David J.
Lovell, Kleoniki Vlachou, Tarek Rabbani, and Alexandre Bayen
Transportation Research Part C: Emerging Technologies, vol.
33, pp. 227-237, 2013.
This paper illustrates a continuum approximation to queuing problems at a
single airport, adapted from the well-known diffusion approximation, as
encapsulated in the Kolmogorov forward equation of stochastic processes or the
Fokker–Planck equation of physics. The continuum model is derived using
special artifacts of the airport problem context, and a numerical solution
scheme based on the finite element method is presented. The results are
compared against known stationary results from the M/M/1 process, as well as
against airport scenarios generated from real demand and supply data. In both
cases, a Monte Carlo simulation is used to provide ground truth results against
which to compare the diffusion model, and is shown that the results between the
Monte Carlo and diffusion models match quite closely.