The Measured Queue

Observe one real queue for at least 90 minutes and report its arrival rate, service rate, utilisation and mean wait, with the method behind each figure.

Due: 26 March 2027 · Weight: 25%

The task#

Measure one queue until you can state its arrival rate, service rate, utilisation and mean wait, and say how much confidence each of those four figures deserves.

This is the first of four pieces and it is worth 25 percent. It is also the queue you keep for the rest of the semester: Whose Time It Was may use it, and The Redesign must. Choose one you can physically reach on two separate days.

Suitable sites include a shop till, a service counter, a lift lobby, a coffee cart, a help desk, a ticket barrier and a bus door. Queues you cannot stand next to, such as phone lines and waiting lists, are covered in week 7 and are not suitable here.

Before you collect anything#

1. Register your queue by 17:00 Friday of week 1. You choose it in the week 1 field session on the Wednesday; registering means posting the site, the service and your two planned observation days to Priya, who confirms it or suggests an alternative within two working days. Changing your queue after week 2 means starting the measurement again.
2. Get permission if the site is private property. Anything indoors with staff needs it. Priya has a one-paragraph email you can send; use it in week 1 rather than week 4.
3. Write your definitions down before you collect data. You need a written rule for what counts as an arrival, what counts as the start of service, and what counts as a departure. Fix these before you start and do not change them between sessions.
4. Run a 15-minute pilot. It exists to break your definitions while it still costs you nothing. The pilot does not count towards the 90 minutes.

Your definitions will have to settle at least these cases, and the report has to state the rule you used for each:

What to do#

1. Observe the queue for at least 90 minutes in total, in blocks of no less than 30 minutes, across two different days. Record the clock time at the start and end of every block.
2. Record every event on a timestamped tally sheet. Paper is fine. A spreadsheet is fine. Counting from memory is not.
3. Time at least 30 complete services. If the queue is slow, extend the observation until you have them.
4. Compute the arrival rate, the service rate, the utilisation and the mean wait. Show the arithmetic for at least one of them in full.
5. Apply Little’s Law and state which boundary you applied it to, the line alone or the line plus the person being served. The two give different answers and both are defensible if you say which one you used.
6. Plot the service times as a histogram, with the bin width stated.

What to submit#

Two files, through the assessment portal on this site, by 17:00 Friday of week 5.

The report is at most 1500 words. The title page, tables, figure captions, reference list and the observation sheets do not count towards that. The sheets are read, so scan or photograph them legibly if they are on paper.

Write for a reader who has taken this course. You do not need to explain Little’s Law or define utilisation.

Report structure#

Use these five sections, in this order, with these headings.

Figures, tables and units#

Number and caption every figure and table. Report every quantity with its unit, the interval it was computed over and the number of observations behind it. “4.2 arrivals per minute, over 40 minutes, n equals 168” is a result; “about four a minute” is not.

What each criterion means#

The weights are in the table below this brief.

Quality of the measurement. Definitions written before collection, the full 90 minutes across two days, sample sizes given for every mean, and arithmetic a marker can reproduce from your appendix.

Correct use of Little’s Law and the variability term. Consistent units, a stated boundary, a stated assumption about steady state, and a spread statistic rather than a mean on its own.

Honesty about what the numbers cannot tell you. Section 5 names one specific quantity and explains the obstacle. A general statement that all measurement has limitations does not earn these marks.

Referencing, integrity and lateness#

Author and date in the text, with a reference list at the end. There is no minimum number of sources; this is a measurement report and the evidence is your own data.

Your observations have to be yours. See the academic integrity section of the policies page, which also covers the use of language models and the standard late penalty. If you need longer, ask for an extension before the deadline.