In modern transportation systems there exists a need to develop fast, responsive and easily adaptable methods for computing optimal (or near-optimal) solutions to problems in which resources must be allocated dynamically in order to satisfy time-varying demands from multiple sources. In this talk we consider the case of a single airport which, in response to a pre-determined schedule of arrivals and departures, must use its runway capacity efficiently in order to minimise an objective function based on weighted second moments of aircraft queue lengths.

In keeping with a well-established convention in the literature, we model departures and arrivals as independent stochastic queues with time-varying arrival and service rates. Service times are assumed to follow Erlang distributions, whereas for the arrival distributions we consider two possible cases: non-homogeneous Poisson processes and pre-scheduled arrivals with random deviations. We discuss how to formulate the problem of optimising airport capacity usage as a Markov decision process (MDP), and introduce a “surrogate problem” which closely resembles our original problem during periods of heavy demand. We then show that, in our surrogate problem, the MDP value function can be represented as a quadratic function of the state variables, and use this principle to develop ADP strategies for optimising capacity utilisation.