The human world is, more and more, an urban world – and that means elevators. Hong Kong, the hometown of physicist Zhijie Feng (Boston University) *, is adding new elevators at a rate of around 1,500 per year … making vertical transport an attractive topic for quantitative research.
“Right in the main building of my undergraduate university, the Hong Kong University of Science and Technology,” Feng explains, “there are 37 elevators, all numbered so we can use them to indicate the location of hundreds. of classrooms. There is always a line outside every elevator hall, and if they are closed, we have to walk for 30 minutes. “
Sidney Redner, a professor at the Feng Institute and Santa Fe, saw an opportunity to explore the factors that determine the transport capacities of elevators. In their new paper in the Journal of Statistical Mechanics, they start by making a deliberately simple “toy” model.
“Engineers have already developed calculation models to simulate elevators as realistically as possible,” says Feng. “Instead, we wanted to get an overview of the basic mechanics, using just enough parameters to describe what we are seeing in a way we can fully understand.”
Their minimally variable simulation is based on six key assumptions: unoccupied buildings, transport first come, first served, identical elevators moving to evenly distributed destination floors, 2.5 seconds to enter or exit elevators, and one second to move from elevators. one floor to another. .
For a 100-story building with an idealized elevator of infinite capacity, Feng and Redner find that wait times are typically between five and seven minutes. With elevators that can carry 20 people each and buildings that can accommodate 100 workers per floor, this cycle requires 500 trips over 2 hours – or 21 elevators – to keep everyone working on time.
“If the elevators are not correlated,” the authors write, the wait time “should equal the cycle time of a single elevator divided by the number of elevators, which is about 15 seconds”. However, this efficient elevator spacing does not last: as passenger demand increases, the elevators start moving together, creating traffic jams in the hall below until several elevators return to the ground floor. pavement at the same time.
These nonlinear dynamics prevent easy answers to the question of how long a person should wait. But for Feng and Redner, this is only the entry level of a larger investigation. “I hope our work could be a model of a ‘pocket version’ to expand from,” Feng remarks. She credits Redner’s textbook, which she read early in her undergraduate studies, with her love for breaking down complex problems into simple models.
Some of the other questions they identify include: “If a building narrows with height, is there a taper angle that minimizes wait time but optimizes office space?”; and “What if some elevators only serve certain floors and others serve different floors?”
Food for thought the next time you’re waiting in the lobby …
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Material provided by Santa Fe Institute. Note: Content can be changed for style and length.