Traffic Experiment Reveals the Nature of Car-Following

Twenty-five cars lined up on a suburban road outside Hefei, China. Every car carried a high-precision GPS unit logging position and speed ten times per second. The lead driver received a simple instruction: hold a steady speed. Everyone else was told to drive normally. No tricks, no sudden braking, no staged drama. Yet, by the time the ripple of that ordinary driving reached the cars at the back of the line, it had grown, sometimes dramatically. Rear vehicles swung through speed ranges of more than 20 kilometers per hour. Some came to a complete stop. Every standard traffic model said that shouldn't happen. That mismatch between theory and data is exactly what Jiang and colleagues set out to explain. To understand why that mismatch matters, you need some background on what’s at stake in traffic physics. Researchers treat vehicular traffic as a self-driven many-particle system far from equilibrium — the same mathematical territory as phase transitions in physics, spontaneous pattern formation, and metastability. The central debate in the field has been whether congested traffic in steady state lies on a single one-dimensional curve — the so-called fundamental diagram relating speed to spacing — or whether it occupies a two-dimensional region. The traditional view states there's a unique relationship: one speed and one corresponding gap. Kerner's three-phase theory, by contrast, insists that congested traffic fills a two-dimensional region in the flow-density plane, with distinct phases he calls free flow, synchronized flow, and wide moving jams. That debate has dragged on for decades because real road data is a mess — loop detectors, video feeds, floating cars — all contaminated by on-ramps, bottlenecks, varying road geometry, and traffic composition. As Daganzo and colleagues noted, no empirical study had managed to trace the complete evolution of a disturbance from birth to decay. You can't run a controlled experiment on a highway. Until Jiang and colleagues did. The setup was precise. On January 19th, 2013, twenty-five passenger cars drove a 3.2 kilometer stretch of Chuangxin Avenue, a suburban road with no traffic lights and at least three lanes in each direction — clean conditions that removed interference from outside vehicles. GPS units logged each car's position to within one meter and speed to within one kilometer per hour every 0.1 seconds. The lead driver held preset constant speeds — 15 kilometers per hour in some runs, about 7, then 20, up to 50 — while every following driver was simply told to drive naturally. Overtaking was forbidden. To control for individual driving personality, the team ran the experiment twice with the physical order of the twenty-five cars rearranged between runs. This wasn't an observation of real traffic. It was a controlled experiment designed to isolate exactly one thing: how does a disturbance travel down a platoon? What the GPS data showed was both simple and striking. Disturbances grew as they moved rearward. Not sometimes, not at certain speeds — consistently. In one run where the lead car held about 25 kilometers per hour, the second car in line maintained a nearly constant speed while its spacing to the car ahead fluctuated around 15 meters — then, after 174 seconds, jumped to more than 30 meters. In another run at around 41 kilometers per hour, spacing for a single car oscillated between roughly 15 and 40 meters while its speed stayed almost constant. In spatiotemporal plots, the team observed stripe patterns where disturbances propagate, grow, dissipate, and merge. When the lead car drove at 15 kilometers per hour, some rear vehicles stopped entirely. At 7 kilometers per hour, stoppages in the rear were even more frequent. Jiang and colleagues quantified this using the standard deviation of each car's speed — which I'll call s-v — computed across runs at the same lead speed. At low lead speeds, s-v increased almost linearly with car number, meaning each successive car showed proportionally more speed variation than the one ahead of it. As lead speed increased, that curve became concave — still growing toward the rear, but at a decreasing rate. Then they ran simulations with four standard car-following models: the Optimal Velocity model, the Full Velocity Difference model, the Intelligent Driver model, and an inertial model. All four produced s-v curves that grew in a convex fashion — the opposite shape from the data. Not a little off. Qualitatively wrong. And the reason is structural. Traditional car-following models rest on a single assumption: for any given speed, there is one correct spacing that a driver will try to maintain. In the Optimal Velocity model, for instance, the preferred speed is computed as eleven point six times the hyperbolic tangent of a scaled, shifted gap — a fixed, nonlinear map from spacing to speed. One input, one output, no variation. That constraint forces disturbance evolution to follow the model's stability picture, which produces that characteristic convex growth pattern. It's not a parameter problem. It's not something you can fix by tuning a coefficient. The assumption itself is wrong. The empirical evidence against it is direct. When Jiang and colleagues plotted each car's speed against its spacing to the vehicle ahead, the result wasn't a curve. It was a cloud — a two-dimensional scatter. Two cars at identical speeds maintained very different gaps. The traffic state doesn't sit on a line; it fills a region. That's the data. And it's what the traditional framework fundamentally cannot accommodate. So the team built a new class of models. They call them two-dimensional car-following models — two-dimensional variants of the Optimal Velocity, Full Velocity Difference, and Intelligent Driver families. The key change is small but consequential: one or more parameters that used to be fixed are now stochastically time-varying. In the two-dimensional Optimal Velocity and Full Velocity Difference implementations, the optimal velocity function includes a multiplicative factor m, drawn uniformly between 0.8 and 1.2 and refreshed randomly at a rate of 0.15 per second. In the two-dimensional Intelligent Driver variant, the desired time headway T — the gap a driver targets in terms of seconds of following distance — is sampled uniformly between 1.6 and 2.4 seconds and also refreshed at that same rate. In plain terms: the gap a driver is trying to maintain isn't fixed. It drifts. Moment to moment, a driver's target spacing varies within a range. That's what creates the two-dimensional scatter in the velocity-spacing plane. The simulations with these two-dimensional models change disturbance growth from convex to concave, matching the experimental data. The two-dimensional Intelligent Driver model, in particular, produces not just qualitative agreement but close quantitative agreement with the measured s-v versus car-number curves across different lead speeds. Spatiotemporal stripe patterns from those simulations resemble those observed in the GPS data. Jiang and colleagues do acknowledge a limitation: the 3.2 kilometer road is finite, which means the platoon can't always reach a long-duration stationary state, so some model-data comparisons remain approximate. But the core result holds. What this establishes is that the traditional fundamental-diagram assumption — one speed and one spacing — isn't just incomplete. The controlled experiment shows it fails to reproduce how real drivers actually behave. That failure has physical consequences: when the state space collapses to a single curve, the model's stability properties are constrained in a way that produces the wrong disturbance dynamics. When you allow that state space to breathe — when you allow a two-dimensional region — small local fluctuations can amplify downstream rather than decay, which is exactly what the GPS data shows happening in real platoons. The broader picture is a self-driven many-particle system in which spontaneous jam formation is not an anomaly but a natural consequence of how individual drivers actually operate. The two-dimensional framework provides that a precise mechanical explanation. In large-platoon simulations with 600 cars, a lead speed of around 65 kilometers per hour stayed stable, while lead speeds of 7 or 15 kilometers per hour produced frequent jams. The experiment doesn't just challenge a theoretical assumption — it points toward concrete, testable predictions about where and when jams form, and why they're so hard to prevent. This lecture was created by ennepō. Go to https://ennepo.ai to Discover, Create and Follow the latest research in your field. Read when you can. Listen when you want to.