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? Mirai Guide’s queue model starts from one structural observation about these events and gets the rest by calibration against history.
The structural fact
The pre-open entry line does not advance. It is a stationary held mass, released all at once at open. That means the entry phase is not a textbook M/M/1 queue — it is accumulate, bulk-release, then per-booth queues, and each phase needs its own treatment.
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 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
Booth throughput is never published, and nobody is counting registers. But sellout time equals stock over service rate — so the historical sellout curve already encodes throughput. An item that sold out at +T tells you its first ~stock buyers cleared in T. Calibrated parameters ship in the published data as observations, per venue tier, which 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.