Philippe BAPTISTE

Air-traffic management (ATM) consists of a predictive component (traffic planning) and an adaptive component (traffic control). The aim of the predictive component is to balance airspace demand with available capacity. The adaptive component has to guide aircraft safely to their destinations, once they are in the air. Uncertainties (e.g delay from connecting flights, technical failure) create the phenomenon of gaps between the predictive and the adaptive component. This causes safety problems and non-optimally used capacity. While the main sources of uncertainties are identified (demand uncertainties, capacity uncertainties, flow control uncertainties) the mechanisms of how they affect the components of air-traffic management remain unknown. Our approach is to analyze past flight data to generate hypotheses about the mechanisms that lead to gaps between the predictive and the adaptive component in ATM. This is a pragmatic first step in the analysis of a physical phenomenon. It is based on probability theory and more precisely on a frequentist interpretation of uncertainty. We use multivariate data analysis techniques and stochastic Point processes to infer new knowledge about the phenomenon. Our main results are (i) there are systematic gaps in each sector evaluated. The size of these gaps can be characterized by Poisson distributions and there is a systematic shift to suppress traffic at high planned levels. This is counter-intuitive because one expects that the different uncertainty factors cancel out in average. We then prove that random disturbances of an arrival process cause systematic gaps in two classes of flight schedules. We conclude that even if all controllable uncertainties in flow planning were eliminated, systematic gaps between the number of planned and realized traffic would remain. This result is useful in tactical flow planning. New constraints in the slot-allocation procedure can be found by identifying classes of flight schedules that are robust to random disturbance. (ii) we show that gaps propagate exclusively on flight routes. No unexpected propagation is identified. This is evidence that no systematic re-routing is initiated by controllers to absorb gaps. We also identify high tail probabilities and two time-series models which describe the second-order characteristics of the process that disturbs the flight schedules. This is evidence that the disturbances are heterogeneous and not independent. This result is empirical and we conjecture that the observed behavior is due to aggregation and long-range dependence at the sector level. As future work we propose to continue the identification of classes of flight schedules that absorb the impact of uncontrollable disturbances and to develop pa st el -0 00 03 21 1, v er si on 1 27 J ul 2 01 0