Twelve weeks, twelve claims, and the four pieces of arithmetic that hold them together.
Lectures run for an hour a week, on Mondays. Each week makes a single claim, and that claim is the line printed underneath the title, so you should be able to disagree with it before you have heard a word of the lecture itself. That is rather the point of putting it there.
The order is not a survey and it does not reshuffle, so it is worth knowing roughly where you are going. Weeks 2 to 4 give you the arithmetic, and you will genuinely need all three of them before week 5 means very much at all. From there the question turns to who that arithmetic gets done to, which takes up weeks 5 to 7, and then to what follows from having done it, which is weeks 8 to 11. Week 12 is really the week 1 argument all over again, except that by then you have everything else attached to it.
Week 2 is the only one that carries a deck, mostly because Little’s Law is easier to show than to describe. The rest are taught on a board.
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The line starts here
First-come-first-served is not the natural state of a queue. It is a policy somebody chose.
Week 1 · 22 February 2027
Little's Law
You can work out how long people are waiting without timing a single one of them.
Week 2 · 1 March 2027
Variability is the tax
A counter running at ninety-five percent of capacity is not a well-run counter. It is one bad morning from collapse.
Week 3 · 8 March 2027
One line or many
The banks changed to a single serpentine line and the supermarkets never did. Both were right.
Week 4 · 15 March 2027
Priority, and who pays for it
Every queue jump is paid for by somebody standing further back who was never told.
Week 5 · 22 March 2027
Triage
Emergency medicine solved the ethics of priority in public and wrote the answer down. It is worth reading.
Week 6 · 29 March 2027
The queues with no visible front
A visible line is a courtesy. The queues that decide the most about a life publish nothing.
Week 7 · 19 April 2027
The felt wait
An unexplained two minutes is longer than an explained five. That is not a failure of the customer.
Week 8 · 26 April 2027
Machines that wait
Your laptop is running a dozen queues right now and its scheduler faces exactly the problem the passport office does.
Week 9 · 3 May 2027
When the queue is the hazard
A crowd crush is a queueing failure, and the arithmetic that predicts it is the arithmetic from week 3.
Week 10 · 10 May 2027
Abolishing the queue
Appointments, lotteries and auctions do not remove waiting. They change who does it and what it costs them.
Week 11 · 17 May 2027
What you can see now
A last hour on what changes once you cannot stand in a line without reading it.
Week 12 · 24 May 2027
The four results#
There are four pieces of maths in this course, and this is genuinely all of them. If that sounds like too few, that is the argument the course is making.
- Little’s Law, week 2. Queue length equals arrival rate times waiting time. It lets you measure a wait you never timed.
- Kingman’s approximation, week 3. Waiting explodes as utilisation approaches one, and variability sets the multiplier.
- Pooling, week 4. One line into many servers beats many lines into one server each, at the same total capacity.
- Ageing, week 9. Raise a job’s priority the longer it has waited, and starvation goes away without losing the benefit of serving short jobs first.
If you happen to have met all four of these before, this is still not a course you have already taken, because not one of the four will answer the question we put to you in week 6.