  Elevators can be regarded as oscillators driven by the calls of passengers
who arrive randomly. We study the dynamic behavior of elevators during the down
peak period numerically and analytically. We assume that new passengers arrive
at each floor according to a Poisson process and call the elevators to go down
to the ground floor. We numerically examine how the round-trip time of a single
elevator depends on the inflow rate of passengers at each floor and reproduce
it by a self-consistent equation considering the combination of floors where
call occurs. By setting an order parameter, we show that the synchronization of
two elevators occurs irrespective of final destination (whether the elevators
did or did not go to the top floor). It indicates that the spontaneous ordering
of elevators emerges from the Poisson noise. We also reproduce the round-trip
time of two elevators by a self-consistent equation considering the interaction
through the existence of passengers and the absence of volume exclusion. Those
results suggest that such interaction stabilizes and characterizes the
spontaneous ordering of elevators.
