Week 7: What can the system honestly promise?

Moving from choosing an ordering rule to deciding what a queue can truthfully tell someone about how long they will wait.

5 April 2027

The first six weeks measured a queue and chose how it orders people. This lecture starts the course’s third movement: once a system has a policy, what is it allowed to say to the person currently waiting inside it?

Outline#

• a wait-time estimate is a claim about the future; the Office’s counter knows how many tickets are currently waiting, which policy is in effect, and whether the case in progress is already overrunning — and nothing about arrivals still to come. The honesty question is about what to do with that specific gap, not how to eliminate it
• the Office’s existing display (“estimated wait: 5 minutes”, fixed, unchanging) as an example of a number that is easy to produce and almost never true
• what an honest estimate would need to account for: the policy now in use (from weeks 4–6), the current queue length, and whether an outlier (week 3) is currently being served
• a range or a confidence statement versus a single number: this course does not require you to build a working estimator, only to reason about what information any honest one would need
• what happens to trust in a system that is confidently wrong versus one that is honestly uncertain

Office of Everything file — synthetic case material. The counter’s “estimated wait: 5 minutes” sign has not been updated since it was installed. It reads 5 minutes during a two-person queue and during a forty-person queue alike.

This week’s Queue Lab asks you to design what the sign should say instead — not a working system, a specific, honest form of words the Office could post given only the information it actually has.