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ROUTING OF AIRPLANES TO TWO RUNWAYS: MONOTONICITY OF OPTIMAL CONTROLS

Published online by Cambridge University Press:  01 October 2004

N. Bäuerle ,
O. Engelhardt-Funke  and
M. Kolonko
N. Bäuerle
Affiliation:
Institut für Mathematische Stochastik, Universität Hannover, Germany, E-mail: baeuerle@stochastik.uni-hannover.de
O. Engelhardt-Funke
Affiliation:
Institut für Mathematik, Technical University Clausthal, D-38678 Clausthal-Zellerfeld, Germany, E-mail: kolonko@math.tu-clausthal.de
M. Kolonko
Affiliation:
Institut für Mathematik, Technical University Clausthal, D-38678 Clausthal-Zellerfeld, Germany, E-mail: kolonko@math.tu-clausthal.de
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Abstract

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 type of airplane. When viewed as a queuing problem, this means that we have dependent service times. The aim is to minimize the waiting times of aircrafts. We consider here a model in which arrivals form a stochastic process and the decision-maker does not know anything about future arrivals. We formulate this as a problem of stochastic dynamic programming and investigate the monotonicity of optimal routing strategies with respect to the workload of the runways, for example. 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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 18 , Issue 4 , October 2004 , pp. 533 - 560
Copyright
© 2004 Cambridge University Press

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References

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