Stochastic Dynamic Programming for Noise Load Management

Abstract

Noise load reduction is among the primary performance targets for some airports. For airports with a complex lay-out of runways, runway selection may then be carried out via a preference list, an ordered set of runway combinations such that the higher on the list a runway combination, the better this combination is for reducing noise load. The highest safe runway combination in the list will actually be used. The optimal preference list selection minimises the probability of exceeding the noise load limit at the end of the aviation year. This paper formulates the preference list selection problem in the framework of Stochastic Dynamic Programming that enables determining an optimal strategy for the monthly preference list selection problem taking into account future and unpredictable weather conditions, as well as safety and efficiency restrictions. The resulting SDP has a finite horizon (aviation year), continuous state space (accumulated noise load), time-inhomogeneous transition densities (monthly weather conditions) and one-step rewards zero. For numerical evaluation of the optimal strategy, we have discretised the state space. In addition, to reduce the size of the state space we have lumped into a single state those states that lie outside a cone of states that may achieve the noise load restrictions. Our results indicate that the SDP approach allows for optimal preference list selection taking into account uncertain weather conditions.