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Stochastic optimisation model for air traffic management

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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, especially in the developing countries. Many developing countries do less to abate this otherwise seemingly invincible 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 management.

Aviation and meteorological data sources at Entebbe International Airport for theperiod 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 had more representative significant number of predicators of nine and ten for departure and arrival respectively. The proportion of the number of aircrafts that delay was established to follow an autoregressive integrated moving average, ARIMA (1,1,1) time series.

The stochastic frontier model estimated the average inefficiencies of aircraft operations over the period to be 15 percent and 20 percent at departure and arrival respectively. Three stochastic optimisation models were developed by relating airport utility and the interaction effect of daily probabilities of delay and 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 post-logistic 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 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 analyses suggest that at this airport, utility of daily delay is greater during aircraft departures 92 percent than at aircraft arrivals 91 percent. Thus, to maximise airport utility over a time period, measures have to be developed to improve overall timeliness of aircraft operations so as to attract accelerated sustainable development. Therefore, more investments are required in human resources to develop more practical tools that inform air traffic management process. Others include equipment and automatic weather monitoring systems in order to reduce the likelihood of aircraft delay and the related technical inefficiency parameters.

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