Spectral Models for Air Transportation Networks

Abstract

From natural disasters to power outages, these events, even geographically-localized ones, often result in widespread disruptions across the air transportation network. In order to engineer resilience and design better proactive mitigation strategies, it is important to identify, characterize, and control the effects of such disruptions. A more resilient and well-prepared air transportation system directly translates to mitigated delay costs and increased service quality.

Current delay performance metrics reflect only the magnitude of incurred flight delays at airports. In the first half of the thesis, we show that it is also important to consider the spatial distribution of delays across a network of airports. We analyze graph-supported signals, leveraging techniques from spectral graph theory and graph signal processing to compute analytical and simulation-driven bounds for identifying outliers in spatial distribution. We then apply these methods to analyze US airport delays from 2008 through 2017. We also perform an airline-specific analysis, deriving insights into the delay dynamics of individual airline sub-networks. We highlight key differences in delay dynamics between different types of disruptions, ranging from nor’easters and hurricanes to airport outages. We also examine delay interactions between airline sub-networks and the system-wide network, as well as compile an inventory of outlier days. This inventory could guide future aviation system planning efforts and research. We demonstrate the generalizability of this outlier identification and characterization framework through a comparative analysis of US and Chinese airport networks.

After establishing the framework of modeling and analyzing airport delays as graph-supported signals, in the second half of the thesis we focus on two applications enabled by this framework: Examining commonly-occurring disruption-recovery cycles in the US airport network, and proposing an approximate network control scheme. In regards to the first application, we study these disruption and recovery cycles through a state-space representation that captures the severity and spatial impact of airport delays. In particular, using US airport delay data from 2008-2017, we first identify representative disruption and recovery cycles. These representative cycles provide insights into the common operational patterns of disruptions and recoveries in the system. We also relate these representative cycles to specific off-nominal events such as airport outages, and elucidate the differing disruption-recovery pathways for various off-nominal events. Finally, we explore temporal trends in terms of when and how the system tends to be disrupted, then subsequently recovers. For the second application, we consider the problem of designing control strategies for high-dimensional systems that lack a detailed model. To do so, we leverage the ability of copulas to represent dependent structures in high-dimensional data, and approximate the state space of airport delays through inverse sampling. We demonstrate the use of the control policies obtained from our methodology through a case study of controlling flight delays within the US air transportation network.

We conclude this thesis with some directions for future work, an example of which is a new hierarchical approach towards air traffic management procedures such as airport ground holding. We also comment briefly on the applicability of the methods developed in this thesis for other transportation and networked systems.