FIND THE REAL BOTTLENECK

The slowest station
sets everyone’s pace.

Jobs move through three stations. Each has a fixed time per job and a few workers. Speed up the wrong one and nothing changes. Find the right one and the queue disappears.

START WITH A QUESTIONPick one · watch the queues · read the charts

THE LINE AS A FLOW DIAGRAM

Arrivals → A → B → C → done

EACH SQUARE = ONE JOB · WAITED0 s15 s30 s+bottleneckqueue growingrush job

Finished0 / 24jobs through inspection

In the line0jobs waiting or being worked on

Throughput0.0jobs/min, last 60 s

Longest wait0.0 sany job, so far

BottleneckB–

WHAT’S HAPPENING

Ready.

Press play to start the clock.

WHERE THE WORK PILES UP

Queues over time

THE ARITHMETIC

Capacity in one line.

A station’s capacity is workers ÷ time per job: the most it could finish if work never stopped coming. The line can never beat its smallest capacity.

PREDICT FIRST

TRY THIS

Three small challenges.

UNDER THE BONNETHow the model works

This is a discrete-event simulation: instead of ticking a clock, it jumps from one event (a job arrives, a worker finishes) to the next. Jobs arrive at fixed intervals. Each station takes the first job in its queue as soon as a worker is free (first in, first out), works on it for exactly the set time, then passes it on instantly.

Capacity = workers ÷ time per job. If arrivals come faster than a station’s capacity, its queue grows by the difference every minute, forever. If they come slower, the queue stays empty and workers stand idle part of the time. Utilisation (“busy”) is the share of the last 30 s a station’s workers spent working.

Little’s law says the average number of jobs in a system equals the rate they flow through times the average time each spends inside: L = λ × W. Here L is measured from the actual job count over time, λ is finished jobs ÷ elapsed time, and W is the average time a finished job took. They meet exactly when the batch is done.

Near 100% busy: with fixed times, a queue only forms when arrivals outrun capacity. But any burst of extra work drains only at the spare capacity, capacity − arrival rate. At 50% busy, spare capacity is half the station; at 90% it is a tenth, so the same rush takes five times longer. Real lines have random times too, which create little bursts constantly: that is why real queues explode as busy-ness nears 100%. The dashed curve on the Near 100% chart shows the classic textbook formula for that random case.

KNOW THE LIMITSWhat this does not show

Every time is fixed. No breakdowns, no slow jobs, no random arrivals, so queues here only form from overload or rushes. Real lines queue earlier.
Buffers between stations are unlimited, so a station never has to stop because the next queue is full.
Moving between stations takes no time; the sliding squares are only animation.
One worker at A and C. Workers do not switch stations, take breaks or get tired.
Throughput is measured over the last 60 s and includes start-up, so it lags behind changes.
The rush recovery estimate is a “fluid” approximation (extra jobs ÷ spare capacity); the measured time can differ by a job or two.
It teaches a mechanism. It is not a forecast for a real business.

GO DEEPERSources & notes

The theory of constraints (Goldratt, The Goal, 1984) popularised the idea that only improvements at the bottleneck raise output. The M/M/1 curve uses the standard result Wq = ρ/(1−ρ) × service time.