Applied maths and modelling · Solid · Dissertation or artefact

Modelling a school canteen queue: a maths EPQ idea

Why it works as an EPQ

You collect your own data, build a model, test changes on it and recommend one. That is the full modelling cycle.

Scope and difficulty

Solid. Solid. Use anonymous counts and times only, and get your school's permission first.

The maths

Builds on these A Level topics: Probability · Statistical distributions · Sampling and data.

You would learn:

• Arrival rates and the Poisson model
• Simulation
• Simple queueing measures

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

One possible plan

1. Record arrival times and service times for several lunchtimes.
2. Fit distributions and check the fit.
3. Build a simulation (spreadsheet or code) and check it reproduces what you saw.
4. Test one or two changes, such as a second till, and recommend with caveats.

Pitfalls

• Collecting personal data: record counts and times, never names.
• A model you never check against reality.

Where to start reading

• Search for: introduction to queueing theory M/M/1
• Search for: discrete event simulation spreadsheet

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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Your EPQ must be your own work. These pages coach: ideas, structure, checklists and planning. Submitting text, proofs, code or analysis written by someone else or by an AI tool as your own is malpractice. How to use help and AI honestly.