Building the show day arrival curve that tells you when to staff the doors

The planning meeting had a number on the slide: 9,840 attendees on day one. Then somebody asked how many stewards to put on the west doors at 09:00, and the number was no help at all, because 9,840 people arriving evenly across the day and 9,840 people arriving in ninety minutes are the same figure and completely different operations.

The show day arrival curve is what turns that total into a staffing decision. It takes one query against your entry scans and about twenty minutes, and it is the single most useful thing you can build from door data before the show opens.

Why is a daily total useless for staffing?

Because doors fail at a rate, and a total has no rate in it.

Nine thousand eight hundred and forty arrivals across an eight hour open day averages 1,230 an hour. If that were the actual arrival pattern, two entry points would clear it comfortably and everybody would go home happy. Real shows do not arrive that way. They arrive in a spike tied to whatever the programme has scheduled first and whatever the trains are doing, and the spike is where the queue, the complaints and the photograph on social media all come from.

Averages are fine for budgeting. The mistake is planning door capacity against a statistic that describes a whole day when the failure happens inside a quarter of an hour.

Fifteen minute bins, one series per door

Build it as a count of first-entry scans per door per 15 minute bin. Three details decide whether it is any use.

Bin at 15 minutes. Hourly bins smooth away the surge you are trying to see. Five minute bins are noisy enough that the shape becomes hard to read at a glance. Fifteen minutes has a long precedent in road capacity work, where the Federal Highway Administration's 2018 traffic data pocket guide describes it as the shortest period over which a flow rate is considered statistically stable.

Bin per door. A show total curve tells you the venue was busy. A per door curve tells you the west entrance was busy while the east entrance was empty, which is the version somebody can act on with a radio.

Use first entries only. A curve built from raw reads counts every double fire and every return from lunch, and both distort the shape in the same direction, making the middle of the day look busier than it was. Getting from raw reads to first entries is the deduplication chain and it has to run before the bins are cut.

One detail catches people out on the first attempt. Readers, panels and registration systems each keep their own clocks, and a drift of two or three minutes between panels is ordinary. At an hourly resolution that is invisible. At 15 minutes it smears the peak across two bins for one door and not for its neighbour, which makes the west entrance look like it peaked before the east entrance when both peaked together. Check the drift by finding a moment you can identify independently, such as the doors opening, and compare the first scan timestamp at each reader. Correct the offsets once at ingest and store the correction, because next edition the panels will drift differently.

Peak to mean, and the peak hour factor

Two numbers summarise a curve well enough to put in a planning document.

The peak to mean ratio is the busiest bin divided by the average bin. On our day, 9,840 arrivals across 32 open bins averages 307.5 per bin. The 10:00 bin held 1,180. That gives a ratio of 3.84, which says the busiest quarter hour ran at nearly four times the day's average intensity.

The peak hour factor comes from road traffic work and transfers cleanly. The Federal Highway Administration's 2018 pocket guide defines it as the hourly volume divided by four times the highest 15 minute count inside that hour, bounded between 0.25 and 1.00, where 1.00 means a perfectly flat hour. Our 10:00 hour held 1,180, 980, 640 and 520 across its four bins, totalling 3,320. The factor is 3,320 divided by 4 times 1,180, which is 3,320 over 4,720, or 0.70.

A factor of 0.70 says the peak hour is heavily front-loaded inside itself. Staffing that hour to its own average would leave you 41 per cent short in its first quarter. Track both numbers across editions, because they move less than the totals do and they tell you more.

What does the curve say about how many lanes to open?

Three different answers, and the choice between them is the actual planning decision.

Plan against the daily mean of 1,230 an hour. The Sports Grounds Safety Authority's Guide to Safety at Sports Grounds, sixth edition published in 2018, sets an upper limit of 660 persons per entry point per hour. That gives 1.86, so two entry points. This is what the slide with 9,840 on it implies, and it produces the queue in the photograph.

Plan against the peak hour of 3,320. That gives 5.03, so six entry points. Better, and still short for the first fifteen minutes of that hour.

Plan against the peak quarter hour of 1,180, which is a rate of 4,720 an hour. That gives 7.15, so eight entry points. Nobody queues, and for most of the day you are paying for staff on empty lanes.

I would plan six and open eight for the first ninety minutes, then close two. The 660 figure is a ceiling written for sports grounds, where the geometry is turnstiles and the crowd is arriving for a fixed kick-off, so treat it as a sanity check on your own measured lane throughput rather than as a rule that binds an exhibition. If your own timing work says a lane passes 1,161 people an hour, as it can at 3.1 seconds of service time, the arithmetic changes and lane throughput is where that number comes from.

What the curve cannot do is tell you about a door you are not measuring. A curve built from eleven instrumented doors describes eleven doors, and the gate coverage work decides how much of the building that represents.

The curve moves, and here is what moves it

Reusing last year's curve is reasonable and it needs adjustment for the things that shift the peak.

Programme start times move it most. A keynote at 09:30 pulls the peak into the 08:45 and 09:00 bins. Move that keynote to 11:00 and the morning flattens by a third while a second peak appears before the session.

Transport moves it next. A new station entrance, an engineering closure, a change to the shuttle frequency: all of them relocate the peak by fifteen to thirty minutes, and shuttle arrivals in particular convert a smooth curve into a series of spikes forty people high.

Weather moves it in a specific direction. Rain compresses arrivals, because people who would have walked in slowly arrive together off the same transport, and coats slow every lane at the same time.

Hall changes move it in ways that surprise people. Shifting a registration desk from inside the hall to the concourse can halve your entry queue and create a new one twenty metres away, which your door counts will read as an improvement.

Days within one edition differ from each other as much as editions differ, and in a predictable way. Day one carries the sharpest peak, because the opening is an event and a large share of the audience wants to be there for it. Day two flattens: the peak bin typically falls by a third against day one while the daily total holds up, because arrivals spread across the morning once the novelty has gone. The final day flattens further and ends early, with the afternoon emptying out well before the published close. Plan each day from its own curve. A single average curve across three days will over-staff the last afternoon and under-staff the first morning, which is the most expensive combination available.

The part that stays stable across editions is the shape of the first two hours as a proportion of the day. The absolute height of the peak bin follows attendance and is the part to re-forecast.

Where this stops

An arrival curve built from badge scans is a curve of successful reads, so everything the readers missed is missing from it, and readers miss most at the peak. The busiest bin is therefore the most understated bin, which biases the peak to mean ratio downwards and makes your staffing plan slightly optimistic in exactly the wrong place.

A related distortion comes from the queue itself. The scan happens when somebody reaches the reader, so a door under load records people at the rate the door can process them rather than the rate they arrived. Once a queue forms, the curve flattens at the top and reports the door's capacity back to you as if it were demand. If your peak bin is suspiciously close to your theoretical lane capacity, that is what has happened, and the true arrival peak was higher than the data shows. Comparing the door counts against a manual count of the queue outside is one way to see it, and the rest of that method sits with the wider attendee analytics work on measurement error.

Start this week by pulling first-entry scans from your last edition into 15 minute bins for one door, and dividing the largest bin by the average. If that ratio is above three, your current door plan was built for a day that did not happen.