Optimal parking in group elevator control

We consider the problem of optimally parking empty cars in an elevator group so as to anticipate and intercept the arrival of new passengers and minimize their waiting times. Two solutions are proposed, for the down-peak and up-peak traffic patterns. We demonstrate that matching the distribution of free cars to the arrival distribution of passengers is sufficient to produce savings of up to 80% in down-peak traffic. Since this approach Is not useful for the much harder case of up-peak traffic, we propose a solution based on the representation of the elevator system as a Markov decision process (MDP) model with relatively few aggregated states, and determination of the optimal parking policy by means of dynamic programming on the MDP model.