🚦 Simulations
Ant Colony Optimisation (ACO)
Route optimisation through pheromone trails. The same principle is
used in traffic optimisation and logistics networks.
Intermediate
Navigation Algorithms
A*, Dijkstra and BFS — the foundation of GPS navigators and urban
transit routing systems.
Intermediate
Route Optimisation (TSP)
The travelling salesman problem — minimising the length of a route.
Applied in delivery logistics and flight scheduling.
Advanced
Interaction Networks
Self-organising transport networks and their topology. Analysis of
hubs, resilience and bottlenecks.
Advanced
NaSch Traffic Model
The Nagel–Schreckenberg cellular automaton for highways. Phantom
jams — traffic jams that appear without any obvious cause.
Intermediate
Pedestrian Flow
The Social Force Model — pedestrian interaction modelled as social
and physical forces. Simulating evacuation and crowd crushes.
Intermediate
City Growth
A cellular automaton of zoning and density. How compact cities and
suburbs affect the transport load.
Intermediate
Bus Bunching
Bus bunching — buses pull together into groups through positive
feedback. The optimal headway and schedule.
Intermediate
Traffic Intersection
Signal timing and queue theory at a 4-way intersection. Webster
formula, Poisson arrivals and level-of-service grades.
Intermediate
📐 Key Concepts
Nagel–Schreckenberg Model
A cellular automaton for traffic: acceleration, braking, random
slowdown and position update. Above ρ > ρc,
self-organising jam waves appear.
Social Force Model
A pedestrian moves under a goal force Fgoal and repulsive
forces from walls and other pedestrians. It explains lane formation
and the "faster is slower" effect.
Fundamental Diagram of Traffic
Flow q = ρ·v — the relationship between density ρ and speed v. At
the critical density ρc the flow is maximal; above it
comes congestion and an abrupt drop in speed.
Braess's Paradox
Adding a new road to a transport network can worsen the average
travel time for everyone. It is related to the Nash equilibrium in
transport games.
Hub Network Topology
Airline and rail networks have a scale-free topology: a few hubs
(nodes) connected to thousands of peripheral nodes. Efficient, but
vulnerable to targeted attacks on the hubs.
Ant Colony Optimisation (ACO)
Route optimisation through pheromone reinforcement: τij(t+1)
= (1−ρ)τij(t) + Δτij. Convergence to a
near-optimal solution without exhaustive search.
📖 Learning Resources
🔗 Related Categories
🚦 Transport simulations have an enormous practical
impact: accurate traffic modelling can cut congestion by 10–30% without
building any new roads. The phantom jam — a traffic jam that appears
"out of nowhere" — is a real phenomenon, demonstrated by Japanese
physicists on a ring road back in 2008.
Key Concepts
Topics and algorithms you'll explore in this category
Interactive ModelReal-time browser simulation with live parameter controls
WebGL / Canvas 2DHardware-accelerated rendering in the browser
Mathematical FoundationDifferential equations and numerical integration
Open SourceMIT-licensed code — inspect, fork, and learn
No Install RequiredRuns directly in Chrome, Firefox, Safari, Edge
Educational FocusBuilt to explain the underlying science clearly
Frequently Asked Questions
Common questions about this simulation category
- Do these simulations require installation?
- No. Every simulation runs entirely in your web browser using WebGL and Canvas 2D. Nothing to install or download — open the page and the simulation starts immediately.
- Can I use these simulations for teaching?
- Yes — all simulations are designed to be educational and run without an account or login. They are widely used in university lectures, high-school science classes, and self-directed learning. Embed them via iframe or link directly.
- What devices do the simulations support?
- All simulations work on desktop browsers (Chrome, Firefox, Edge, Safari). Many work on mobile and tablets too, though some physics-heavy simulations benefit from the GPU performance of a desktop or laptop.