Week 2 Lab: Lab 2 — Breaking a Queue on Purpose

Run a queue by hand with dice, then add variance and watch it fall over without adding a single customer.

1 March 2027

Before the lab#

Read the week 2 lecture notes, and bring a phone with a stopwatch. We supply the dice.

In the lab#

This runs as a tabletop simulation, in groups of four, and it is deliberately low-tech — you will meet the software version soon enough, and it is much easier to disbelieve a computer than your own tally sheet.

Run one, sixty ticks. One person is the clock. One rolls arrivals, one rolls service, one keeps the queue as a row of counters. Arrivals and service are both set so that ρ ≈ 0.8, with no variance: exactly four arrivals per five ticks, exactly one service per tick. Record queue length every tick.

Run two, sixty ticks. Identical average rates. Now roll for both. Same mean arrivals, same mean service, same ρ. Record queue length every tick.

The averages are the same. The graphs are not, and every group gets the same qualitative result, which is the point of doing it collectively rather than watching one demo.

Then push it. Change nothing except the arrival rate, taking ρ from 0.8 to 0.9 to 0.95. Sixty ticks each. Plot maximum queue length against ρ on the whiteboard, all groups on the same axes. The curve that appears is the one the lecture asserted, drawn from your own dice.

Afterwards#

Keep your tally sheets. In week 9 you will run the same experiment in software and compare the two, and having your own hand-rolled data to check the simulator against is a much better position than trusting it.

Tomáš will be looking at how you recorded, not what you found. The finding is already known; the recording is the skill.