Stochastic analysis of Air-Traffic System and its corresponding application in parameters prediction

In this paper we propose using one of the stochastic methods - Probabilistic Collocation Method (PCM) to find simplified polynomial mapping between two uncertain Air-Traffic System (ATS) parameter data sets. These two parameter sets can be two distinguished collection of measured parameters depicting various aspects of one specific air-traffic system, and the knowledge of parameters distribution is not a requirement. We show that PCM can be applied to air-traffic systems from immense systems like United States´ National Air-space System (NAS), down-scale to middle-sized systems as New York City metro-area air-traffic system with combination of three major airports (JFK, EWR and LGA) or even smaller systems like Chicago O´Hare International Airport (ORD). Compared with commonly used direct polynomial fitting method, PCM has the advantages in both efficient calculation and high accuracy. Along with the mapping relation of PCM from historical parameter data sets, we applied such polynomial mapping relation to predict the future air-traffic within the same system. By comparing the predicted data with the real recorded or FACET simulated data, we have reached the conclusion that the PCM performs excellent in analyzing current data and predicting future value based on historical mapping formula. The capability of forecasting by applying PCM serves as one powerful tool in launching control on air-traffic system as well as managing the system in advance based on the known traffic data.