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

Yujun Qi; Yangyang Guan

physics.soc-phAug 29, 2026

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

Authors: Yujun Qi, Yangyang Guan

Organizations: College of Civil Engineering, Nanjing Tech University, Nanjing, China

Abstract

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).

Figures & tables

Work	Year	LLM role	Setup	New collective mechanism
Villarreal et al. [12]	2023	K (RL designer)	RR (RL benchmark)	No
Fu et al. [13]	2023	D	HW (HighwayEnv)	No
LLMLight [14]	2023	S	UR intersections	No
GenFollower [15]	2024	P	HW (Waymo, open-loop)	No
xTP-LLM [16]	2024	T	UR	No
DriveGen [17]	2025	G	UR scenarios	No

Table 1

Axis	Control	Modified component	Hypothesis
Stochasticity	1: White noise	Add N(0, 0.9) m/s2 acceleration noise	Random perturbations?
	2: OU noise	Ornstein-Uhlenbeck (θ = 2.0, σ = 0.9)	Coloured perturbations?
	6: Temperature ablation	LLM T ∈ {0.1, 0.3, 0.6, 0.9}	Sampling stochasticity?
Population variance	3: Heterogeneity	Per-vehicle IDM parameter draws (T~~U[0.3,0.7], s0~~U[0.5,1.5])	Parameter spread?
Dynamical instability	4: Time delay	τ = 0.5 s input delay, T = 0.43 s, s0 = 0.95 m	String instability?
	5: OV model	Replace IDM with Optimal-Velocity (V0=8.33, d_c=4.5, α∈{0.2,0.5})	OV instability?

Table 2

car_id	gap (m)	Δv (m/s)	CoT conclusion (translated from Chinese)	target_delta (m/s)
1	5.47	0.06	“Slightly reduce speed to match the leader’s speed and maintain a comfortable gap”	−0.1
2	5.21	0.43	“Slightly reduce speed to match the leader’s speed and maintain a comfortable gap”	−0.1
3	5.01	0.30	“Increase speed slightly to reach the target speed while maintaining a safe gap”	+0.5

Table 3

Axis	Mechanism	v_std (m/s)	Ratio to LLM	Status
SH	LLM (T = 0.6, p = 1.0)	2.12	1.00×	-
Stoch.	White noise (σ = 0.9)	0.157	0.074×	Ruled out
Stoch.	OU noise (θ = 2.0)	0.366	0.174×	Ruled out
Pop. var.	Parameter heterogeneity	<0.001	0×	Ruled out
Dyn. inst.	IDM + 0.5 s delay	<0.001	0×	Ruled out
Dyn. inst.	OV model (α = 0.5, worst)	≤ 0.035	0.017×	Ruled out

Table 4

ρ (veh/km)	n	p_c (approx)	n_LLM at transition	Physical regime
43.5	10	>1.0 (no transition)	-	Free flow at all p
60.9	14	≈ 0.79	11	Sharp single-step drop
78.3	18	≈ 0.50	9	Mid-density transition
95.7	22	≈ 0.23	5	Dense urban flow

Table 5

Observable	Sugiyama 2008	LLM (n=22, ρ=95.7)
c_back (km/h)	≈20 [1]	18.7-19.0 (≈5% lower)
T_wave (s)	≈45-55 [24]	43.6-44.2
σ_v (m/s)	≈1-3 [24-26]	1.96-2.03

Table 6

Column	Type	Example	Meaning
time	float	0.0	Time of decision (s)
car_id	int	0	Vehicle index (0…21)
speed	float	7.0000	Current speed (m/s)
gap	float	5.9519	Gap to leader (m)
leader_speed	float	8.3258	Leader’s current speed (m/s)
relative_speed	float	-1.3258	speed − leader_speed (m/s)

Table 12

Metric	seed 42	seed 123	seed 456
KEEP_STEADY	5,833 (44.2%)	5,616 (42.5%)	6,104 (46.2%)
ADJUST_SPEED	6,978 (52.9%)	7,181 (54.4%)	6,719 (50.9%)
ADJUST_GAP	373 (2.8%)	384 (2.9%)	355 (2.7%)
other	16 (0.1%)	19 (0.1%)	22 (0.2%)
v_desired, mean ± σ (m/s)	5.77 ± 2.01	5.74 ± 1.96	5.83 ± 2.07

Table 13

p	n = 22 (reference)	n = 44 (3 seeds)
0.18	3/10 congested (10 seeds)	3/3 free-flow (v̄ > 7.88)
0.23	6/11 congested (11 runs)	3/3 free-flow (v̄ > 7.88); v_std ∈ {0.40, 0.70, 0.92}
0.27	10/10 congested (10 seeds), v_std = 1.79 m/s	0/3 congested; 1/3 in v̄ gap, 2/3 free-flow; v_std ∈ {0.75, 0.84, 1.12}

Table 14

Condition	v_mean (m/s)	v_std_late (m/s)	v_std_early (m/s)
Perturbed (Car 0 = 7.0 m/s)	5.42	1.98	2.33
Unperturbed (all = 8.33 m/s)	5.75	1.99	2.20

Table 15

σ (m/s2)	v_mean (m/s)	v_std (m/s, mean ± std over 3 seeds)	σ value / LLM v_std (2.12 m/s)
0.3	7.808	0.0522 ± 0.0011	0.0246×
0.6	7.803	0.1044 ± 0.0022	0.0493×
0.9	7.794	0.1569 ± 0.0033	0.0740×
1.2	7.781	0.2096 ± 0.0045	0.0989×
1.5	7.764	0.2628 ± 0.0058	0.124×

Table 16

Run	Phase	Time window	Per-agent std (m/s)	Per-call std (m/s)	Ratio (per-call / per-agent)
v6_220149 (unperturbed)	free flow	0–16 s	0.011	0.011	1.0×
v6_234125 (unperturbed)	free flow	0–4 s	0.299	0.801	2.7×
v6_235655 (unperturbed)	free flow	0–2 s	0.004	0.004	1.0×
v6_105739 (unperturbed)	free flow	0–22 s	0.128	0.608	4.8×
v6_130834 (unperturbed)	free flow	0–11 s	0.013	0.025	1.9×
v81_080653 (congested)	congested	0–8 s	0.041	0.151	3.6×

Table 17

Statistic	Value
Cars with consistent bias sign across 5 seeds	0 / 22
Cars with bias sign flipping ≥1 time across 5 seeds	22 / 22 (100%)
Mean per-car	mean target_delta
Max per-car	mean target_delta

Table 18

Run	d=3 c_road (m/s)	c (km/h)	T (s)
s42	5.28	19.0	43.6
s123	5.21	18.7	44.2
s456	5.20	18.7	44.2
Pooled (3 seeds)	5.21	18.7	44.2
Sugiyama 2008 [1]		17-20	45-55

Table 19

Observable	Sugiyama 2008 (humans)	LLM (this work)	Agreement
n	22	22	exact
Track length L (m)	230	230	exact
Density ρ (veh/km)	95.7	95.7	exact
Target speed (km/h)	≈ 30	≈ 30 (prompt)	exact
Kinematic wave speed / jam backward vel. c (km/h)	17-20 (jam backward velocity)	18.7-19.0 (per-seed), 18.7 (pooled median)	LLM range within Sugiyama
Wave period T (s)	≈ 45-55	43.6-44.2 (per-seed), 44.2 (pooled median)	LLM range within Sugiyama

Table 20

Observable	Source (experiment)	LLM (this work)	Deviation
Jam cluster size	Sugiyama 2008 [1]: 5 vehicles	5 vehicles (qualitative, n=22)	exact
Jam backward velocity c_back	Sugiyama 2008 [1]: ~20 km/h	18.7-19.0 km/h (per-seed, §4.4)	in range
Free-flow velocity (v̄)	Tadaki 2013 [24]: ~8 m/s	8.21-8.33 m/s (n=10, p≈0.10, exp2)	<3%
Critical density (ρ_c)	Tadaki 2013 [24]: 0.08-0.09 m⁻¹	ρ_c not directly measured in LLM runs; the n=10 (ρ=43.5 veh/km) pure-LLM run shows no transition (free flow), and the p_c(ρ) trend from §4.3 is consistent with Tadaki 2013’s ρ_c ≈ 0.08–0.09 m⁻¹ in the sense that LLM transitions emerge at comparable densities but at sub-unity LLM penetration	qualitative match
Free-flow unimodal / jammed bimodal	Tadaki 2016 [25]: qualitative	σ_v=0.07 free-flow, 2.12 m/s jammed (n=22)	qualitative match
Three-stage jam formation	Nakayama 2009 [23]: early→meta→jammed	observed in exp6_full trajectory	qualitative match

Table 21

Primary decision	N (39,600)	\|target_speed_delta\| mean (m/s)	target_speed_delta std (m/s)	% with \|Δ\| < 0.05 m/s
KEEP_STEADY	17,553 (44.3%)	0.0000	0.0008	100.0%
ADJUST_SPEED	20,935 (52.9%)	1.1958	1.2129	1.8%
ADJUST_GAP	1,112 (2.8%)	0.0069	0.0861	99.1%

Table 22

Primary decision	% target_speed_delta > 0	% target_speed_delta = 0	% target_speed_delta < 0
KEEP_STEADY	0.0%	100.0%	0.0%
ADJUST_SPEED	67.2%	1.8%	31.0%
ADJUST_GAP	0.0%	99.1%	0.9%

Table 23

Seed	KEEP_STEADY (N)	KEEP_STEADY \|Δ\| std (m/s)	ADJUST_SPEED (N)	ADJUST_SPEED \|Δ\| mean (m/s)	ADJUST_SPEED \|Δ\| std (m/s)
42	5,833	0.0013	6,994	1.2041	1.2116
123	5,616	0.0000	7,200	1.1971	1.2173
456	6,104	0.0000	6,741	1.1858	1.2094

Table 24

Work	Year	LLM role	Setting	Why excluded from novelty claim
Yao et al. [27] (CoMAL)	2024	D (planner for IDM parameters)	Ring road, figure-eight, merge	Architecture overlap, but different research goal and different control hierarchy : CoMAL uses LLM as a “planner” to set IDM parameters (target speed, max acceleration, minimum gap) for flow optimisation on the Flow benchmark, not to identify a novel mechanism. In CoMAL the LLM is queried at intervals τ_LLM (≥ 1 s in their reported experiments) to update IDM parameters, and the IDM dynamics execute the actual longitudinal control at each 0.1 s physics timestep; the LLM’s per-cycle output is therefore low-pass filtered by the IDM before reaching the vehicle. By contrast, in the present work the LLM is queried every 0.5 s and directly outputs a target_speed_delta that is applied (after a hard collision-avoidance clamp) to the vehicle’s target speed; the vehicle’s actual acceleration is not low-pass filtered by an intermediate controller. This direct-variance pathway is the microscopic mechanism that enables the SH cascade to develop (§2.2). No systematic control experiments, no per-cycle target-delta variance analysis, no chain-of-thought-as-microscope treatment, no phase-boundary mapping. The CoMAL Execution Module uses IDM with LLM-set parameters; the present work uses LLM as a target-speed controller with IDM only as a hard safety clamp (§3.1).

Table 25

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Population Physics, Population Problems: Safety and Emergence in LLM Societies

Adrian de Wynter

Microsoft & The University of York

Multi-Agent LLM Systems Large Language Model-Based Social Simulation LLM Agent Safety Emergent Behavior in Multi-Agent Systems

Open paper AskPDF arXiv

The collective behaviour of large language model (LLM) societies is not the sum of their individual outputs. It yields statistically distinct, sometimes-unpredictable phenomena, for which the tools we use to study single agents may not scale. Due to recent incidents involving autonomous agentic systems, however, understanding these systems is paramount. For that we introduce a framework for measuring self-organisation in LLM social systems and apply it to three such systems: a Schelling grid, a social network (Moltbook), and a Twitter-like misinformation simulation ('Rogue'). All three exhibit statistically significant self-organisation. Moreover, their relaxation dynamics vary with the environmental information available to the agents, with open-ended systems (Moltbook, Rogue) exhibiting sharp, phase-transition-like dynamics. Further results show that population-level pathologies can emerge even when the LLMs are safety-tuned or monitored, being primarily driven by the coordinated activity of a population subset. We also show when self-organisation does not emerge under two additional scenarios (a commons dilemma, GovSim, and a LLM-as-a-judge deliberation scheme, ChatEval). We argue that measuring signatures of this kind offers a lightweight, agent-agnostic diagnostic layer for detecting coordinated collective behaviour in deployed multi-agent systems without relying on natural language or model versioning.

Abstract

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