Gondola Throughput and Queue

What is modelled

Cabins leave the lower terminal at a fixed spacing along the rope, so the headway is the spacing divided by the line speed and the capacity is the seats per cabin divided by the headway. Passengers arrive at random with a demand curve peaking at 10:00. Each cabin takes the people at the front of the queue. In the afternoon the wind rises from 3 m/s to the chosen value: the operator slows the line between 12 and 20 m/s and closes it above 20 m/s, and the cabins swing out sideways.

Equations

• Headway h = s / (f v), capacity C = n f v / s × 3600, speed factor f from the wind rule.
• Cabin swing tan θ = ½ ρ CdA w² / (m g).
• Queue q(t) = arrivals − departures; Little's law L = λ W in the form ∫ q dt = sum of waits.
• Arrivals: thinned Poisson process with rate λ(t).

Checks run in the page

• Arrival count against the integral of the demand curve.
• Passenger conservation and cabin capacity.
• Little's law from a minute-by-minute queue count.
• A damped pendulum integration against the swing formula.

Honest simplifications

One terminal, no loading delay, no group booking, no walk-up balking, a fixed day-long wind ramp and a made-up wind rule. Real lifts also have station dwell, cabin gaps, skier behaviour and detailed anemometer limits, so these numbers are not an operating plan.

• Press Wind picks up and watch the capacity curve step down at noon while the queue grows.
• Press Storm closure to see the line stop completely and the queue build until 16:00.
• Press Capacity upgrade, with 10 seats and tighter spacing, and watch the queue vanish.