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REVIEW 4 major objections 5 minor 31 references

Traffic Wave Properties for Automated Vehicles During Traffic Oscillations via Analytical Approximations

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper derives an analytical formula showing that the traffic wave speed between an automated vehicle and its leader becomes time-dependent and vehicle-dependent under oscillations, tied to the AV's control transfer function.

desk verdict A useful analytical bridge from AV control to a wave-speed-like quantity, but the central identification with physical wave speed has a sign error that needs fixing before the propositions can be taken at face value. read the letter →

arxiv 2411.16937 v1 pith:DA2DUQ3C submitted 2024-11-25 eess.SY cs.SY

Yang Zhou , Sixu Li , Wissam Kontar , Fan Pu , Anupam Srivastava , Soyoung Ahn This is my paper · ORCID
classification eess.SYcs.SY MSC 90B20
keywords Automatedvehiclestrafficoscillationswavepropagationcar-followingfrequency-domainanalysisdescribingfunctionheterogeneousspeedheterogeneity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that when automated vehicles follow a leader through oscillatory stop-and-go traffic, the traffic wave between them does not travel at the constant congestion speed assumed in classical kinematic wave theory. Instead, the wave speed is a time-varying, vehicle-dependent quantity determined by the AV's control transfer function, the oscillation frequency, the oscillation amplitude, and the equilibrium spacing and speed. The authors derive a closed-form approximation for this wave speed, extend it to heterogeneous platoons and weak nonlinearities, and verify it in numerical simulations. If correct, AV control parameters become direct levers on how congestion waves propagate in mixed traffic, with consequences for string stability and wave damping.

What carries the argument

The central object is the car-following transfer function $G(j\omega)=\hat p_{i-1}(s)/\hat p_i(s)=\hat v_{i-1}(s)/\hat v_i(s)$, evaluated at the oscillation frequency $\omega_m$; its magnitude $|G(j\omega_m)|$ is the disturbance amplification ratio and its phase $\angle G(j\omega_m)$ is the response lag. Combined with Newell's shift view of car-following, this yields the wave-speed formula $W_{0-1}(t)=\frac{\omega_m(s_e+(1-|G(j\omega_m)|)A_m\sin(\omega_m t))}{-\angle G(j\omega_m)}-v_e$, which is the load-bearing identity of the paper. The same formula with powers $|G|^i$ and accumulated phases gives each link of a platoon, and a describing-function replacement $G^{nl}$ handles speed-limit saturation.

What would settle it

Simulate a homogeneous AV platoon with leader speed $v_e+A_m\cos(\omega_m t)$, track the time-space slope of a constant-speed or constant-deceleration feature between each leader-follower pair over a full cycle, and compare with Eq. (10); the formula predicts a slope that oscillates with period $2\pi/\omega_m$ and varies with vehicle index, whereas the constant-wave-speed view predicts a fixed slope.

Watch

Extended reading notes

Core claim

The paper claims that in oscillatory traffic, the wave speed between an automated vehicle and its leader is not the constant congestion speed of Newell's simplified theory but a function of time and vehicle index, given explicitly by $W_{0-1}(t)=\frac{\omega_m(s_e+(1-|G(j\omega_m)|)A_m\sin(\omega_m t))}{-\angle G(j\omega_m)}-v_e$, where $G(j\omega_m)$ is the AV's car-following transfer function at the oscillation frequency. It further claims that the same structure, with $|G|^i$ and accumulated phase angles, governs each link of a homogeneous or heterogeneous platoon, yielding intra-vehicle time variation, inter-vehicle variation, sequence-independence of the average wave, associative decomposition by sub-platoons, and a possible shift of the dominant frequency as the wave travels downstream. The paper validates these predictions in simulations of a third-order linear ACC-type controller and extends the linear result to speed-boundary saturation using describing-function analysis.

Load-bearing premise

The load-bearing premise is that the quantity $h_{0-1}(t)/(-\angle G(j\omega_m)/\omega_m)-v_e$ defined in Eqs. (9) and (10) is the physical traffic wave speed, a definition introduced in this paper whose sign convention is not reconciled with the ordinary backward-moving congestion wave.

Editorial extensions

If this is right

  • In a homogeneous AV platoon excited by a single-frequency oscillation, the wave speed between each leader-follower pair oscillates with time, so wave speed is not a single number even within one congested platoon.
  • Wave speed also changes from link to link along the platoon, growing or shrinking with $|G(j\omega_m)|^{i-1}$; string-stable controllers therefore produce smaller wave-speed oscillation downstream, while string-unstable controllers amplify it.
  • For heterogeneous controllers without active nonlinear boundaries, the total wave travel time and cumulative shift distance are independent of the order in which controllers appear, and the whole platoon wave equals the sum of sub-platoon waves.
  • When speed limits saturate, the linear transfer function no longer holds; the describing-function approximation shows saturation can reduce oscillation amplification and thereby shrink wave-speed oscillation, even when the linear controller is string-unstable.
  • If several oscillation frequencies are present, the dominant frequency can change as the wave travels down the platoon, so the apparent wave speed can switch character along the vehicle string.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct empirical test would be to run a platoon of production ACC vehicles behind a leader whose speed oscillates at one frequency and extract the time-space slope of a fixed speed contour; the formula predicts periodic modulation at the oscillation frequency visible in trajectory data.
  • Because the formula reduces to Newell's constant speed in the low-frequency limit where $|G|=1$ and $\angle G=-\omega\tau$, the framework could be used to derive correction terms for macroscopic wave speed as a function of AV market penetration and controller gains.
  • The same describing-function machinery can treat acceleration and deceleration limits, which the paper leaves to future work; a natural extension is a controller-design problem that targets a desired wave-speed profile rather than only string stability.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes an analytical approximation framework for traffic wave speed in platoons of automated vehicles under oscillatory disturbances. It models AV car-following with a linear controller, derives a transfer function G(jω), and, using a generalized Newell-type geometric construction, defines a wave speed W_{0-1}(t) in Eq. (10) that depends on control gains, oscillation frequency, amplitude, and time. It then states propositions on intra- and inter-heterogeneity, commutativity, associativity, and predominant-frequency shift, and it presents numerical simulations using the same linear controller as validation.

Significance. If the identification of Eq. (10) with the physical traffic wave speed were correct, the paper would offer a useful bridge between AV control design and macroscopic wave properties, replacing the constant Newell wave speed with a control-dependent, time-varying speed for AV traffic. The algebraic part is mostly transparent and trackable, with no fitted free parameters in the main derivation; the propositions are explicitly stated with proofs, which is a strength. However, the central identification is not yet established and is in fact in error as written, which currently undermines the physical interpretation of all derived wave-speed results. The framework can likely be repaired by redefining the wave speed as -h/τ, after which the qualitative heterogeneity claims may still hold; the present manuscript requires this correction before its conclusions can be accepted.

major comments (4)
  1. [Section 2, Eqs. (9)–(10)] The quantity W_{0-1}(t) defined in Eq. (10) is not the physical speed of the wave segment constructed in Eq. (9). With τ' = -∡G(jω_m)/ω_m, Eq. (9) gives h_{0-1}(t)=p_0(t)-p_1(t+τ'), i.e., h is the spatial separation between the leader at emission time and the follower at arrival time. The segment connecting these two points in the time-space diagram has speed [p_1(t+τ')-p_0(t)]/τ' = -h_{0-1}(t)/τ'. Equation (10) instead computes h/τ'-v_e. In the Newell limit (|G|=1, ∡G=-ω_m τ, s_e=s0+v_e τ), h=s0 and Eq. (10) gives s0/τ-v_e, whereas Newell's simplified car-following model gives the backward congestion wave speed -s0/τ. The manuscript never states a coordinate frame or sign convention that reconciles this discrepancy; Remark 1 addresses sampling times only. Consequently, Propositions 1 and 2 and the numerical figures describe a constructed ratio, not the physical wave speed, unless Eq. (10) is replaced by W=-h/τ (and Eqs. (16), (36), and (44) adjusted accordingly). This is the central load-bearing step of the paper.
  2. [Section 2, Eq. (4) and Section 3, Eq. (12)] The transfer function is written as G(s)=p̃_0(s)/p̃_1(s)=ṽ_0(s)/ṽ_1(s) in Eq. (4) and as G(s)=p̃_{i-1}(s)/p̃_i(s) in Eq. (12), but every subsequent use of G treats it as the follower-to-leader transfer function p̃_i/p̃_{i-1}. For example, Eq. (7) sets p̃_1(t)=A_m|G(jω_m)|sin(ω_m t+∡G(jω_m)), and the string-stability conditions in Section 4.3 identify |G|<1 with disturbance dampening, which is consistent only with G=p_i/p_{i-1}. The Laplace transform of Eq. (2) indeed yields the follower-to-leader ratio; the ratios in Eqs. (4) and (12) should be inverted. As printed, the derivation from Eq. (2) to Eq. (10) is internally inconsistent, though the intended relation is recoverable.
  3. [Section 3, Proposition 4 proof] The expression for h_{N2}(t) is algebraically wrong. The proof states h_{N2}(t)=Σ_{i=k+1}^N s_{e,i}+v_e t_w(N2)+A_m(∏_{h=k+1}^N |G_h(jω_m)| - ∏_{h=1}^k |G_h(jω_m)|) sin(ω_m t), but the oscillation amplitude entering vehicle k+1 is A_m∏_{h=1}^k |G_h(jω_m)|, so the correct term is A_m∏_{h=1}^k |G_h(jω_m)|(∏_{h=k+1}^N |G_h(jω_m)| - 1) sin(ω_m t). With the printed formula, h_{N1}+h_{N2}=Σ s_e+v_e t_w(N)+A_m(∏_{h=k+1}^N |G_h|-1) sin(ω_m t), which is not equal to h_N(t). The stated associativity property can be recovered with the corrected factor, but the proof as written does not establish it.
  4. [Section 4] The numerical experiments validate only the internal algebra of the framework, not the identification of W with a physical wave speed. The simulations use the same linear controller and the same transfer function G(jω) that appears in Eq. (10), and the reported 'wave speed' is computed as the analytic W(t), not measured from trajectories as the slope of a wave front. Therefore, matching curves between simulation and Eq. (10) is a self-consistency check; it cannot supply evidence for the key assumption that W is the traffic wave speed. Independent validation would require, for example, tracking a speed-change front or a contour of constant oscillation phase through the simulated time-space diagram and comparing its slope with the proposed formula.
minor comments (5)
  1. [Throughout] The text contains many typographical and typesetting artifacts: 'Laplacian' should be 'Laplace', 'ω = 2π/f' should be 'ω = 2πf', and several equations contain fragmented symbols such as 'j_m' and 's s s'; a careful editing pass over the notation is needed.
  2. [References] The citations 'Li and Ouyang, 2013' (Section 2), 'Thieman et al., 2005' and 'Zhou et al., 2020' (Section 3) do not appear in the reference list; please add them or adjust the citations.
  3. [Section 2, Fig. 1 discussion] The phrase 'by the wave propagation routine practice as Fig. (3)' should refer to Fig. 1; the figure number is incorrect.
  4. [Figure 5 caption] The subfigure labels are garbled: the caption gives '(a) k_s=0.2; (b) k_s=0.6; (c) k_S=1; k_s=1.4', which mixes the label for subfigure (c) with the parameter value for (d); the enumeration should be completed and corrected.
  5. [Section 2, Eqs. (24)–(32)] The describing-function cases contain undefined or inconsistently used symbols (e.g., θ, G as a scalar, B) and some conditions are stated with mismatched variables, such as Case 2 using |G_sn(jω_m)|B without defining B; the sentences introducing β1 and β2 are also incomplete and should be rewritten for clarity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the wave-speed formulas are derived, not fitted, from the stated control model; self-citations are background only.

full rationale

The derivation of W_{0-1}(t) in Eq. (10) uses the analytically obtained follower trajectory Eq. (8), the transfer-function magnitude and phase from the linear controller, and a geometric "shifted distance" h_{0-1}(t). Propositions 1 and 2 are algebraic corollaries of that expression rather than independent empirical predictions, but algebraic implication from stated assumptions is not circularity. No parameter is fitted to data and then renamed a prediction; the numerical experiments implement the same controller used in the analytical model, making them self-consistency checks, but the analytical claims do not depend on those simulations. The cited prior work [30] supplies the example control law and background on gain effects; it is not the sole justification of the wave-speed propositions. The possible sign/offset issue with the congestion-wave-speed convention (e.g., the Newell limit yielding s0/tau - v_e instead of -s0/tau) is a correctness or modeling-identification concern, not a circularity of the derivation chain. Therefore no circular step meets the evidentiary bar.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No parameters are fitted to data to produce the central wave-speed results; k_s, k_v, tau, and phi are inputs from the chosen ACC control law. The key theoretical assumptions are the linearized control structure, sinusoidal steady state, the low-pass describing-function approximation, and the new wave speed definition in Eq. (10). No new physical entities are postulated.

assumptions (4)
  • domain assumption The AV car-following law is linear or linearizable as in Eq. (2) with a first-order actuation lag phi.
    The entire transfer function G(jomega) and the subsequent wave speed formulas are based on this linearized control structure. Real AV controllers may have nonlinearities beyond speed bounds, such as acceleration limits, which the paper leaves to readers with interest.
  • domain assumption The leading vehicle's oscillation is sinusoidal with a single (or predominant) frequency, and the analysis focuses on the steady-state oscillatory response.
    Laplace and describing function analysis assume sinusoidal steady state; real traffic oscillations are more complex, and the multi-frequency extension relies on the predominant frequency assumption A_p >> A_m in Section 3.
  • standard math The describing function's low-pass assumption holds, so only the first harmonic of the output is retained.
    Used in Eqs. (17)-(20) to derive the nonlinear transfer function; if higher harmonics are not negligible, the magnitude and phase formulas for the nonlinear cases become inaccurate.
  • ad hoc to paper The quantity h_{0-1}(t)/(-angle G/omega_m) - v_e in Eq. (10) is the physical traffic wave speed.
    This is a new definition introduced by the paper; it is not derived from the standard kinematic wave definition and its sign convention is not reconciled with the usual backward-moving congestion wave speed. This is the load-bearing assumption of the whole framework.

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Pith. "Pith review of Traffic Wave Properties for Automated Vehicles During Traffic Oscillations via Analytical Approximations." pith.science (2026). https://pith.science/paper/DA2DUQ3C

@misc{pith2026241116937,
  author       = {Pith},
  title        = {Pith review of: Traffic Wave Properties for Automated Vehicles During Traffic Oscillations via Analytical Approximations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DA2DUQ3C}},
  note         = {Machine review of arXiv:2411.16937}
}
read the original abstract

This paper presents an analytical approximation framework to understand the dynamics of traffic wave propagation for Automated Vehicles (AVs) during traffic oscillations. The framework systematically unravels the intricate relationships between the longitudinal control model of the AVs and the properties of traffic waves. We apply Laplacian Transformation and Describing Function Analysis to mathematically derive the traffic wave properties of an AV in car-following scenarios. Further, we incorporate Newell's car-following model to determine the speed of the traffic waves. Our analysis extends to both homogenous and heterogenous traffic, systematically handling intra-heterogeneities and inter-heterogeneities in traffic wave propagation using the established analytical framework. We validate our approach via numerical simulations and show the connections between the AV control system and traffic wave properties. This research emphasizes the importance of rethinking our understanding of traffic wave properties when AVs are present in the traffic system.

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Reference graph

Works this paper leans on

31 extracted references · 21 canonical work pages

  1. [1]

    Richards, P. I. Shock Waves on the Highway. Operations Research, V ol. 4, No. 1, 1956, pp. 42–51. https://doi.org/10.1287/opre.4.1.42. Zhou, Li, Kontar, Pu, Srivastava, and Ahn 23

    doi:10.1287/opre.4.1.42 1956

  2. [2]

    Newell, G. F. A Simplified Theory of Kinematic Waves in Highway Traffic, Part I: General Theory. Transportation Research Part B: Methodological , V ol. 27, No. 4, 1993, pp. 281–287. https://doi.org/10.1016/0191-2615(93)90038-C

    doi:10.1016/0191-2615(93)90038-c 1993

  3. [3]

    Newell, G. F. A Simplified Theory of Kinematic Waves in Highway Traffic, Part II: Queueing at Freeway Bottlenecks. Transportation Research Part B: Methodological , V ol. 27, No. 4, 1993, pp. 289–303. https://doi.org/10.1016/0191-2615(93)90039-D

    doi:10.1016/0191-2615(93)90039-d 1993

  4. [4]

    J., and G

    Lighthill, M. J., and G. B. Whitham. On Kinematic Waves II. A Theory of Traffic Flow on Long Crowded Roads. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, V ol. 229, No. 1178, 1997, pp. 317–345. https://doi.org/10.1098/rspa.1955.0089

    arXiv 1997

  5. [5]

    M., and W

    Zhang, H. M., and W. L. Jin. Kinematic Wave Traffic Flow Model for Mixed Traffic. Transportation Research Record, V ol. 1802, No. 1, 2002, pp. 197–204. https://doi.org/10.3141/1802-22

    work page doi:10.3141/1802-22 2002

  6. [6]

    Yi, J., H. Lin, L. Alvarez, and R. Horowitz. Stability of Macroscopic Traffic Flow Modeling through Wavefront Expansion. Transportation Research Part B: Methodological , V ol. 37, No. 7, 2003, pp. 661–679. https://doi.org/10.1016/S0191-2615(02)00044-9

    work page doi:10.1016/s0191-2615(02)00044-9 2003

  7. [7]

    Logghe, S., and L. H. Immers. Multi-Class Kinematic Wave Theory of Traffic Flow. Transportation Research Part B: Methodological , V ol. 42, No. 6, 2008, pp. 523–541. https://doi.org/10.1016/j.trb.2007.11.001

    work page doi:10.1016/j.trb.2007.11.001 2008

  8. [8]

    A Kinematic Wave Theory of Lane-Changing Traffic Flow

    Jin, W.-L. A Kinematic Wave Theory of Lane-Changing Traffic Flow. Transportation Research Part B: Methodological, V ol. 44, No. 8, 2010, pp. 1001–1021. https://doi.org/10.1016/j.trb.2009.12.014

    doi:10.1016/j.trb.2009.12.014 2010

Show all 31 references
  1. [9]

    J., and G

    Lighthill, M. J., and G. B. Whitham. On Kinematic Waves I. Flood Movement in Long Rivers. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, V ol. 229, No. 1178, 1997, pp. 281–316. https://doi.org/10.1098/rspa.1955.0088

    1997

  2. [10]

    Carlson, R. C., I. Papamichail, M. Papageorgiou, and A. Messmer. Optimal Mainstream Traffic Flow Control of Large -Scale Motorway Networks. Transportation Research Part C: Emerging Technologies, V ol. 18, No. 2, 2010, pp. 193–212. https://doi.org/10.1016/j.trc.2009.05.014

    2010 doi

  3. [11]

    Ahn, and A

    Chen, D., S. Ahn, and A. Hegyi. Variable Speed Limit Control for Steady and Oscillatory Queues at Fixed Freeway Bottlenecks. Transportation Research Part B: Methodological , V ol. 70, 2014, pp. 340–358. https://doi.org/10.1016/j.trb.2014.08.006

    2014 doi

  4. [12]

    For cases 𝐴𝐴/𝑣𝑣𝑏𝑏𝑏𝑏𝑏𝑏𝑠𝑠𝑏𝑏 = 0.8 and 𝐴𝐴/𝑣𝑣𝑏𝑏𝑏𝑏𝑏𝑏𝑠𝑠𝑏𝑏 = 0.9, the limits have not been reached, resulting in the same |𝐺𝐺(𝑗𝑗𝜔𝜔)|

    It is observed that the oscillation damping becomes more effective when the limits are reached in the case 𝐴𝐴/𝑣𝑣𝑏𝑏𝑏𝑏𝑏𝑏𝑠𝑠𝑏𝑏 = 1. For cases 𝐴𝐴/𝑣𝑣𝑏𝑏𝑏𝑏𝑏𝑏𝑠𝑠𝑏𝑏 = 0.8 and 𝐴𝐴/𝑣𝑣𝑏𝑏𝑏𝑏𝑏𝑏𝑠𝑠𝑏𝑏 = 0.9, the limits have not been reached, resulting in the same |𝐺𝐺(𝑗𝑗𝜔𝜔)|. As seen in Fig. 12(b),...

  5. [13]

    Chen, and S

    Han, Y ., D. Chen, and S. Ahn. Variable Speed Limit Control at Fixed Freeway Bottlenecks Using Connected Vehicles. Transportation Research Part B: Methodological, V ol. 98, 2017, pp. 113–134. https://doi.org/10.1016/j.trb.2016.12.013

    2017 doi

  6. [14]

    Han, Y ., and S. Ahn. Stochastic Modeling of Breakdown at Freeway Merge Bottleneck and Traffic Control Method Using Connected Automated V ehicle. Transportation Research Part B: Methodological, V ol. 107, 2018, pp. 146–166. https://doi.org/10.1016/j.trb.2017.11.007

    2018 doi

  7. [15]

    Hegyi, A., S. P. Hoogendoorn, M. Schreuder, and H. Stoelhorst. The Expected Effectivity of the Dynamic Speed Limit Algorithm SPECIALIST - A Field Data Evaluation Method. Presented at the 2009 European Control Conference (ECC), 2009

    2009

  8. [16]

    Hegyi, A., and S. P. Hoogendoorn. Dynamic Speed Limit Control to Resolve Shock Waves on Freeways - Field Test Results of the SPECIALIST Algorithm. Presented at the 13th International IEEE Conference on Intelligent Transportation Systems, 2010

    2010

  9. [17]

    Newell, G. F. A Simplified Car-Following Theory: A Lower Order Model. Transportation Research Zhou, Li, Kontar, Pu, Srivastava, and Ahn 24 Part B: Methodological , V ol. 36, No. 3, 2002, pp. 195–205. https://doi.org/10.1016/S0191 - 2615(00)00044-8

    2002 doi

  10. [18]

    Ahn, S., M. J. Cassidy, and J. Laval. Verification of a Simplified Car -Following Theory. Transportation Research Part B: Methodological , V ol. 38, No. 5, 2004, pp. 431–440. https://doi.org/10.1016/S0191-2615(03)00074-2

    2004 doi

  11. [19]

    Laval, Z

    Chen, D., J. Laval, Z. Zheng, and S. Ahn. A Behavioral Car-Following Model That Captures Traffic Oscillations. Transportation Research Part B: Methodological , V ol. 46, No. 6, 2012, pp. 744–761. https://doi.org/10.1016/j.trb.2012.01.009

    2012 doi

  12. [20]

    Chen, D., J. A. Laval, S. Ahn, and Z. Zheng. Microscopic Traffic Hysteresis in Traffic Oscillations: A Behavioral Perspective. Transportation Research Part B: Methodological, V ol. 46, No. 10, 2012, pp. 1440–1453. https://doi.org/10.1016/j.trb.2012.07.002

    2012 doi

  13. [21]

    Wu, and Z

    Jiang, R., Q. Wu, and Z. Zhu. Full Velocity Difference Model for a Car-Following Theory. Physical Review E, V ol. 64, No. 1, 2001, p. 017101. https://doi.org/10.1103/PhysRevE.64.017101

    2001 doi

  14. [22]

    A., and L

    Laval, J. A., and L. Leclercq. A Mechanism to Describe the Formation and Propagation of Stop-and- Go Waves in Congested Freeway Traffic. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences , V ol. 368, No. 1928, 2010, pp. 4519–454...

    1928

  15. [23]

    Treiber, M., and A. Kesting. An Open -Source Microscopic Traffic Simulator. IEEE Intelligent Transportation Systems Magazine, V ol. 2, No. 3, 2010, pp. 6–13

    2010

  16. [24]

    Leclercq

    Chiabaut, N., and L. Leclercq. Wave Velocity Estimation through Automatic Analysis of Cumulative Vehicle Count Curves. Transportation Research Record , V ol. 2249, No. 1, 2011, pp. 1–6. https://doi.org/10.3141/2249-01

    2011 doi

  17. [25]

    Taylor, J., X. Zhou, N. M. Rouphail, and R. J. Porter. Method for Investigating Intradriver Heterogeneity Using Vehicle Trajectory Data: A Dynamic Time Warping Approach. Transportation Research Part B: Methodological, V ol. 73, 2015, pp. 59–80. https://doi.org/10.1016/j.trb.20...

    2015 doi

  18. [26]

    Zheng, Z., S. Ahn, D. Chen, and J. Laval. Freeway Traffic Oscillations: Microscopic Analysis of Formations and Propagations Using Wavelet Transform. Procedia - Social and Behavioral Sciences, V ol. 17, 2011, pp. 702–716. https://doi.org/10.1016/j.sbspro.2011.04.540

    2011 doi

  19. [27]

    Tian, J., C. Zhu, D. Chen, R. Jiang, G. Wang, and Z. Gao. Car Following Behavioral Stochasticity Analysis and Modeling: Perspective from Wave Travel Time. Transportation Research Part B: Methodological, V ol. 143, 2021, pp. 160–176. https://doi.org/10.1016/j.trb.2020.11.008

    2021 doi

  20. [28]

    Zhou, H., A. Zhou, T. Li, D. Chen, S. Peeta, and J. Laval. Significance of Low -Level Controller for String Stability under Adaptive Cruise Control. http://arxiv.org/abs/2104.07726. Accessed Aug. 2, 2024

    2024 arXiv

  21. [29]

    Zhong, Q

    Zhou, Y ., X. Zhong, Q. Chen, S. Ahn, J. Jiang, and G. Jafarsalehi. Data -Driven Analysis for Disturbance Amplification in Car -Following Behavior of Automated Vehicles. Transportation Research Part B: Methodological , V ol. 174, 2023, p. 102768. https://doi.org/10.1016/j.trb....

    2023 doi

  22. [30]

    Jiang, J., Y . Zhou, X. Wang, and S. Ahn. On Dynamic Fundamental Diagrams: Implications for Automated Vehicles. Transportation Research Part B: Methodological , 2024, p. 102979. https://doi.org/10.1016/j.trb.2024.102979. Zhou, Li, Kontar, Pu, Srivastava, and Ahn 25

    2024

  23. [31]

    Kontar, W., T. Li, A. Srivastava, Y . Zhou, D. Chen, and S. Ahn. On Multi-Class Automated Vehicles: Car-Following Behavior and Its Implications for Traffic Dynamics. Transportation Research Part C: Emerging Technologies, V ol. 128, 2021, p. 103166. https://doi.org/10.1016/j.tr...

    2021

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