Applied mathematics and modelling · Maths EE idea · Ambitious

Why traffic jams travel backwards

A research question to start from

How does a continuum model of traffic flow explain jams that move backwards along a road, and how fast do they travel?

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Why it works as a maths EE

A partial differential equation explained with characteristics at an accessible level.

Mathematics you would need

Density–flow relationships
Conservation laws
Characteristics
Shock speed

Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.

One possible line of attack

Build the flow–density model.
Derive wave speeds and show they can be negative.
Compute shock speeds for a jam forming.

Scope and difficulty

Ambitious. Ambitious; restrict to a simple density–flow function.

Pitfalls

Too much PDE theory.
No worked example.

Where to start reading

Search a library catalogue or a university's open lecture notes for: Lighthill Whitham traffic model characteristics shock speed. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).

Make it your EE

Plan this EEOpens the free EE planner with this question as a starting point. Sharpen the questionSix quick checks for a focused research question. Self-check a draftCheck a section against each criterion, free.