Are air traffic models chaotic?

Abstract

Network queueing models, including some models of air traffic, exhibit sensitivity to very small changes in the times of events that are nominally simultaneous, such as flight departures (pushbacks). Such models might exhibit chaotic behavior when the ordering of otherwise simultaneous (or closely spaced) departures are changed. This paper explores the question as to whether such models do, indeed, exhibit chaotic behavior, or whether the effect is bounded. study of delays in National Airspace System (NAS) simulations. The study consisted of 32 replications of a NAS scenario, in which scheduled departures were given a small pseudorandom pushback delay, independent across replications and across airports. The simulated scenario was a hypothetical one configured for a generally good weather day. The standard deviation of total (viz., 59-airport) at-gate delays is reported; it exceeds the simulated reduction in delay that would be produced by increasing arrival capacity by ten percent at any airport, except for the five most-congested airports. We further analyze the results to determine whether chaotic effects are manifest in the mathematical model. This question is explored using an empirical

Looking into the Future of Air Transportation Modeling and Simulation: A Grand Challenge

“…For example, an aircraft arriving late (or early) may not have a gate ready for it at the terminal. Callaham and Wieland [11] demonstrated that just a change in the take-off order of aircraft scheduled to depart at the same time can cause a standard deviation in the variation in the delays experienced in the USA as a manifestation of deterministic chaos of equivalent magnitude to increases by 10% of the capacity of the major airports in the USA. Therefore, scheduling often requires some slack to be built in: reserve crews remain on call, extra time is scheduled for turn-around at the gate, and flight schedules build in the in-flight delays predicted from recent operations.…”

“…The air transportation system is a large, adaptive and nonlinear system. Many of its components are so intertwined and so close to capacity that any change to one aspect of the system can quickly impact many other aspects (e.g., [11,14]). As a result, the importance of modeling and simulation to design and evaluate proposed changes to the air transportation system has been widely recognized by the larger air transportation community.…”

“…These endeavors raise a new question: Even if increased processing power makes them computationally feasible, can we make detailed simulations with large scope merely by adding detail to current large-scope representations and/or by creating multiple interacting replications of detailed simulations? As illustrated by Callaham and Wieland [11], the air transportation system can exhibit significant chaotic components. As such, modeling errors negligible in small-scope simulations using detailed models may grow when all these models are combined to model larger scopes.…”

Towards Validation of an Adaptive Flight Control Simulation Using Statistical Emulation

“…It also tends to assume that people are the only adaptive elements of the system, and those people can be trusted to do the right thing. At this point, few of these assumptions hold true for the National Airspace, 19 and, arguably, NextGen will be even more difficult to reliably validate. The NextGen airspace has been optimized to allow for maximum traffic, and optimized systems are inherently more non-linear.…”