Abstract
It is well known that the faster runs a train, the more dissipates its energy. In train schedule the running time is settled in advance, so the train needs to be operated in fixed time between stations. As the train could adopt various operation patterns in the fixed schedule, the requisite energy for the train operation varies according to its patterns even in the fixed time and distance. We can, therefore, consider a train operation method which minimizes the requisite energy.
Our simple model of train operation enables to show that the train running energy is minimized when it runs in constant speed as long as possible in a specific time and distance supposing that the train moving energy were collected by the regenerating process in the brake operation.
While in case of no regeneration of the energy we gained another operation pattern of the minimum energy. The minimum energy has followed from the train operation that after keeping the constant train speed and coasting, the brake should be applied at the instant of a calculated speed when the train stops. But a commuters' train can not take the sufficient coasting time in it's frequently stopped and comparatively high speed operation. We have made clear the energy minimum operation of such a commuters' train as a special case of the no energy regeneration.
