Nonlinear Dynamics Approach for modeling of air traffic disruption and recovery

Abstract

The inclusion of a priori knowledge on random disturbance into stochastic and robust optimisation of arrival and departure scheduling for controller assistance is a topic of ongoing research. One direction is the development of advanced algorithms utilizing stochastic models of empirical traffic rate and delay time statistics derived from hundreds of flights over limited periods of time. The typically asymmetric delay distributions usually include some extreme disturbances (X-events, e.g. low pressure weather situations) which often are disregarded as outliers. In this contribution we focus on the modeling of disruption and recovery dynamics of performance during single X-events. Based on previous work in the literature for formalizing performance disruption and systems resilience we analyse the potential of a simple logistic function aproach for deriving characteristic performance parameters from empirical data. We provide initial results obtained with time dependent control parameters (e.g. disruption / recovery time constants) dependent, e.g. on wind/gust speed variation, for dynamic performance simulation using nonlinear first and second order dynamics. This stationary state transition model is analogous to the incoherent – coherent phase transition in the laser and due to its predictability features has the potential for combining single X-events models with stochastic and robust optimization based scheduling.