How many times have you stood in a lobby waiting for an elevator to arrive wondering to yourself, Should I just take the stairs? New research published in in the Journal of Statistical Mechanics from an international collaboration of researchers capitalizes on that question, digging into the mechanics behind vertical transportation with a toy model to simulate the factors that affect elevator speed.
What inspired this alternative study? Boston University physicist Zhijie Feng says, "Just in the main building of my undergraduate university, Hong Kong University of Science and Technology, 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 each elevator lobby, and if they are shut down, we have to hike for 30 minutes." Hong Kong is constructing approximately 1500 new elevators annually and as global construction continues to grow upward instead of outward, elevators will only become a larger part of our daily lives.
Feng and colleague Sidney Redner, a professor at Sante Fe Institute, note that their interest in elevators encouraged them to take a new perspective. "Engineers have already developed computational models for simulating elevators as realistically as possible," says Feng. "Instead, we wanted insight into basic mechanisms, using just enough parameters to describe what we see in a way we can fully understand."
Their toy model includes the following six assumptions within its simulations: unoccupied buildings, first-come-first-served transport, identical elevators traveling to uniformly distributed destination floors, 2.5 seconds to enter or exit elevators, and one second to travel from one floor to the next.
The authors explain that ideally, "If the elevators are uncorrelated," wait time "should equal the single elevator cycle time divided by the number of elevators, which is roughly 15 seconds." But the reality of this isn’t sustainable because of essentially a traffic buildup within the mechanisms, resulting in multiple elevators arrive back on the ground floor at the same time. Because of this, figuring out how long people will have to wait is a more complicated equation.
"I hope our work could be a 'pocket version' model to extend from," Feng remarks. For example, future investigations could focus on answering questions such as, "If a building tapers with height, is there a taper angle that minimizes waiting time but optimizes office space; and what if some elevators only service certain floors, and others service different floors?"
