We consider a network of periodically running railway lines. Investments are possible to increase the speed and to improve the synchronisation of trains. The model also includes random delays of trains and the propagation of delays across the network. We derive a cost‐benefit analysis of investments, where the benefit is measured in reduced waiting time for passengers changing lines. We also estimate the actual mean waiting time simulating the train delays. This allows us to analyse the impact that an increasing synchronisation of the timetable has on its stability. Simulation is based on an analytical model obtained from queueing theory. We use sophisticated adaptive evolutionary algorithms, which send off avant‐garde solutions from time to time to speed up the optimisation process. As there is a high correlation between scheduled and estimated waiting times for badly synchronised timetables, we are even able to include the time consuming simulation into our optimisation runs.

Summary: In this paper we examine a model for the landing procedure of aircrafts at an airport. The characteristic feature here is that due to air turbulence the safety distance between two landing aircrafts depends on the types of these two machines. Hence, an efficient routing of the aircraft to two runways may reduce their waiting time.First, we use M/SM/1 queues (with dependent service times) to model a single runway. We give the stability condition and a formula for the average waiting time of the aircrafts. Moreover, we derive easy to compute bounds on the waiting times by comparison to simpler queuing systems. In particular we study the effect of neglecting the dependency of the service times when using M/G/1-models.We then consider the case of two runways with a number of heuristic routing strategies such as coin flipping, type splitting, Round Robin and variants of the join-the-least-load rule. These strategies are analyzed and compared numerically with respect to the average delay they cause. It turns out that a certain modification of join-the-least-load gives the best results.

: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 queueing problem, this means that we have dependent service times. The aim is to minimise 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.

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