Collaborative virtual queueing has been proposed as a mechanism to mitigate airport surface congestion while preserving airline autonomy over aircraft-level pushback decisions. A central coordinator can regulate aggregate pushback capacity but cannot directly control which specific aircraft are released, limiting its ability to steer system-level performance. We propose a noncooperative coordination mechanism for collaborative virtual queueing based on the correlated equilibrium concept, which enables the coordinator to provide incentive-compatible recommendations on aircraft-level pushback decisions without overriding airline autonomy. To account for uncertainty in airlines' internal cost assessments, we introduce chance constraints into the correlated equilibrium formulation. This formulation provides explicit probabilistic guarantees on incentive compatibility, allowing the coordinator to adjust the confidence level with which airlines are expected to follow the recommended actions. We further propose a scalable algorithm for computing chance-constrained correlated equilibria by exploiting a reduced-rank structure. Numerical experiments demonstrate that the proposed method scales to realistic traffic levels up to 210 eligible pushbacks per hour, reduces accumulated delay by up to approximately 8.9% compared to current first-come-first-served schemes, and reveals a trade-off between confidence level, deviation robustness, and achievable cost efficiency.
Figures & tables
Figure 1: Illustration of the collaborative virtual queue coordination setting. A central coordinator regulates aggregate pushback capacity \raisebox{-.9pt}{1}⃝ but does not control aircraft-level decisions directly. Released aircraft contribute to taxiway congestion c(t) ( \raisebox{-.9pt}{2}⃝ – \raisebox{-.9pt}{3}⃝ ) and to runway queue delay δf(t) \raisebox{-.9pt}{4}⃝ , while departures are governed by runway service rates μr \raisebox{-.9pt}{5}⃝ . Airlines retain autonomy over pushback decisions \raisebox{-.9pt}{6}⃝ , creating a noncooperative coordination problem.
Method
CE formulation
Uncertainty-aware
CENT
–
–
FCFS
–
–
Full-CCCE
Full formulation eq. 21
Yes
RR-Nominal
Reduced formulation eq. 24
No
RR-CCCE
Reduced formulation eq. 24
Yes
TABLE I : Comparison of coordination mechanisms
Figure 2: Departure rates per runway for each 4-minute epoch across a 60-minute horizon. Red and blue bars correspond to Runway 1 and Runway 2, respectively. The schedule is synthetically generated with an average departure rate of 1.05 flights per minute.
Figure 3: Scalability comparison between Full-CCCE and RR-CCCE . Wall-clock computation time (log scale) is shown as a function of the number of eligible aircraft per epoch. The horizontal dotted line indicates the epoch duration (4 minutes), representing the real-time constraint for online deployment. Median marked by ∘ .
Figure 4: Comparison of realized delay cost across coordination mechanisms. CENT serves as an idealized performance benchmark. Full-CCCE and RR-CCCE outperform FCFS as traffic increases. RR-CCCE exhibits a performance gap relative to Full-CCCE due to equilibrium-set approximation. Median marked by ∘ .
Figure 5: Performance under cost uncertainty ( α=90% , six airlines). (a) Delay cost distribution as a function of cost noise level σ . (b) Deviation rate versus σ . Horizontal lines within boxplots indicate mean values.
Figure 6: Performance under varying confidence levels ( σ=20 , six airlines). (a) Delay cost distribution as a function of confidence level α . (b) Deviation rate versus α . Horizontal lines within boxplots indicate mean values.
Figure 7: Accumulated delay cost over a 16-epochs rolling simulation. Two uncertainty settings are compared: σ=0 and σ=100 . Each boxplot summarizes repeated runs with identical traffic realization and varying cost noise. Median marked by ∘ .
Figure 8: Equilibrium-space characteristics. (a) Average number of chance-constrained pure Nash equilibria (CC-PNE) and solver failure rate as the number of eligible aircraft increases ( α=90% , σ=20 ). (b) Average number of CC-PNE and failure rate as cost uncertainty σ increases ( ∣F(t)∣=8 , α=90% ). Increasing problem size expands the equilibrium set, whereas higher uncertainty reduces discoverable equilibria and increases failure probability.
Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin · The Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin
The University of Texas at Austin, 110 Inner Campus Drive, Austin, 78712, Texas, United States · École Nationale de lAviation Civile, 7 Avenue Édouard Belin, CS 54005, Toulouse Cedex 4, 31055, France