مدل سازی تاخیر احتمالی نامتقارن ورود هواپیما   Modelling the asymmetric probabilistic delay of aircraft arrival

1. Introduction Most studies addressing dichotomous outcomes, such as success vs. failure, use classical logit and probit models, and therefore assume that the responses are symmetric. Nevertheless, in practice, the real proportion of (for example) successes and failures may not be symmetric. If this is the case, application of these classical models can led to model misspecification and a misinterpretation of the marginal effects and unidentified predictors, the consequences of which could be very significant. In the present study, we examine data corresponding to aircraft arrival and departure delays, which often present just this kind of asymmetry. Arrival and departure delays in the airspace system are important variables because they cause significant losses to airlines and create problems for passengers, airports and staff. Delays can be categorised into gate delay, taxieout delay, eneroute delay, terminal delay and taxiein delay (see Mueller and Chatterji, 2002). Since traffic management decisions are influenced by the predicted demand, better demand forecasting is always desirable. Departure time uncertainty is the major cause of demand prediction error; therefore, increased departure time reliability will directly increasethe accuracy of demand prediction (Mueller and Chatterji, 2002). In consequence, scheduling and policy decision makers should seek to minimise the risk of delay and thus improve the forecasting accuracy of departure times when a probabilistic delay time model is used. Accordingly, it is important to determine the causes of delays in the airspace system, such as factors related to aircraft, airline operations, changes of procedure and traffic volume. Several approaches can be taken to analyse this issue. On the one hand, we can attempt to estimate the actual duration of the delay. For example, Allan et al. (2001) analysed several determinants of flight delay at one US airport (Newark International Airport) and showed that adverse weather conditions influenced flight delays. On the other hand, Mueller and Chatterji (2002) modelled delay assuming it to be a random variable that follows a statistical distribution. Their study, seeking to improve delay prediction, analysed the departure, eneroute and arrival delays of aircraft that operated out of one of ten major U.S. hub airports. Kwan and Hansen (2011) analysed causal factors including airport congestion, total traffic and eneroute weather. The estimation results obtained suggested that airport congestion, measured by arrival queuing delay, was a major contributor to average delay (about 32%). Nevertheless, these authors concluded that a model with a single explanatory variable is inadequate to describe the reality of a system. Wong and Tsai (2012) analysed flight delay propagation employing a survival method (the Cox proportional hazard model). These authors developed departure and arrivaldelay models that showed how flight delay propagation can be formulated through repeated chain effects in aircraft rotations performed by a Taiwanese domestic airline. Other papers have also analysed delay propagation using other econometric methods; see, for example, Xu et al. (2005, 2007), Liu and Ma (2008) and Cao and Fang (2012), among others, who used a Bayesian network approach, Pyrgiotis et al. (2013), who analysed a network of airports using a queuing model, and Derudder et al. (2010) and Diana (2011), who analysed the prediction of arrival delays using spatial analysis.