Empirical exploration of air traffic and human dynamics in terminal airspaces

Air traffic is widely known as a complex, task-critical techno-social system, with numerous interactions between airspace, procedures, aircraft and air traffic controllers. In order to develop and deploy high-level operational concepts and automation systems scientifically and effectively, it is essential to conduct an in-depth investigation on the intrinsic traffic-human dynamics and characteristics, which is not widely seen in the literature. To fill this gap, we propose a multi-layer network to model and analyze air traffic systems. A Route-based Airspace Network (RAN) and Flight Trajectory Network (FTN) encapsulate critical physical and operational characteristics; an Integrated Flow-Driven Network (IFDN) and Interrelated Conflict-Communication Network (ICCN) are formulated to represent air traffic flow transmissions and intervention from air traffic controllers, respectively. Furthermore, a set of analytical metrics including network variables, complex network attributes, controllers' cognitive complexity, and chaotic metrics are introduced and applied in a case study of Guangzhou terminal airspace. Empirical results show the existence of fundamental diagram and macroscopic fundamental diagram at the route, sector and terminal levels. Moreover, the dynamics and underlying mechanisms of "ATCOs-flow" interactions are revealed and interpreted by adaptive meta-cognition strategies based on network analysis of the ICCN. Finally, at the system level, chaos is identified in conflict system and human behavioral system when traffic switch to the semi-stable or congested phase. This study offers analytical tools for understanding the complex human-flow interactions at potentially a broad range of air traffic systems, and underpins future developments and automation of intelligent air traffic management systems.Comment: 30 pages, 28 figures, currently under revie

Stability and bifurcation in network traffic flow: A Poincar\'e map approach

Previous studies have shown that, in a diverge-merge network with two intermediate links (the DM network), the kinematic wave model always admits stationary solutions under constant boundary conditions, but periodic oscillations can develop from empty initial conditions. Such contradictory observations suggest that the stationary states be unstable. In this study we develop a new approach to investigate the stability property of traffic flow in this and other networks. Based on the observation that kinematic waves propagate in a circular path when only one of the two intermediate links is congested, we derive a one-dimensional, discrete Poincar\'e map in the out-flux at a Poincar\'e section. We then prove that the fixed points of the Poincar\'e map correspond to stationary flow-rates on the two links. With Lyapunov's first method, we demonstrate that the Poincar\'e map can be finite-time stable, asymptotically stable, or unstable. When unstable, the map is found to have periodical points of period two, but no chaotic solutions. Comparing the results with those in existing studies, we conclude that the Poincar\'e map can be used to represent network-wide dynamics in the kinematic wave model. We further analyze the bifurcation in the stability of the Poincar\'e map caused by varying route choice proportions. We further apply the Poincar\'e map approach to analyzing traffic patterns in more general $(DM)^n$ and beltway networks, which are sufficient and necessary structures for network-induced unstable traffic and gridlock, respectively. This study demonstrates that the Poincar\'e map approach can be efficiently applied to analyze traffic dynamics in any road networks with circular information propagation and provides new insights into unstable traffic dynamics caused by interactions among network bottlenecks.Comment: 31 pages, 10 figures, 2 table

Uncertainty damping in kinetic traffic models by driver-assist controls

In this paper, we propose a kinetic model of traffic flow with uncertain binary interactions, which explains the scattering of the fundamental diagram in terms of the macroscopic variability of aggregate quantities, such as the mean speed and the flux of the vehicles, produced by the microscopic uncertainty. Moreover, we design control strategies at the level of the microscopic interactions among the vehicles, by which we prove that it is possible to dampen the propagation of such an uncertainty across the scales. Our analytical and numerical results suggest that the aggregate traffic flow may be made more ordered, hence predictable, by implementing such control protocols in driver-assist vehicles. Remarkably, they also provide a precise relationship between a measure of the macroscopic damping of the uncertainty and the penetration rate of the driver-assist technology in the traffic stream

Modeling Supply Networks and Business Cycles as Unstable Transport Phenomena

Physical concepts developed to describe instabilities in traffic flows can be generalized in a way that allows one to understand the well-known instability of supply chains (the so-called ``bullwhip effect''). That is, small variations in the consumption rate can cause large variations in the production rate of companies generating the requested product. Interestingly, the resulting oscillations have characteristic frequencies which are considerably lower than the variations in the consumption rate. This suggests that instabilities of supply chains may be the reason for the existence of business cycles. At the same time, we establish some link to queuing theory and between micro- and macroeconomics.Comment: For related work see http://www.helbing.or