We study the dynamical behavior of elevators in the morning peak traffic. We present a stochastic model of the elevators to take into account the interactions between elevators through passengers. The dynamics of the elevators is expressed in terms of a coupled nonlinear map with noises. The number of passengers carried by an elevator and the time-headway between elevators exhibit the complex behavior with varying elevator trips. It is found that the behavior of elevators exhibits a deterministic chaos even if there are no noises. The chaotic motion depends on the loading parameter, the maximum capacity of an elevator, and the number of elevators. When the loading parameter is superior to the threshold, each elevator carries a full load of passengers throughout its trip. The dependence of the threshold (transition point) on the elevator capacity is clarified.
