Routing of Airplanes to Two Runways: Monotonicity of Optimal Controls Corrected Version

We consider the problem of routing incoming airplanes to two runways of an airport. Due to air turbulence, the necessary separation time between two successive landing operations depends on the types of the airplanes. When viewed as a queuing problem, this means that we have dependent service times. The aim is to minimize waiting times of aircrafts. We consider here a model where arrivals form a stochastic process and where the decision maker does not know anything about future arrivals. We formulate this as a problem of stochastic dynamic programming and investigate monotonicity of optimal routing strategies with respect e.g. to the workload of the runways. We show that an optimal strategy is monotone (i.e. of switching type) only in a restricted case where decisions depend on the state of the runways only and not on the type of the arriving aircraft. Surprisingly, in the more realistic case where this type is also known to the decision maker, monotonicity need not hold. ∗Inst. für Mathematische Stochastik, Universität Hannover, Germany †Institut für Mathematik, Technical University Clausthal, Erzstr. 1, D-38678 Clausthal-Zellerfeld, Germany, email: [email protected]