The synchronization of elevators when not all passengers will ride the first-arriving elevator

TL;DR

This study investigates how passenger behavior and inflow rates influence elevator synchronization during peak times using numerical simulations and mathematical modeling.

Contribution

It introduces a quantitative analysis of elevator synchronization phenomena considering passenger choices and inflow variations, supported by simple mathematical models.

Findings

Increased passenger inflow promotes synchronization and increases round-trip time.

Higher proportion of passengers riding the first elevator promotes synchronization and decreases round-trip time.

Mathematical models effectively reproduce and explain the observed dynamics.

Abstract

The cluster motion of busy multiple elevators is considered to be one of the synchronization phenomena of autonomous oscillators. In this study, we used numerical simulations to quantitatively explore differences in the elevators' dynamics during down peaks under isolated and coupled conditions. We introduced the proportion of passengers who are set to ride the first-arriving elevator as a control parameter and investigated the behaviors of elevators when the proportions of those passengers and the inflow of passengers were varied. When we increased the inflow of passengers, the synchronization was promoted and the round-trip time increased. On the other hand, when we increased the proportion of those passengers, the synchronization was promoted while the round-trip time decreased. To elucidate the relationship between the parameters and dynamics and clarify the mechanism, we established simple mathematical models; First, we reproduced the round-trip time by a self-consistent equation considering the inflow of passengers and the proportion of passengers set to ride the first-arriving elevator. Then, we estimated an order parameter of the synchronization.