A diffusion approximation to a single airport queue

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.

► We develop a diffusion model for a stochastic queuing model at a single airport.
► We develop a hybrid finite difference/finite element solution procedure.
► We incorporate dynamics and boundary conditions reflective of the airport context.
► The FEM solution converges to the known equilibrium results for the M/M/1 queue.
► The model performs well for real airport demand and capacity profiles.