings, ITSC, 2010, pp. 519–524

    2010

  63. [63]

    Zhang, Z

    Y. Zhang, Z. Zhang, M. Qui¨ nones-Grueiro, W. Barbour, C. Weston, G. Biswas, and D. Work, in 2024 IEEE 27th Inter. Conf. on ITS (ITSC), 2024, pp. 776–783

    2024

  64. [64]

    Khondaker and L

    B. Khondaker and L. Kattan, Transportation Letters, 7, 264–278, 2015

    2015

  65. [65]

    Herman, E

    R. Herman, E. W. Montroll, R. B. Potts, and R. W. Rothery, Oper. Res. 7, 86 (1959)

    1959

  66. [66]

    D. C. Gazis, R. Herman, and R. B. Potts, Oper. Res. 7, 499 (1959)

    1959

  67. [67]

    D. C. Gazis, R. Herman, and R. W. Rothery, Oper. Res. 9, 545 (1961)

    1961

  68. [68]

    Kometani and T

    E. Kometani and T. Sasaki, J. Oper. Res. Soc. Jap. 2, 11–26 (1958)

    1958

  69. [69]

    Kometani and T

    E. Kometani and T. Sasaki, Oper. Res. 7, 704–720 (1959)

    1959

  70. [70]

    Kometani and T

    E. Kometani and T. Sasaki, Oper. Res. Soc. Jap. 3, 176–190 (1961)

    1961

  71. [71]

    Kometani, T

    E. Kometani, T. Sasaki, in Theory of Traffic Flow, ed. by R. Herman (Elsevier, Amsterdam, 1961), pp. 105– 119

    1961

  72. [72]

    G. F. Newell, Transp. Res. B 36, 195 (2002)

    2002

  73. [73]

    P. G. Gipps, Transp. Res. B 15, 105–111 (1981)

    1981

  74. [74]

    P. G. Gipps, Transp. Res. B. 20, 403 (1986)

    1986

  75. [75]

    Wiedemann, Simulation des Verkehrsflusses (Univer- sity of Karlsruhe, Karlsruhe, 1974)

    R. Wiedemann, Simulation des Verkehrsflusses (Univer- sity of Karlsruhe, Karlsruhe, 1974)

    1974

  76. [76]

    H. J. Payne, in Research Directions in Computer Con- trol of Urban Traffic Systems, ed. by W. S. Levine (Am. Soc. of Civil Engineers, New York, 1979), pp. 251–265

    1979

  77. [77]

    H. J. Payne, Tran. Res. Rec. 772, 68 (1979)

    1979

  78. [78]

    Aw and M

    A. Aw and M. Rascle, SIAM J. Appl. Math. 60, 916 (2000)

    2000

  79. [79]

    Nagel and M

    K. Nagel and M. Schreckenberg, J. Phys. (France) I 2, 2221 (1992)

    1992

  80. [80]

    Bando, K

    M. Bando, K. Hasebe, A. Nakayama, A. Shibata, Y. Sugiyama, Jpn. J. Appl. Math. 11, 203 (1994)

    1994

Showing first 80 references.