Research notes
Mirai Guide: modeling the goods queue
A three-phase queue model where the sellout clock, not register counts, reveals booth throughput.
How long will the goods line be after doors open?
That is the question everyone actually wants answered, and it is harder than it sounds because the textbook queue model does not apply here.
The Structural Fact
The pre-open entry line does not advance.
It is a stationary held mass, released all at once at open. So the entry phase is not an M/M/1 queue at all. It is accumulate, bulk-release, then per-booth queues, and each phase needs its own treatment.
Everything else in the model follows from getting that one thing right, plus calibration against history.
Three Phases
- Pre-open accumulation. People pile up from the earliest permitted line-up time. Your position is everyone ahead of you, and the integral of the arrival rate up to open gives the peak line length at the doors.
- Bulk release at open. The gate drains the held mass at a measurable rate - on the order of 40-50 people per minute, with roughly the 500th person clearing in about ten minutes. Arriving before open costs you the wait until open plus your share of the drain. Arriving after open, the remaining entry wait falls off at roughly a minute per minute.
- Per-booth goods queues. Each booth’s queue starts with its share of the released mass - popularity share times the opening surge - then evolves as arrivals minus service. The wait at a booth is its queue length over its service rate, and a booth sells out when cumulative sales exhaust its stock.
The Coupling That Makes It Tractable
Here is the problem with phase 3. Booth throughput is never published, and nobody is standing there counting registers.
But sellout time equals stock over service rate. Which means the historical sellout curve already encodes throughput. An item that sold out at +T tells you its first ~stock buyers cleared in T.
So I don’t need the number. I need the clock.
Calibrated parameters ship in the published data as observations, per venue tier. That is also why venue identity across years matters - the calibration attaches to the hall, not to one edition’s naming.
The model’s job is honest expectation-setting. “This line will be long but moves fast” versus “this sells out before you clear entry”, using only public observables and the crowd’s own reports.