Traffic flow · TASEP simulation

Why does a road jam — and is there a best density at which it carries the most cars?

▶ Run the simulationSee the measured result

Units: cars per bond per sweep — the maximal TASEP steady-state current J_max = ¼ at half filling (L → ∞); secondary knowns: J(ρ) = ρ(1−ρ), finite-ring J_L = ρ(1−ρ)·L/(L−1), rival zero-range current ρ/(1+ρ)

How the lab tests it

Run the totally asymmetric exclusion process (TASEP) on nine rings of L=200 sites at densities ρ=0.1…0.9: each car hops one step forward only if the site ahead is empty (hard-core exclusion). Measure each ring's steady current J = hops/attempts under random-sequential updates and overlay the nine points on the exact fundamental diagram.

What it checks

the closed-form current J(ρ) = ρ(1−ρ) — a downward parabola peaking at J = ¼ at ρ = ½ (flow is MAXIMAL at half-occupancy; packing in more cars past that point lowers throughput) and obeying particle–hole symmetry J(ρ) = J(1−ρ) (a 90%-jammed road carries the same flow as a 10%-empty one). TASEP's current fluctuations are themselves in the KPZ class