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Sustained Heterogeneity: an emergent collective mechanism in LLM-driven traffic

Yujun Qi, Yangyang Guan

arXiv:2608.29174v1physics.soc-phcs.MAnlin.AO

TL;DR

The microscopic origins of traffic instability remain difficult to study because human driving decisions are inaccessible, and LLMs had not previously served as direct, real-time car-following controllers. This study deploys LLM agents in closed-loop traffic and identifies Sustained Heterogeneity, a distinct collective mechanism associated with reproduced stop-and-go dynamics.

  • Problem

    Human micro-decisions underlying traffic instability remain inaccessible, while prior LLM traffic studies had not used agents as direct, real-time, physically coupled car-following controllers.

  • Method

    The study deploys LLM agents as direct, real-time car-following controllers and examines their decision logs alongside matched control mechanisms and traffic dynamics.

  • Results

    The study identifies Sustained Heterogeneity as a collective mechanism and reproduces macroscopic and qualitative features of the Sugiyama traffic paradigm, including three-stage jam formation and free-flow unimodal versus jammed bimodal velocity distributions.

  • Takeaways & Limitations

    Sustained Heterogeneity is structurally distinct from the tested candidate mechanisms, while safety-oriented LLM reasoning does not suppress per-cycle target-speed divergence across agents.

  • Takeaways & Limitations

    The evidence is limited to GLM-4-Flash, Chinese prompts, one track length and IDM parameterisation, homogeneous instructions, and manually tuned safety-layer thresholds.

Abstract

from arXiv · show

Large language models (LLMs) are increasingly adopted as closed-loop controllers in physical multi-agent systems, yet their emergent collective dynamics remain incompletely characterised. We deploy 22 LLM agents as direct, real-time target-speed controllers (per 0.5 s cycle, with IDM as collision-avoidance clamp) on a 230 m ring road under the Sugiyama 2008 paradigm, reproducing human-like stop-and-go waves. Six matched controls spanning stochasticity (white noise, OU noise, temperature), population variance, and dynamical instability (delay, OV model) are systematically excluded. The surviving phenomenon, termed Sustained Heterogeneity (SH), is the persistent, approximately temperature-insensitive (approx. 8 percent across a 6x T sweep), per-cycle divergence in LLM-chosen target-speed adjustments, propagating through a three-stage cascade of drift, gap erosion, and nonlinear braking. Across four traffic densities, the critical LLM penetration fraction p_c decreases monotonically from no transition at density 43.5 veh/km to p_c approx 0.23 at density 95.7 veh/km, consistent with an initiation-threshold model governed by trigger distance, stochasticity, and fleet size. Chain-of-thought analysis of 39,600 decisions across three seeds shows agents engage in multi-factor safety reasoning, yet systematic divergence persists, implying stability must be enforced at the dynamics layer. This is the first study to identify a previously uncharacterised collective mechanism in LLM-controlled traffic and map a density-dependent phase boundary p_c(rho).

1. Introduction

The study uses LLM agents as direct closed-loop car-following controllers to revisit spontaneous stop-and-go waves in the Sugiyama ring-road paradigm. It identifies Sustained Heterogeneity (SH), a collective mechanism linking persistent target-speed divergence to macroscopic instability.

  • Motivation: The work addresses an 18-year-old puzzle by exposing microscopic decisions that human-driver experiments cannot observe.Every LLM prompt, chain-of-thought rationale, and resulting action is logged at each 0.5 s decision cycle.
  • Study setup: 22 LLM-controlled vehicles on a 230 m ring road reproduce spontaneous oscillatory stop-and-go waves under the Sugiyama 2008 paradigm.The LLMs act as direct real-time target-speed planners, while a deterministic IDM layer enforces collision-free dynamics.
  • Experimental contribution: Six matched controls spanning stochasticity, population variance, and dynamical instability systematically exclude classical candidate mechanisms as sufficient explanations.The controls test alternative sources of the observed phase transition rather than only varying the LLM configuration.
  • Interpretability: Chain-of-thought logs show multi-factor safety reasoning coexisting with persistent per-cycle target_delta divergence across agents.The result suggests that collective stability cannot rely solely on cognitive reasoning and must also be enforced at the dynamics layer.
  • Central finding: SH propagates through target-speed drift, IDM-gap erosion, and nonlinear braking, producing velocity variance 5.8× to more than 2000× larger than classical controls.The mechanism is proposed as structurally distinct from the tested candidate mechanisms.

2. Related work

Prior work established LLMs as useful analogues of human participants and began applying them to driving, but had not combined direct closed-loop control with collective mechanism discovery in a ring-road system. This study fills that specific gap.

  • LLM agents as human analogues: Earlier LLM-agent studies reproduced aggregate human-like patterns mainly in discrete, single-decision domains.The present work extends that paradigm to continuous, physically coupled traffic control.
  • LLM traffic research: Existing LLM traffic studies include RL-policy design, single-agent highway driving, and collaborative traffic planning, but address different roles or objectives.The cited prior systems do not directly study collective dynamics as the mechanism-discovery target.
  • Positioning: The present work deploys LLM agents as direct closed-loop car-following controllers in the Sugiyama ring-road paradigm.This differs from using an LLM as an RL-policy designer or planner whose output is executed by another controller.
  • Novel contribution: Its distinguishing combination is direct control, a ring-road setup, and identification of a previously uncharacterised collective mechanism using systematic controls and chain-of-thought observability.Table 1 frames these dimensions as the main comparison with representative prior work.

3. Methods

The methods combine a logged LLM car-following pipeline, a deterministic IDM safety layer, matched controls, and chain-of-thought analysis. These components expose per-cycle decisions while testing whether SH can be explained by simpler stochastic, heterogeneous, or unstable dynamics.

  • LLM control pipeline: A separate IDM safety layer clamps the LLM target-speed adjustment to a collision-free acceleration value.The safety layer is implemented in code rather than delegated to the prompt.
  • LLM control pipeline: Each vehicle observes speed, leader gap, relative velocity, and a 5 s history before LLM inference every 0.5 s.The LLM returns a structured decision including target_speed_delta, while the simulation advances with a 0.1 s physics timestep.
  • Control design: Six matched controls test sampling stochasticity, population parameter variance, time delay, and optimal-velocity dynamics as alternative mechanisms.Control parameters are deliberately calibrated to favour the competing hypotheses where possible.
  • Control design: The control calibration uses conservative alternatives: white-noise amplitude 0.9 m/s2, OU correlation time matching the 0.5 s LLM cycle, aggressive IDM parameter ranges, and OV sensitivity above the string-stability threshold.A supplementary baseline-delay run still yields v_std ≈ 0, indicating that delay alone does not destabilise the system at this density.
  • Chain-of-thought analysis: Chain-of-thought analysis across three seeds examines 39,600 decisions and finds persistent heterogeneity in LLM target-speed outputs.At identical initial inputs, agents can produce 9 distinct desired speeds within one 0.5 s cycle, while the closed-loop state amplifies this divergence.
  • Chain-of-thought analysis: Similar local traffic states can produce opposite-sign target-speed adjustments, demonstrating per-cycle directional divergence rather than only magnitude variation.Across seed 42, 107 of 600 cycles contain at least one similar-state agent pair with opposite-sign target_delta.
  • Chain-of-thought analysis: The per-call component exceeds the per-agent component in every unperturbed run, identifying closed-loop state coupling as the amplifier of the per-cycle seed.The reported per-call/per-agent ratio ranges from 1.0–4.8× across seven runs.

4. Results

LLM-controlled traffic develops self-sustained stop-and-go oscillations through Sustained Heterogeneity (SH), a persistent per-cycle divergence in target-speed adjustments that survives matched classical controls. The instability shows a density-dependent penetration threshold and reflects safety-aware reasoning that does not prevent dynamical-level collective breakdown.

  • Macroscopic instability: At density 95.7 veh/km, the all-LLM fleet reaches self-sustained oscillations with v_std ≈2.1 m/s, versus < 0.001 m/s for matched IDM-only traffic.The LLM fleet has mean velocity 5.44 ± 0.05 m/s, while the IDM baseline has 7.81 m/s.
  • Mechanism: SH is the surviving explanation after controls exclude unstructured stochasticity, parameter heterogeneity, and dynamical instability as sufficient mechanisms.The tested controls include white and correlated noise, temperature variation, parameter variance, delay, and the OV model.
  • Mechanism: SH begins with divergent target_delta values within one 0.5 s cycle, then propagates through gap erosion and nonlinear braking into stop-and-go waves.From a homogeneous initial state, agents produce 9 distinct v_desired values with cross-vehicle standard deviation ≈0.06 m/s.
  • Penetration threshold: At n_LLM = 5, the critical distribution is bimodal: 5 of 11 runs remain in free flow and 6 of 11 collapse to congestion.At n_LLM = 6, all 10 scanned seeds are congested; the transition midpoint is reported as p_c ≈0.23.
  • Density dependence: The critical penetration decreases with density: no transition occurs at 43.5 veh/km, while transitions occur between p = 0.64–0.79, 0.33–0.50, and 0.18–0.27 at higher densities.The four densities are 43.5, 60.9, 78.3, and 95.7 veh/km.
  • Density dependence: The density trend supports a qualitative initiation-threshold model, but its specific functional form is not a precise predictor because key erosion quantities lack independent density-resolved measurements.The model is intended to identify dependencies of p_c rather than provide sharp numerical extrapolation.

5. Discussion

The paper identifies Sustained Heterogeneity (SH) as a persistent source of collective traffic breakdown distinct from six tested alternatives, and links it to density-dependent deployment risk. Cognitive safety reasoning does not prevent the per-cycle target-speed divergence; stability therefore remains a dynamics-layer concern within the studied setting.

  • Sustained Heterogeneity: SH produces macroscopic traffic breakdown from individually within-IDM-tolerance LLM decisions and is structurally distinct from six tested candidate mechanisms.The perturbation is persistent and re-injected every 0.5 s, while closed-loop state coupling produces emergent per-agent differentiation.
  • Cognitive origins of SH: 13,200 decisions show multi-factor safety reasoning, yet per-vehicle target-speed divergence and the proposed SH cascade persist.Agents evaluate spacing, velocity, and approach dynamics, while target_delta differences remain across vehicles.
  • Cognitive origins of SH: 39,600 decisions show ADJUST_SPEED has |target_delta| = 1.20 ± 1.21 m/s, while 31.0% of such actions are decelerations that contribute to per-cycle divergence.KEEP_STEADY is effectively zero-speed adjustment, whereas the decelerating ADJUST_SPEED subgroup supplies the divergence not visible from the macro-action label alone.
  • Deployment boundary: At densities below 50 veh/km, no transition is observed even at p = 1.0; p_c falls from ~0.79 at 60.9 veh/km to ~0.50 at 78.3 veh/km and ~0.23 above 90 veh/km.The boundary is presented as a density-specific structural safety constraint for mixed-fleet deployment.
  • Scope and outlook: The p_c(rho) shape is expected to be class-wide, but absolute p_c values are model-specific to GLM-4-Flash and require cross-model validation.The study also identifies possible extensions to other LLM-controlled physical multi-agent systems under specified continuous, nonlinear, amplifying dynamics.
  • Limitations and outlook: The study is limited by one model, Chinese prompts, one track length and IDM parameterization, homogeneous instructions, and untested alternatives including a shared-target-speed control.Temperature ablation was conducted only at p = 1.0, so dependence of p_c on temperature at intermediate penetration remains open.

6. Conclusion

The study identifies Sustained Heterogeneity as a previously uncharacterised collective mechanism in directly LLM-controlled traffic and maps its density-dependent phase boundary. Chain-of-thought observability shows that safety reasoning coexists with persistent target-speed divergence, so stability must be addressed at the dynamics layer.

  • The study identifies Sustained Heterogeneity as a previously uncharacterised collective mechanism in LLM-controlled multi-agent traffic.It is distinguished from tested candidate mechanisms through systematic matched controls.
  • LLM agents act as direct, real-time closed-loop target-speed controllers while IDM provides a hard collision-avoidance clamp.The system uses a multi-agent ring-road simulation and chain-of-thought reasoning for microscopic observability.
  • The work maps a density-dependent phase boundary p_c(ρ) for LLM-based driving deployment.The boundary is supported by an initiation-threshold model involving trigger distance, stochasticity, and fleet size.
  • Safety-vigilant LLM reasoning does not suppress per-cycle target-speed adjustment divergence across agents.The contribution argues that collective stability cannot rely solely on the cognitive layer and must be enforced at the dynamics layer.

8. Author contributions

Y.Q. led the research design, implementation, analysis, and manuscript writing, while Y.G. conducted parameter sweeps, baseline comparisons, and contributed to analysis and drafting.

  • Y.Q. conceived the research design, implemented the simulation software, analysed the results, and wrote the manuscript.
  • Y.G. conducted parameter sweeps and baseline comparisons and participated in experimental analysis and manuscript preparation.

11. Code availability

The simulation framework is released as open-source software under the MIT licence, with public availability planned upon publication.

  • The release includes the LLM agent pipeline, IDM safety layer, and all experiment drivers.
  • The simulation framework is licensed under MIT and is to be made public upon publication.

Figure captions

The figures establish SH as a distinct mechanism, characterize its penetration threshold and density-dependent phase boundary, and validate the platform against the Sugiyama traffic paradigm. They also connect macroscopic stop-and-go waves to persistent microscopic target-speed divergence and safety reasoning.

  • Figure 1: The LLM fleet reaches v_std = 2.12 m/s, versus 0.16 m/s for white noise and 0.37 m/s for OU noise.The temperature control gives 1.97 m/s, or 0.93× the LLM value, supporting approximate temperature insensitivity.
  • Figure 1: The LLM fleet oscillates between approximately 4.3 and 6.8 m/s, while the matched IDM baseline remains flat at 7.81 m/s.The full-run LLM range is 3.4–8.4 m/s.
  • Figure 2: At n_LLM = 5, the penetration transition has midpoint p_c ≈ 0.23 and a width of approximately 2–4 vehicles.At the same point, 45% of runs remain in free flow and 55% collapse to the congested attractor.
  • Figure 2: Dangerous-approach events increase by approximately 2.6× between n_LLM = 5 and n_LLM = 6.The figure defines dangerous approaches as gaps below 2.5 m.
  • Figure 3: The critical penetration p_c decreases monotonically with density, from no transition at 43.5 veh/km to approximately 0.23 at 95.7 veh/km.At higher density, smaller equilibrium gaps allow fewer LLM vehicles to erode the safety buffer and trigger the cascade.
  • Figure 4: The platform produces oscillatory stop-and-go waves and places LLM transitions at approximately 50–60 veh/km, earlier than the human ring-road baseline at approximately 80–90 veh/km.The deterministic IDM baseline has no transition.
  • Figure 5: Across 22 LLM vehicles, safety-vigilant reasoning coexists with persistent per-cycle target_delta divergence.This supports interpreting the instability as a robust multi-agent dynamical feature rather than a superficial stochastic artefact.

Supplementary Information

The prompt defines a steady, safety-oriented driver with a roughly 30 km/h target, cautious gap management, delayed braking, and structured self-checks before each decision.

  • Output format: Each response uses strict JSON with a decision type plus target-speed and desired-gap adjustments.The allowed decisions are ADJUST_SPEED, ADJUST_GAP, and KEEP_STEADY; target_speed_delta ranges from -2.0 to 2.0 m/s and desired_gap_delta from -1.0 to 2.0 m.
  • Driver role: The LLM is cast as a smooth driver on a 230 m circular track, targeting roughly 30 km/h without aggressive acceleration or braking.The prompt emphasizes comfortable following distance and decisive reactions to danger.
  • Driving habits: The driver should keep creeping at 5–10 km/h when the leader slows, rather than stopping completely.Brake-light cues matter, but the agent should first assess whether the gap is actually shrinking rapidly.
  • Safety floor: The safety floor forbids collisions and instructs decisive braking when the gap feels too close, while modeling roughly half a second of reaction delay.The delay is explicitly treated as part of the driving behavior.
  • Decision checks: Before deciding, the agent evaluates immediate safety, approach speed, gap size, and whether recent conditions are improving or worsening.These questions operationalize multi-factor temporal assessment.
  • Inputs: The prompt supplies current speed, leader speed, gap, relative speed, brake-light state, time-to-collision, and a five-second trend history.Speed quantities are converted into the prompt’s displayed units, and time-to-collision receives qualitative danger labels.

S1.2.4 User prompt (English reference).

The English-reference appendix documents the LLM decision interface and the downstream five-mode safety-fusion pipeline, then records supplementary robustness, control, and wave-dynamics analyses.

  • S1.2.4 User prompt (English reference).: The prompt presents current and historical traffic state, asks for a decision, and returns structured speed, gap, and reasoning fields.The history covers ten samples over the preceding five seconds, while the output uses bounded numerical deltas and three discrete actions.
  • S1.4 Safety fusion layer.: The safety-fusion pipeline resolves five priority-ordered acceleration modes sharing common IDM parameters.Earlier modes intercept execution before later modes can run.
  • S1.4 Safety fusion layer.: The default proportional mode converts target_speed_delta into acceleration over the 0.5 s decision cycle and applies state-dependent deceleration floors.The floors are -8.0 m/s² for s < 3 m with Δv > 2 m/s, -5.0 m/s² for s < 5 m with Δv > 1 m/s, and otherwise -2.5 m/s².
  • S1.4 Safety fusion layer.: Low-speed startup replaces the proportional path with physical acceleration rules conditioned on leader motion and gap thresholds.Very close gaps trigger creep at 0.3 m/s², while insufficiently favorable conditions can produce zero acceleration.
  • S1.4 Safety fusion layer.: IDM dynamic override and emergency braking intervene under shrinking-gap, small-gap, or low-TTC conditions.Emergency braking can clip acceleration to [-8.0, 3.0] m/s², while the default path additionally uses a jerk limiter and final clip.
  • S1.5 Decision-log schema (one example).: Decision logs record time, vehicle state, target-speed and gap deltas, desired speed, action, and reasoning, with a released 16-cycle sample containing 352 decisions.The example run uses n = 22, p = 1.0, T = 0.6, and seed = 42.
  • S1.5 Decision-log schema (one example).: The supplementary analyses report stable qualitative chain-of-thought patterns across three seeds and show that doubling ring size increases cumulative IDM damping over a wave round trip.The latter interpretation attributes the stability gain to more IDM-stabilized vehicles in the loop, not a denser local buffer.
  • S1.5 Decision-log schema (one example).: Initial-condition perturbations affect early variability but not the late steady state, whereas additive white-noise controls scale linearly with noise amplitude and remain much smaller than LLM variability.The perturbed and unperturbed late-window standard deviations are 1.98 and 1.99 m/s; the white-noise fit is v_std ≈ 0.1748·σ with R2 > 0.999, while the largest tested control gives 0.263 m/s.

S8. Per-agent vs per-call decomposition of microscopic LLM variance

The decomposition separates persistent per-agent averages from cycle-by-cycle cross-agent variation and supports per-call sampling variability as the primary microscopic seed of SH.

  • Interpretation: The analysis contrasts stable individual driving styles with independent sampling noise as competing explanations for target_delta variance.These interpretations make different predictions about whether agent-specific tendencies should persist across runs.
  • Method: Per-agent variability is the inter-car standard deviation of each vehicle’s run-average target_delta, whereas per-call variability averages cross-car standard deviations at each cycle.Both metrics use raw target_delta values without post-processing.
  • Results: Across seven runs, per-agent standard deviation ranges from 0.004 to 0.30 m/s, while per-call standard deviation ranges from 0.004 to 0.80 m/s.The per-call/per-agent ratio spans 1.0–4.8× and is usually 1.9–4.8×.
  • Results: 0 of 22 cars preserve the sign of their average target_delta across five independent unperturbed seeds.This indicates that apparent per-agent acceleration or braking preferences are not reproducible across runs.
  • Interpretation: The combined decomposition supports an emergent interpretation in which per-call sampling is the microscopic seed and state-dependent coupling amplifies it into per-agent variation.The per-agent component varies from seed to seed rather than reflecting a fixed intrinsic preference.
  • Wave analysis: Wave-speed analysis uses cross-correlation between spatially separated velocity traces, with d = 3 selected to avoid local-noise and spatial-aliasing problems.The method compares LLM trajectories with digitized Sugiyama 2008 data.
  • Wave analysis: The pooled wave speed is c = 5.21 m/s, with per-seed values from 5.20 to 5.28 m/s across three seeds.The corresponding period is T = 44.2 s, and the per-seed spread is 0.04 m/s.
  • Wave analysis: The canonical cross-correlation period is T = 44.2 s, while an ACF robustness analysis gives 49.5 ± 2.5 s and per-vehicle periods near 22.0 ± 2.1 s.These measures differ because cross-correlation estimates spatial propagation time whereas ACF measures temporal decorrelation.

S10. Connection to the original Sugiyama 2008 paradigm

The LLM ring-road experiment matches the Sugiyama setup and reproduces its kinematic wave mechanics, while reporting additional LLM-side measurements with explicit comparison limits.

  • Setup: The experiment matches the Sugiyama configuration with 22 vehicles on a 230 m ring, 4.5 m vehicle length, density 95.7 veh/km, and an approximately 30 km/h target.The measured observables include fleet velocity, velocity variation, wave speed, wave period, and congestion fractions.
  • Macroscopic reproduction: The comparison table reports exact agreement in vehicle count, track length, density, and target speed between the human and LLM settings.These matched conditions provide the basis for comparing wave mechanics.
  • Macroscopic reproduction: 18.7 km/h is the pooled LLM kinematic wave speed, within the Sugiyama human-driver range of 17–20 km/h.Per-seed LLM values span 18.7–19.0 km/h.
  • Macroscopic reproduction: 44.2 s is the pooled LLM wave period, within the Sugiyama range of approximately 45–55 s.Per-seed LLM periods range from 43.6 to 44.2 s.
  • Macroscopic reproduction: The LLM fleet mean is approximately 19.6 km/h, but Sugiyama does not directly report a comparable fleet-level mean.The manuscript therefore treats this as an LLM-side measurement rather than a quantitative human comparison.
  • Macroscopic reproduction: The per-vehicle congested fraction is approximately 89–90%, while fleet-level congestion is reported separately using a mean-speed threshold.The two congestion metrics are not interchangeable, and the table flags differing definitions and limited direct comparison.
  • Macroscopic reproduction: Per-vehicle oscillation periods are about half the fleet-mean period, indicating two coexisting wavefronts in the LLM ring.This relationship is reported as a 2:1 ratio to the fleet-mean period of 44.2 s.
  • Data availability: The verification scripts and analysis code for the Sugiyama comparison and wave measurements are released with the simulation code.The released materials include verify_sugiyama_comparison.py, verify_wave_speed3.py, and analyze_deep.py.

S10b. Cross-paper validation summary: LLM platform vs Tadaki 2013/2016, Nakayama 2009/2016

The LLM platform qualitatively reproduces key macroscopic observables reported in the Sugiyama-group traffic literature, with quantitative agreement generally within 14% where configurations are directly comparable.

  • Macroscopic observables: 5 vehicles is the reported Sugiyama 2008 jam cluster size used for comparison with the LLM platform.The cross-paper table lists this observable as directly comparable.
  • Macroscopic observables: ~8 m/s is the reported Tadaki 2013 free-flow velocity used as the experimental comparison value.The LLM free-flow speed is drawn from mostly IDM n = 10, p ≈ 0.10 runs corresponding to the free-flow regime.
  • Phase boundary: No transition occurs in the pure-LLM n = 10 run at ρ = 43.5 veh/km, while p_c(ρ) decreases with increasing density.The comparison is consistent with Tadaki 2013’s reported critical-density range, though ρ_c was not directly measured in the LLM runs.
  • Qualitative structure: The LLM trajectories qualitatively match the reported three-stage jam formation and free-flow unimodal versus jammed bimodal velocity structure.Additional qualitative matches include jam-internal minimum headway and its observation in the exp6_full trajectory.
  • Cross-paper validation: Within 14%, the LLM platform matches reported Sugiyama-group observables across systems of 22–40 vehicles and 230–314 m tracks.The closest matches concern jam cluster size, free-flow velocity, jam-internal minimum headway, and jam backward velocity.

S11.2 Statistical test.

The chain-of-thought decision category is strongly reflected in target-speed actuation, but variability within ADJUST_SPEED remains the main source of per-cycle divergence relevant to SH.

  • Statistical test: KS statistic = 0.9820 and Cohen’s d = 2.37 show that ADJUST_SPEED and KEEP_STEADY have strongly separated |target_speed_delta| distributions.The KS test uses N = 20,935 ADJUST_SPEED and N = 17,553 KEEP_STEADY decisions from 39,600 total decisions.
  • Within-category variance: The ADJUST_SPEED distribution is broad and stable across seeds, while KEEP_STEADY remains essentially deterministic zero.The seed-to-seed spread of the ADJUST_SPEED |Δ| mean is 1.6%.
  • Category–actuation coupling: 100% of KEEP_STEADY decisions produce zero target_delta, whereas 98.2% of ADJUST_SPEED decisions produce non-zero target_delta.The decision category therefore predicts whether speed actuation occurs, rather than being decoupled from actuation.
  • Within-category variance: 1.21 m/s is the ADJUST_SPEED standard deviation of target_speed_delta, comparable to its 1.20 m/s mean absolute magnitude.The 31% negative sub-population is identified as the source of per-cycle target-delta divergence driving the SH cascade.
  • Interpretation: The cognitive category and actuation category align, but actuation magnitude—and partly sign within ADJUST_SPEED—remains a per-call sampling draw.This distinction separates informative cognitive observability from dynamics-layer stability.

S12.1 The one excluded but related work.

CoMAL is the closest related work, but it differs from this study in research goal, mechanism testing, cognitive observability, and density-dependent phase-boundary analysis.

  • Research goal and control hierarchy: CoMAL uses an LLM to set IDM parameters for flow optimisation, whereas this work uses LLM agents as direct target-speed controllers to identify SH.In CoMAL, IDM executes longitudinal control at each 0.1 s physics timestep after less frequent LLM updates.
  • Mechanism analysis: CoMAL does not report a density-dependent phase transition, measure p_c, or provide matched control experiments.The present work instead maps a density-dependent phase boundary and uses six controls spanning stochasticity, population variance, and dynamical instability.
  • Cognitive observability: The present work treats chain-of-thought as a per-cycle observability layer, while CoMAL does not analyse LLM reasoning in that role.The study reports a 13,200-decision CoT analysis for multi-vehicle traffic simulation.
  • Phase boundary: The present work measures p_c at four densities from 43.5–95.7 veh/km and identifies a monotonically decreasing boundary.This density-dependent phase-boundary analysis is absent from CoMAL.
  • Novelty scope: The narrow novelty claim remains supported as a first systematic study of collective instability from direct real-time LLM target-speed control in a multi-agent ring-road simulation.The scope is explicitly limited to this configuration and mechanism-focused comparison.
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