Game-theoretic Decentralized Coordination for Airspace Sector Overload Mitigation

TL;DR

The paper addresses sector overload in decentralized air traffic management by casting sector interactions as a game with a tunable cooperativeness factor $\kappa$. It proves convergence of best-response dynamics to a pure Nash equilibrium under mild restrictions and characterizes a sufficient condition under which overload-free solutions correspond to global optima of the potential function. Numerical experiments on 24 hours of European flight data show that even minimal cooperation ($\kappa$ just above 0) yields substantial overload reductions, with performance comparable to centralized solvers and better than FCFS baselines, while maintaining scalability. The work demonstrates that effective decentralized coordination does not require full altruism, enabling practical deployment of decentralized ATM with limited coordination and distributed computation.

Abstract

Decentralized air traffic management systems offer a scalable alternative to centralized control, but often assume high levels of cooperation. In practice, such assumptions frequently break down since airspace sectors operate independently and prioritize local objectives. We address the problem of sector overload in decentralized air traffic management by proposing a mechanism that models self-interested behaviors based on best response dynamics. Each sector adjusts the departure times of flights under its control to reduce its own congestion, without any shared decision making. A tunable cooperativeness factor models the degree to which each sector is willing to reduce overload in other sectors. We prove that the proposed mechanism satisfies a potential game structure, ensuring that best response dynamics converge to a pure Nash equilibrium, under a mild restriction. In addition, we identify a sufficient condition under which an overload-free solution corresponds to a global minimizer of the potential function. Numerical experiments using 24 hours of European flight data demonstrate that the proposed algorithm substantially reduces overload even with only minimal cooperation between sectors, while maintaining scalability and matching the solution quality of centralized solvers.

Figures (6)

• Figure 1: Illustration of sector overload mitigation. (Left) A sector with a capacity limit of three aircraft is overloaded with five active flights (red region). (Right) Two flights (green) adjust their flight schedule (red dashed arrows), removing the overload and restoring the sector to a feasible state (green region).
• Figure 2: Traffic demand profiles on July 27, 2023. The plots illustrate temporal variations in traffic demand at two different levels of spatial aggregation: (a) European airspace grouped by 12 countries, and (b) BREST FIR divided into 28 individual sectors.
• Figure 3: Traffic demand profiles in BREST FIR. Top (a): initial schedule. Bottom (b–e): outcomes under different cooperativeness factor ($\kappa$) settings and algorithms. Side boxes report solution quality measures: total overload [aircraft-min] and maximum instantaneous occupancy [number of aircraft].
• Figure 4: (a) Final overload cost comparison across $\kappa$ values and baselines. A purely self-interested regime ($\kappa=0$) leaves substantial overload unresolved, while other cooperation factors eliminate overload. (b) Normalized computation time comparison. Computation times are normalized by the median runtime of the centralized solver so that all results are shown on a common dimensionless scale. For the decentralized cases ($\kappa \in \{0,10^{-6},0.5,1.0\}$), the blue upper boxplots show the total runtime, while the lower dotted boxplots show the average runtime per sector. The green side boxplots indicate the time required for the decentralized algorithm to reach the overload level achieved by the centralized solver.
• Figure 5: Stress test with reduced sector capacity ($D=7$). (a) Final overload cost comparison. Unlike the $D=10$ case where all $\kappa>0$ values eliminated overload, here residual overload remains and performance differences between $\kappa$ values become evident. (b) Normalized computation time comparison. Computation times are normalized by the median runtime of the centralized case. Nonzero $\kappa$ values incur longer runtime, exceeding that of the centralized solver.

Theorems & Definitions (26)

• Definition 1: Best-response dynamics book_shohamswensonBRD
• Definition 2: Potential game book_shoham
• Definition 3: Self-prioritizing cooperative behavior
• Theorem 1: Sufficient bound on $\kappa$ for self-prioritization
• proof
• Theorem 2: Potential game under fixed overload set
• proof
• Lemma 1: Potential game for $\kappa=0$ or $\kappa=1$
• proof
• Definition 4: No-new-overload restriction