The present invention is directed to an elevator dispatching system for controlling the assignment of elevator cars. More particularly, the present invention is directed to a method of determining the commencement and/or conclusion of UP-PEAK and DOWN-PEAK periods of operation. For example, for commencing UP-PEAK operation, a lobby boarding count is predicted, based on historical information of the number of passengers boarding the elevators at the lobby. The predicted lobby boarding count is compared with a predetermined threshold value. If the predicted lobby boarding count is greater than the predetermined threshold value, UP-PEAK is commenced. In the preferred embodiment, the predetermined threshold value is a predetermined percentage of the building's population. Additionally, the present invention is directed to a method of adjusting the threshold value based on actual passenger traffic. For example, once UP-PEAK is commenced, the load of the first few elevators leaving the lobby within a predetermined time interval is determined, and the threshold value is adjusted based on their determined load. If the determined load is greater than a certain percentage of the elevator car's capacity, indicative of starting UP-PEAK too late, the threshold value is decreased. Similarly, if the determined load is less than a certain percentage of the elevator car's capacity, indicative of starting UP-PEAK too soon, the threshold value is increased.