Calculating the knee
Each fleet faces the same traffic profile. That paired comparison makes the improvement from one extra car much easier to see.
This sensitivity grid reruns the building at six traffic levels. Orange cells are overloaded or still benefit strongly from another car; green cells have crossed the selected diminishing-return threshold.
Choose the fleet size where you think the following elevator first becomes a marginal addition. Your guess is scored against the full paired simulation. Change the building first to make a new puzzle.
Taller bars are better. This combines passenger time saved with an illustrative per-car operating cost, showing why the mathematically fastest fleet is rarely the economical fleet.
This is a discrete-event model, not an elevator-code calculation. It creates individual passenger calls, assigns cars, accounts for travel, stops, doors, capacity, and measures the full distribution of waiting times. Its purpose is to reveal the shape of diminishing returns.
The chart compares average wait with 1 through 12 cars. For each added car it computes (old wait − new wait) ÷ old wait. The reported knee is the first fleet where the following car improves average wait by less than your threshold.
Every fleet size receives the same seeded arrival times and destinations. A quiet run cannot accidentally make one fleet look better. Change a control and a new, still-paired experiment is generated.
Up-peak sends most riders from the lobby to occupied floors, the classic morning office load. Two-way traffic adds inter-floor and down trips, which causes more scattered stops and normally moves the knee upward.
Nearest-car dispatch assigns the car that can reach a call soonest. Destination grouping also favors cars already serving nearby destinations, reducing stops and improving handling capacity, especially in tall buildings.
Travel time grows with floor distance. Every pickup and destination adds door and exchange time. A full car leaves riders behind for another car. In shorter buildings, door time often matters more than rated speed.
Average wait describes typical service; the 95th percentile exposes rare painful waits. Two fleets with similar averages can feel very different if one produces long tails during bursts.
Arrival burstiness clusters passengers instead of spacing them evenly, exposing queue shocks hidden by averages. The outage switch removes one installed car from service, answering whether a lean fleet still works during maintenance or a breakdown.
Zoning assigns half the fleet to lower floors and half to upper floors. It can reduce long cross-building trips in tall towers, but too few cars per zone can make the system brittle. The paired fleet sweep tests that tradeoff directly.
The frontier values passenger waiting time using your hourly slider, then subtracts an illustrative operating charge for every active car. It complements the percentage knee with a cost-aware answer; it is a comparison tool, not a construction estimate.
The knee challenge turns the curve into a prediction problem. Shuffle the seeded traffic day, inspect the building assumptions, and choose the fleet where you expect diminishing returns to begin.
Shuffle traffic day changes arrival bursts and service-time noise. All 12 fleet sizes still receive the same day, so differences remain attributable to elevator count rather than luck.
The demand grid repeats the calculation from a quiet period through an extreme peak. It shows whether the reported knee is stable or jumps when occupancy and arrival intensity are underestimated.
Use 2% for a strict economic cutoff or 10–15% if passenger experience is paramount. The slider makes that judgment explicit.
A fleet can technically transport everyone while still producing unacceptable waits. Designers also check interval, crowding, accessibility, redundancy, fire strategy, and local codes.
Add cars until arrivals no longer outrun handling capacity, then stop when the next car’s measured wait reduction falls below the value you assign to better service.