Stochastic optimisation models for air traffic flow management

Abstract

Air traffic delay is not only a source of inconvenience to the aviation passenger, but also a major deterrent to the optimisation of airport utility. Many developing countries do less to abate this otherwise seemingly invisible constraint to development. The overall objective of this study was to investigate the dynamics of air traffic delays and to develop stochastic optimisation models that mitigate delays and facilitate efficient air traffic flow management.

Aviation and meteorological data sources at Entebbe International Airport for the period 2004 to 2008 on daily basis were used for exploratory data analysis, modelling and simulation purposes. Exploratory data analysis involved logistic modeling for which post-logistic model analysis estimated the average probability of departure delay to be 49 percent while that for arrival delay was 36 percent. These computations were based on a delay threshold level at 60 percent which presented more significant predicators of nine and ten for departure and arrival respectively. The proportion of aircrafts that delay was established to follow an autoregressive integrated moving average, ARIMA (1,1,1) time series.

The stochastic frontier model estimates show the average inefficiencies of aircraft operations as 15 and 20 percent at departure and arrival respectively. The final category of output of the study was three stochastic optimisation models developed by relating airport utility and the interaction effects of daily probabilities of delay and airport inefficiency estimates. The three models measure daily airport utility at aircraft departures, arrivals and aggregated aircraft departures and arrivals. In this formulation, the stochastic frontier model inefficiency estimates and the postlogistic delay probability estimates were used as inputs into the stochastic optimisation models to enforce the models’ theoretical underpinning.

Model sensitivity analysis adduced that the utility level for a given time period at an airport with higher levels of inefficiency was significantly less than the utility level with lower levels of inefficiency. Furthermore, lower estimates of probabilities for departure and arrival delay resulted into a higher operational utility level of the airport. Further analysis suggests that Entebbe International Airport operates at almost the same utility levels for aircraft departures, 92 percent and aircraft arrivals, 91 percent. To maximise airport utility over a time period, measures have to be developed to improve overall timeliness of aircraft operations at departures and arrivals respectively.