Where the work happens
Long-run capacity & utilizationUtilization is the process flow rate divided by each stage’s capacity. These are steady-state values, so they exclude the startup and finish of this finite run.
Every passenger has a story
First 10 passengers · click a row to follow someoneFollow the numbers
| Passenger | ID check | Metal detector | Luggage X-ray | Time waiting | Finished at |
|---|
One airport. Different possibilities.
Compare the homework scenarios using 100 passengers.
Click any scenario to run it on the screening floor.
How long until everyone is through?
Shorter is fasterThe trade-offs, side by side
| Scenario | Passengers | Total time | Time saved¹ | Capacity / hour | Bottleneck |
|---|
Why isn’t two X-rays exactly the same as one faster X-ray?
Both alternatives can screen 240 passengers per hour once the line is moving. But a 15-second machine finishes the first passenger sooner. With two 30-second machines, the last pair finishes at 25m 15s and 25m 25s. The faster machine finishes all 100 at 25m 15s: a 10-second advantage.
Question 4 · Answers & calculations
Check the model, not just the answer
7 / 7 passedThese checks compare the simulation with independent scheduling formulas and the full 10-person completion trace. The downloaded Python version runs the same checks when started.
Model assumptions & what the numbers mean
All passengers are waiting when the first ID check begins at 5:30 a.m. The stations start empty. Passengers follow ID check, metal detector, and luggage X-ray in that order. Each stage uses first-come, first-served processing, with passenger number breaking simultaneous-arrival ties. Parallel stations at a stage have identical processing times. Processing times are fixed; walking time, breaks, and random delays are excluded. Waiting space is unlimited.
Total processing time means the time from the first ID check starting until the last passenger finishes the X-ray. Time in the system is a passenger’s finish time minus their arrival time (zero here). Cycle time here is the average interval between completions in steady operation: the largest processing-time-per-station ratio. With parallel stations, actual gaps between individual completions can alternate. Capacity is the theoretical steady-state hourly rate, rather than passengers divided by this finite run’s duration.