Applied maths and modelling · Solid · Dissertation or artefact

Timing traffic lights: a maths EPQ idea

Why it works as an EPQ

A real optimisation with competing aims (cars, pedestrians, fairness) that you can model, simulate and evaluate.

Scope and difficulty

Solid. Solid. One junction, two or three phases. Observe from a safe public place.

The maths

Builds on these A Level topics: Algebra and functions · Probability · Differentiation.

You would learn:

• Simple queue growth models
• Optimisation with constraints
• Simulation

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

1. Count arrivals for each approach at different times of day.
2. Model queue length through a cycle and the delay per vehicle.
3. Find the split of green time that minimises total delay, analytically or by simulation.
4. Compare with the current timings and discuss pedestrians and fairness.

Pitfalls

• Safety: never stand in the road.
• Ignoring the minimum green time and pedestrian phases.

Where to start reading

• Search for: Webster's formula optimal cycle length
• Search for: traffic signal timing queue model

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

Making something? Read the artefact guide first: an artefact still needs a research-based written report.

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