In IE 468, Virtual Manufacturing, at UIC I built a discrete-event model of a theme park to answer that. This page rebuilds it: every guest tries to ride all eight rides with the least time in line, a queueing engine runs a full simulated day in milliseconds, and a sweep across attendance levels finds the point where seats stay full but the lines stay short.
| Ride | Seats | Cycle | Load | /hr | Wait | Queue |
|---|
Runs the current rides, arrival profile and routing rule across a range of attendance levels, several seeded repetitions each, in a background worker. Reports the largest tested attendance that met all three criteria below in every repetition. It does not interpolate between tested levels and does not claim the true optimum lies exactly there.
Guests arrive on a chosen profile, ride each of eight rides once in an order set by a routing rule, then leave. No rerides, no shows or food breaks, straight-line walking at a random per-guest speed, and posted waits guests can actually see: queue length divided by the ride's real throughput.
The obvious lever, more rides, barely moves the average wait. The lever that matters is admission: below a threshold, seats run empty and lines stay short; a little past it, the same rides produce lines that grow the rest of the day. The threshold is sharp, not gradual.
Ride throughput is fixed by seats and cycle time, not by how many people are admitted. When arrivals bunch up faster than the rides can absorb them, a queue is one possible consequence. This simulation runs that mechanism forward under its stated assumptions rather than asserting a single formula predicts the outcome.