Effective attractive and repulsive interactions behind lift synchronization

Abstract Synchronization is a ubiquitous phenomenon in nonequilibrium systems. One intriguing example found in every-day life is lifts installed next to each other, that move closely and arrive almost simultaneously during a busy time. However, the basic mechanism behind this lift synchronization is yet to be elucidated. Here, we investigate the effective interaction acting between the lifts quantitatively. Through the analysis on the time-series data obtained by numerically solving a rule-based discrete model of lifts, in which passengers at each floor show up stochastically and call a lift that is expected to arrive first, we find that the effective interaction acting between the lifts consists of not only attraction but also repulsion. By changing the parameters of the rule-based model, we are successful to tune the ratio of these competing interactions and to control the dynamics of lifts, realizing the transition between in-phase and anti-phase synchronization. In principle, our strategy for extracting effective interaction is applicable to the data of real lifts. Thus, we believe that this study provides a prototype of novel approach to design optimal transportation, which is of great importance in improving sustainability of social systems.