A ring of deterministic Nagel-Schreckenberg traffic (

PHYSICS · Multi-part · Fermi University Physics · Computational Physics · Thermal, Statistical & Complex Systems · Monte Carlo and lattice simulation of physical systems

Many Parts, One Behaviour, Ch Emergence and self-organisation: collective order from local rules

Problem

A ring of deterministic Nagel-Schreckenberg traffic (ps=0p_{\rm s}=0, vmax⁡=5v_{\max}=5 cells per step) is held at fixed density ρ=0.30\rho=0.30 car per cell, above the density ρ∗=1/6\rho^*=1/6 at which the flow J(ρ)=min⁡(ρvmax⁡,1−ρ)J(\rho)=\min(\rho v_{\max},1-\rho) peaks. Cells are 7.5 m7.5\,\mathrm{m} long and one step is 1 s1\,\mathrm{s}. ((a)) Find the flow JJ at this density, in vehicles per hour. ((b)) Find the mean speed of a car, vˉ=J/ρ\bar v=J/\rho, in kilometres per hour. ((c)) Find the linear density in vehicles per kilometre.

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