Optimisation and game theory · Maths EE idea · Solid

How long is the queue?

A research question to start from

How do the average queue length and waiting time in a single-server queue depend on how busy the server is?

A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.

Why it works as a maths EE

A probability model with exact formulas and a striking blow-up as the server becomes fully busy.

Mathematics you would need

Poisson processes
Exponential distributions
Steady-state balance equations
Geometric distributions

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

Set up the balance equations.
Derive the steady-state distribution and averages.
Test with timed observations or a simulation and discuss assumptions.

Scope and difficulty

Solid. Solid.

Pitfalls

Observation project with thin theory.
Formulas without derivation.

Where to start reading

Search a library catalogue or a university's open lecture notes for: M/M/1 queue balance equations derivation; Little's law. 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.