What happens and why
Why the buffer does not grow above the goal
The source releases a part on a clock edge only if at that moment the buffer is below the goal. It released one — the buffer is one larger. It reached the goal — the next ticks are skipped until Herbie takes a part and the IR pair after him says «−1». So the buffer never exceeds the goal, and between ticks it moves between «goal − 1» and «goal».
Why Herbie stands with goal 1
The buffer counts all the parts from the source to Herbie — including those still travelling through machines 1 and 2. With goal 1 there is one part in the line: while it passes two belts and two machines, Herbie has nothing to do. The goal must cover the way to the bottleneck — as many parts as fit on the way, plus a margin.
Why a stock, if Herbie is the same on average
With a die Herbie sometimes falls behind, and sometimes makes several parts in a row very fast. At those moments he needs several parts at once. If they are not there, he waits, and that time is lost for the whole factory: Herbie is the bottleneck, nobody will make up for his idle time. The more unevenly the bottleneck works, the bigger the buffer it needs. But an extra stock is no use either: in our factory goal 6 makes as much as 7 and 8, and holds fewer parts.
| Herbie with die | Made | Idle | Inside |
|---|---|---|---|
| no rope | 93–100 | 6–9 s | ≈ 20 |
| goal 4 | 85–87 | 18–26 s | ≈ 5.5 |
| goal 6 | 93–99 | 7–9 s | ≈ 8 |
«Inside» — how many parts are in the shop on average during the shift.
A timetable and feedback
The SLOW switch is a timetable: «release a part every 2 seconds». It does not know what is happening in the shop. While Herbie works evenly, the timetable is good. Herbie became uneven — the timetable sometimes sends a part late. Herbie was sped up — the timetable did not notice at all.
The rope is feedback: the output of the system (how many parts wait for Herbie) goes back to its input (whether to release a new one). Such a system fits itself. The same principle keeps the temperature in a fridge, the speed of an engine and the volume of a phone. For feedback to work, the system has to be measured — that is why half the kit went into the buffer counter.
What's next
So far our machines do not break down. In a real factory a machine can stop for repair, and then the buffer before the bottleneck shows what it was kept for: while the machine before Herbie is being repaired, Herbie works from the stock. Breakdowns and repair are the next kit in the series.