Elevator traffic

Rest-to-rest time under jerk j, acceleration a, and rated speed v has three regimes. If the run is shorter than 2 a³ / j², acceleration never reaches a and time is 4 (d / 2j)^(1/3). If it reaches a but not v, peak speed solves v² + v (a² / j) − a d = 0 and time is 2v/a + 2a/j. If the run is long enough to cruise, t = d/v + v/a + a/j. Distance to rated speed is v²/(2a) + v a /(2j). At 6 m/s, 1.1 m/s² and 2 m/s³ that distance is about 18 m — more than four floors. A single 4 m floor never sees rated speed. The nameplate 8–12 m/s only exists on the express.

Door time dominates the short hop. Center-opening doors on a passenger car are about 1.9 s open and 2.9 s close; the close is the slow one because kinetic energy at the leading edge is limited. Dwell is a minimum hold, not an add-on to transfer: lobby time is open + max(3.2 s, passengers × 1.0 s) + close. A floor stop is open + max(dwell, alighters × 0.9 s) + close. Usable area, not the stamped kilogram rating, sets how many of those passengers fit. A 1,600 kg class car is on the order of 3.6 m² and 21 persons at 75 kg; traffic design fills about 80% of that. Past that, the door reopen from a blocked beam costs more than the last passenger was worth.

Conventional collective learns destinations only after boarding, so P passengers headed uniformly for N floors produce S = N (1 − ((N−1)/N)^P) stops and a highest reversal H = N − Σ (i/N)^P. On this plant the closed form at the current boarding load is 10.79 stops and reversal floor 17.37. The simulator’s collective morning trip is 10.88 stops. Destination dispatch cuts that entropy by refusing to mix arbitrary floors in one cabin: zones, plus a cap on distinct destinations. The flight bench is the microscope. The overhead line under it is the reason the cap exists.

Handling capacity is HC5 = 300 × passengers per trip × cars / round-trip time, then divided by population. Interval is RTT / cars in the sub-fleet that can actually serve you. With deterministic spacing, mean wait is half that interval, plus the walk from a destination terminal when there is one. Turnstile dispatch keeps the same trips and cuts the walk from 11 s to 4 s, because the credential is read during a walk that was going to happen anyway. Up-peak supervisory does not beat collective: there is only one hall-call floor. Down-peak supervisory does beat collective, because the call floor is the information sectoring needs.

The matrix is the morning up-peak of whatever the capacity bench is set to. Lunch and evening are in the bench, not here — they do not rank the same way. Door-cycle wear tracks stops per trip: fewer stops is the maintenance argument, and it is real only when the cap is actually binding.

J(a) = Σᵢ (wW · Wi + wT · Ti + wE · Ei) + wL · [max(0, Wi + age − 60 s)]²

Wi is predicted wait, including delay to people not yet aboard. Ti is ride time, including delay imposed on passengers already committed. Ei is extra shaft travel and extra starts, not a utility bill. The squared term is how a 90-second waiter outranks several ordinary 20-second waits. The perception rule used in dispatch is wW ≥ 2 wT: standing still is counted at least twice rolling. Age in this lab is 20 s already spent before the optimizer runs, so the penalty starts when system wait exceeds 40 s.

Three solvers share that objective. A genetic algorithm keeps a population of assignment strings and scores them on a short horizon; it is truncated to the control cycle, typically well under half a second, so it returns a good feasible string rather than a proven optimum. Mixed-integer programming is exact on a single new call — binary x for “this passenger, this car” — and too slow if it is asked to reshuffle every locked passenger. Production code therefore prices one insertion per car and optionally checks the winner. A neural heuristic can rank the same cars in milliseconds from a state embedding; it does not get to skip the capacity, direction, and lock constraints. Those stay in a shield that can reject the network.

[Badge scan / floor selection at turnstile]
        -> [State vector: position, velocity, load, committed stops]
        -> [Cost matrix across cars still allowed to take the call]
        -> [Immediate target-car assignment]
        -> [Deterministic path lock]

• Up-peak cars leave full. The destination cap limits distinct floors; it does not shrink the load when the lobby queue is deep.
• Zones split the group evenly. A zone with one car has an interval equal to its own round trip.
• Wait is half the relevant interval. No queueing formula beyond that, no bunching random variable except where a regime is defined as uncoordinated.
• Down-peak collective runs every car the full height. Supervisory and destination dispatch use the same sectors. The 3% stop trim on destination dispatch is bookkeeping, and the text treats it that way.
• Closed-form stops 10.79, reversal 17.37, population 1620.

{
  "heightPx": 600,
  "regime": "up",
  "series": [
    {
      "regime": "up",
      "system": "collective",
      "averageWaitS": 14.5,
      "transitS": 69.3,
      "timeToDestinationS": 83.9,
      "handlingCapacityPct": 10.2,
      "stopsPerRoundTrip": 10.9,
      "roundTripS": 174.3,
      "intervalS": 29,
      "doorCyclesPerCarHour": 245.3
    },
    {
      "regime": "up",
      "system": "supervisory",
      "averageWaitS": 14.5,
      "transitS": 69.3,
      "timeToDestinationS": 83.9,
      "handlingCapacityPct": 10.2,
      "stopsPerRoundTrip": 10.9,
      "roundTripS": 174.3,
      "intervalS": 29,
      "doorCyclesPerCarHour": 245.3
    },
    {
      "regime": "up",
      "system": "dcs",
      "averageWaitS": 34.5,
      "transitS": 32.2,
      "timeToDestinationS": 66.7,
      "handlingCapacityPct": 19,
      "stopsPerRoundTrip": 4,
      "roundTripS": 93.9,
      "intervalS": 47,
      "doorCyclesPerCarHour": 192.9
    },
    {
      "regime": "up",
      "system": "turnstile",
      "averageWaitS": 27.5,
      "transitS": 32.2,
      "timeToDestinationS": 59.7,
      "handlingCapacityPct": 19,
      "stopsPerRoundTrip": 4,
      "roundTripS": 93.9,
      "intervalS": 47,
      "doorCyclesPerCarHour": 192.9
    }
  ]
}