Cars drive around a circular track using the Intelligent Driver Model (IDM) of Martin Treiber and co-authors. Even without obstacles, small perturbations grow into stop-and-go waves — the classic Sugiyama experiment.
Enable the Driver noise slider to add stochastic acceleration error and compare three stochastic car-following models: white noise (B-IDM), a Gaussian-process kernel from Zhang & Sun (2024), MA-IDM, and an autoregressive process from Zhang, Wang & Sun (2024), dynamic-regression IDM.
The line is the measuring arc's time trajectory, so its loops are real loading/unloading cycles. The faint dots are four spatial sub-bins sampled at the same instants — a cross-section, deliberately left unconnected.
traffic-sim is a free, open-source simulator that runs the Intelligent Driver Model on a one-lane circular road entirely in your browser. You set the traffic density, the IDM parameters and the driver-noise model, then watch whether the ring settles into uniform flow or breaks into stop-and-go waves. There is nothing to install, and no data leaves your machine.
Because dense car-following is unstable. Each driver reacts to the car ahead with a delay and with imperfect precision, so a small speed fluctuation is amplified rather than damped as it travels back through the queue. Past a critical density the amplification wins and the disturbance grows into a stopped cluster that moves backwards against the traffic — a phantom jam. Sugiyama and colleagues demonstrated exactly this with real drivers on a real circular track in 2008. Press Perturb to seed one here.
The IDM is a microscopic car-following model published by Treiber, Hennecke and Helbing in 2000. It gives every vehicle a continuous acceleration derived from only its own speed, the gap to the vehicle ahead and the rate of approach, using five interpretable parameters: desired speed v₀, safe time headway T, minimum gap s₀, maximum acceleration a and comfortable braking b. It is collision-free by construction and is the standard deterministic baseline in traffic-flow research. The models page gives the equations.
Driver noise is the acceleration residual that is left over after a deterministic model has been fitted to a real trajectory — everything the equation does not explain. Measured on HighD data that residual has a standard deviation of roughly 0.2 m/s² and stays correlated for several seconds, so it is not white noise. The colour matters because a car-following chain behaves like a low-pass amplifier: white noise is mostly high-frequency jitter that averages out along the platoon, whereas correlated noise puts the same variance into the low frequencies the chain amplifies into jams.
All three add a random residual to the same IDM acceleration and differ only in the process that generates it. B-IDM uses independent Gaussian noise with no memory. DR-IDM uses an AR(p) process, so the residual is a weighted sum of its own recent past plus a fresh innovation. MA-IDM uses a Gaussian process with a stationary kernel, so memory is governed smoothly by a lengthscale of about 1.4 s rather than by a fixed number of lags. The compare page runs all three side-by-side on identical rings.
Yes. The Copy link button writes every control into the URL fragment, so the link reopens the simulator with the same scenario. Add seed=<integer> (non-zero) to that URL and the random-number stream is seeded as well, which makes the run reproducible bit for bit.
No, and it is not meant to. It is a research-inspired teaching demo. Every driver here shares one parameter vector, whereas both papers’ ring experiments draw heterogeneous per-driver parameters from a joint posterior that was never published. Integration is semi-implicit Euler rather than the papers’ ballistic update, the Gaussian process is approximated with 32 random Fourier features instead of conditional Gaussian sampling, and flow is computed as density × space-mean speed rather than from detector crossings. The README lists every deviation.
Any modern browser with JavaScript and HTML5 canvas. There is no build step, no framework and no dependency — the simulator is a handful of plain JavaScript files. You can also clone the repository and open index.html straight from disk, or serve the folder with python -m http.server.
Cite the two underlying papers — the BibTeX is in the Citation card above, and CITATION.cff in the repository carries the same metadata in machine-readable form: Zhang & Sun (2024), Bayesian Calibration of the Intelligent Driver Model, IEEE T-ITS, doi:10.1109/TITS.2024.3354102; and Zhang, Wang & Sun (2024), Calibrating Car-Following Models via Bayesian Dynamic Regression, Transportation Research Part C, doi:10.1016/j.trc.2024.104719.
If this simulator is useful in your work, please cite the underlying papers:
@article{zhang2024maidm,
title = {Bayesian Calibration of the Intelligent Driver Model},
author = {Zhang, Chengyuan and Sun, Lijun},
journal = {IEEE Transactions on Intelligent Transportation Systems},
year = {2024},
doi = {10.1109/TITS.2024.3354102}
}
@article{zhang2024dynamicidm,
title = {Calibrating Car-Following Models via Bayesian Dynamic Regression},
author = {Zhang, Chengyuan and Wang, Wenshuo and Sun, Lijun},
journal = {Transportation Research Part C: Emerging Technologies},
year = {2024},
pages = {104719},
doi = {10.1016/j.trc.2024.104719}
}