The queue is two sums, not one
While the crowd is still arriving, people join faster than the fixtures release them and the line grows at the difference between the two rates. That growth stops the moment the last person arrives. After that the line only shrinks, at the rate the fixtures manage, and the time it takes to shrink to nothing is what the person at the back is waiting.
So the worst wait is the peak queue divided by the clearing rate, and the peak queue is the arrival rate minus the clearing rate, times the length of the arrival ramp. Both halves matter and people usually only think about the first one.
What the defaults produce
Nine hundred in the house, split down the middle. Room A: 450 people, 55 percent of them go, so 248 arrive over five minutes — 49.5 a minute. Eight fixtures at 90 seconds each clear 5.3 a minute. The queue grows by 44 people a minute for five minutes and peaks at 221. Draining 221 people at 5.3 a minute takes 41 minutes, and the interval is twenty.
Room B: 450 people, 30 percent go, so 135 over five minutes is 27 a minute. Twelve fixtures at 45 seconds clear 16 a minute. The queue peaks at 55 and drains in 3.4 minutes. Everyone in room B is done at 8.4 minutes into a break with 17 usable minutes in it.
Same building, same interval, same crowd. One room finishes in eight minutes and the other has not finished by the time the second act ends. That gap is not a quirk of these particular numbers — it is what happens when a fixture count is split evenly across two groups whose demand is not.
The reshuffle line is the useful one
Twenty fixtures in the building. Room A is carrying 248 people at 90 seconds — 371 fixture-minutes of work. Room B is carrying 135 at 45 seconds, or 101. That is 79 percent of the work against 21, and the fixtures are split 40 to 60 the other way.
Split the same twenty in proportion to the work and it comes out 16 and 4. The page recomputes both rooms at that split and prints the new worst wait beside the old one. It prints it rather than claiming it, because the answer is not always an improvement: if the split you typed already matches the work, nothing moves, and rounding to whole fixtures can occasionally make it slightly worse. Read the two numbers.
What none of that settles is whether the resulting split is lawful. Fixture counts in a building are set by the plumbing code the jurisdiction has adopted and by the building official who signs the plan. This page does not know that code, does not contain it, and cannot tell you whether a room has enough of anything. It tells you how long a line takes at the fixtures that are there.
Two levers that are not on the form
Spreading the arrival ramp is the cheapest one. The peak queue is proportional to the ramp length only through the gap between the rates, so stretching a five minute ramp to eight — by releasing the house in sections, or by simply having a bar queue that holds people back — cuts the peak substantially. Try it in the field and watch the drain time fall.
Lengthening the interval does not change any rate. It moves the finish line. At the defaults room A needs 46 minutes to clear, so a 25 minute interval does not fix it and a 50 minute one is not an interval any more. Capacity is the only thing that moves the drain time.
Where the model is wrong
It assumes a steady arrival rate and a steady service rate, and neither is true. A whole row stands up at once. Somebody spends four minutes in there. A fixture is out of order and nobody told the house manager. The fluid model averages all of that away, which is fine for sizing and useless for predicting any particular evening.
It also treats the two rooms as sealed. In real buildings people walk to the other one when the line is long, which mixes the two problems in a way no simple model catches. If your venue has more than two rooms, run the page once per pair and take the worst.
Questions people ask
How long is the restroom line at an interval?
At the values in the form, 41 minutes at the back of the line in room A and 3.4 minutes in room B. The arithmetic is the arrival rate minus the clearing rate, times the arrival ramp, divided by the clearing rate. Change any of the four inputs and the answer moves a long way, which is why the page asks for your own timings rather than assuming any.
How many fixtures does a venue need?
That is not a question this page answers or can answer. The required fixture count for a building is set by the plumbing code the jurisdiction has adopted and by the building official who approves the plans. What this page does is take the fixtures that are actually there, which you count or read off the approved plan, and work out how long a queue at them takes to clear. It issues no adequacy or compliance verdict.
Why is one room always so much worse?
Because the demand splits unevenly and the fixtures usually do not. At the defaults one room is carrying 79 percent of the fixture-minutes of work with 40 percent of the fixtures. The page prints the work in each room precisely so that mismatch is visible as a number instead of as a queue out the door.
Does making the interval longer help?
Only by moving the deadline. It changes nothing about the rate at which people are cleared, so a queue that needs 46 minutes to drain still needs 46 minutes. What does help is spreading the arrivals — a longer ramp lowers the peak queue and therefore the drain — and adding capacity, which is the only thing that changes the drain rate itself.
What service time should I use?
Your own, measured. Time twenty people door to door at your own venue with a stopwatch and take the average. The 90 and 45 seconds sitting in the fields are placeholders to replace, not figures about buildings in general, and this is the input the answer is most sensitive to after the fixture count.