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.