Optimal dispatching control for elevator systems during uppeak traffic

In this paper we develop optimal dispatching controllers for elevator systems during uppeak traffic. An uppeak traffic period arises when the bulk of the passenger traffic is moving from the first door up into the building (e.g., the start of a business day in an office building). The cars deliver the passengers and then return empty to the first floor to pick up more passengers. We show that the structure of the optimal dispatching policy minimizing the discounted or average passenger waiting time is a threshold-based policy. That is, the optimal policy is to dispatch an available car from the first floor when the number of passengers inside the car reaches or exceeds a threshold that depends on several factors including the passenger arrival rate, elevator performance capabilities, and the number of elevators available at the first floor. Since most elevator systems have sensors to determine the car locations and the number of passengers in each car, such a threshold policy is easily implemented. Our analysis is based on a Markov decision problem formulation with a batch service queueing model consisting of a single queue served by multiple finite-capacity bulk servers. We use dynamic programming techniques to obtain the structure of the optimal control policy and to derive some of its important properties. Several numerical examples are included to illustrate our results and to compare the optimal threshold policy to some known ad hoc approaches. Finally, since many transportation systems can be modeled as multiserver batch service queueing systems, we expect our results to be useful in controlling those systems as well.