Car-Following Model: Traffic Shockwaves (Time-Space Diagram)

Rather than solving one macroscopic density equation, this simulation gives every vehicle its own equation of motion: the Intelligent Driver Model, a car-following ODE that reacts only to the gap and closing speed to the car directly ahead. A lane-closure bottleneck lowers each driver's own desired speed inside its zone, and pushing upstream demand past what that zone can sustain makes cars queue up behind it — a shockwave that emerges purely from local, per-vehicle rules, with no notion of "density" built in anywhere. Watch it appear live on a scrolling time-space (trajectory) diagram, the same x-position-vs-time plot traffic engineers use to read shockwaves off real detector data, with measured throughput, queue length and Rankine-Hugoniot shock speed updating in real time.