Pathfinders in the Sky: Formal Decision-Making Models for Collaborative Air Traffic Control in Convective Weather

TL;DR

Pathfinders in the Sky develops a discrete-time Markov chain with four states (Gate Closed, Pathfinder Selection, Pathfinding, Gate Opened) to model convective-weather–driven airspace openings and analyzes the steady-state distribution $pi$. It also introduces flight-centric and controller-centric stylized decision models for the pathfinder selection phase and conducts a worst-case analysis to study resilience under rejection. The framework is grounded with FAA NTML data, yielding $Paccept=0.81$ and $Psuccess=0.87$, and demonstrates how steady-state probabilities shift as weather reliability $Pgood$ varies. The results show how selfless behavior and environmental uncertainty influence system resilience, and the work outlines data-driven validation and extensions, including integration with Sherlock trajectory data.

Abstract

Air traffic can be significantly disrupted by weather. Pathfinder operations involve assigning a designated aircraft to assess whether airspace that was previously impacted by weather can be safely traversed through. Despite relatively routine use in air traffic control, there is little research on the underlying multi-agent decision-making problem. We seek to address this gap herein by formulating decision models to capture the operational dynamics and implications of pathfinders. Specifically, we construct a Markov chain to represent the stochastic transitions between key operational states (e.g., pathfinder selection). We then analyze its steady-state behavior to understand long-term system dynamics. We also propose models to characterize flight-specific acceptance behaviors (based on utility trade-offs) and pathfinder selection strategies (based on sequential offer allocations). We then conduct a worst-case scenario analysis that highlights risks from collective rejection and explores how selfless behavior and uncertainty affect system resilience. Empirical analysis of data from the US Federal Aviation Administration demonstrates the real-world significance of pathfinder operations and informs future model calibration.

Figures (8)

• Figure 1: Markov chain representation of the aircraft pathfinding process. The model consists of four states: Gate Closed (state 0), Pathfinder Selection (state 1), Pathfinding (state 2), and Gate Opened (state 3). Transition probabilities are governed by $P_{\mathrm{good}}$, $P_{\mathrm{accept}}$, and $P_{\mathrm{success}}$, capturing weather observations, acceptance of pathfinder offers, and pathfinding success, respectively.
• Figure 2: Steady-state distribution ($\pi_0$ to $\pi_3$) of a four-state Markov chain under varying values of $P_{\mathrm{good}}$ and $P_{\mathrm{accept}}$, for two different values of $P_{\mathrm{success}}$: 0.1 (top row) and 1.0 (bottom row). Each column corresponds to one of the four system states: Gate Closed, Pathfinder Selection, Pathfinding, and Gate Opened. Color intensity represents the steady-state probability $\pi_i$ for each state. The same color scale is used within each column for fair comparison between the two $P_{\mathrm{success}}$ settings.
• Figure 3: $P_{\mathrm{accept},\,i}$ as a function of utility $U_i$ for various values of the sensitivity parameter $\beta_i$. Higher $\beta_i$ values make the agent's decision more deterministic, resulting in a sharper transition from rejection to acceptance as utility increases, while lower $\beta_i$ values cause decisions to be more randomized across a wider range of utilities.
• Figure 4: Worst case probability $W(\alpha)$ as a function of the rejective agent ratio $\alpha$. The red dashed horizontal line indicates the system failure threshold $\delta = 0.1$, and the green dash-dotted vertical line shows the critical point $\alpha^*$ where $W(\alpha^*) = \delta$, under $n = 10$, $U^- = -2$, $U^+ = 2$, and $\beta = 1$.
• Figure 5: Visualization of worst case analysis across different degrees of selfishness ($S=0$: selfless, $S=1$: selfish) under $n=10$, $U^+ = 2$, $U^- = -2$, $\beta=1$$\gamma = 2.5$, and $R = 0.5$. (a) Tipping point $\alpha^*$ as a function of the system failure threshold probability $\delta$. (b) Agent rejection probability $P_{\mathrm{reject}}$ as a function of the observed collective rejection ratio $R$. Solid and dashed lines indicate receptive and rejective groups, respectively. (c) Worst case probability $W(\alpha)$ over different $\alpha$ values.