Traffic Jam Paper — Modelling Stop-and-Go Traffic Waves from Scratch

Abstract

Every driver has been there: traffic is moving fine, then it suddenly stops — no accident, no merge, nothing visible ahead. These phantom jams appear out of nowhere and are completely repeatable. In 2008, Sugiyama et al. put 20 cars on a circular track with no obstacles, and within minutes, stable flow spontaneously collapsed into stop-and-go waves that never died out.

The weird part? The standard math used by traffic engineers predicts the opposite — that small disturbances should smooth themselves out over time. They consistently fail to reproduce what actually happens on real roads.

We built a new model to fix that. The core idea is that drivers don't react the same way in every situation. When you're tailgating someone who suddenly brakes, your foot is already moving. On an empty highway with plenty of space ahead, you're relaxed. Classical models ignore this — they assume you always react with the same intensity regardless of how dangerous the gap is. Our model makes that reaction scale with how close and how fast the gap is closing, and adds a realistic human reaction delay on top.

The result is a model that actually produces stop-and-go waves. Our fitted reaction delay came out to ~107ms — physically plausible for human perception-response time. Oscillation amplitude reached 63% of what Sugiyama observed in real life, compared to 52% for the best classical model. Neither the adaptive sensitivity nor the delay alone gets you there — you need both working together.