Flight and passenger efficiency-fairness trade-off for ATFM delay assignment
Introduction
Airports are limited in capacity by operational constraints (Bazargan et al., 2002; Gilbo, 1993), generating in some cases, a significant imbalance between capacity and demand. Air Traffic Flow and Capacity Management (ATFCM) initiatives are then implemented to smooth traffic arrivals, transferring costly airborne delay, carried out with holdings and/or path stretching, to pre-departure on-ground delay (Carlier et al., 2007).
When a capacity-demand imbalance is detected, a Ration by Schedule (RBS) prioritisation of flights is the current practice for slot assignment (EUROCONTROL, 2015a). RBS policy is considered by the different stakeholders to be the fairest delay assignment, since it respects the original slot planning, but economical optimum cannot be guaranteed and only arrival delay is considered. Nevertheless, while airline reported delay was 14.7 min per flight in Europe in 2018, reactionary delay was responsible for of it, heavily influenced by the impact of first-rotation delays (EUROCONTROL, 2019), and should thus not be neglected.
In the current operational environment, the system is optimised considering a flight-centred perspective, however, different stakeholders might experience ATM system performances differently. In particular, passenger-centric metrics might differ from their equivalent flight-centric ones (Cook et al., 2012). In (Montlaur and Delgado, 2017), performances for flight and passenger delays of an extended arrival manager (E-AMAN) were analysed in conjunction with a pre-tactical optimisation of flights. In that work, the assignment of slots was optimised considering either arrival delay for flights, arrival delay for passengers, total delay for flights (considering reactionary delay) or total delay for passengers (considering outbound connections). Results showed that in the scope of an E-AMAN, the distances and possible delays that can be assigned do not justify the application of a more sophisticated strategy than RBS. Nevertheless, when the scope of optimisation was enlarged to include the pre-tactical phase, benefits (and trade-offs) were obtained by optimising the assignment of delay instead of only considering flight schedules. While minimising the total delay for passengers is, as expected, the best strategy from the passengers perspective, it leads to higher reactionary delay for flights with respect to a flight-centric optimisation. Though optimisation carried out in (Montlaur and Delgado, 2017) focused on only one stakeholder at a time and did not include an explicit consideration of equity, it was shown that if focus is given to flight total delay, the benefit per passenger remains similar to the passenger centred optimisation and the variability with respect to the RBS delay assignment was reduced, improving the fairness of the solution.
Equity from a flight perspective was explicitly included in (Montlaur and Delgado, 2018), where flight and passenger delays and equity were conjointly considered in the optimisation scheme. Preliminary conclusions showed how focusing on one objective would affect the two others. The work presented in (Montlaur and Delgado, 2018) focused on the optimisation of three metrics (flight and passenger delays and flight-fairness) at the same time, allowing a better understanding of the trade-offs between performance from a flight delay, passenger delay and flight fairness perspective. The work focused on allowing decision makers to consider informed a posteriori articulation of preferences when optimising the delay assignment. To that end, the concept of price of performance (understood as price of trade-off) and price of efficiency as the ones defined in (Bertsimas et al., 2012) were used.
Previous research, focusing on three variables at the same time, lacked some applicability and a definition of fairness for passengers was missing. This paper has three main goals: 1) It considers a classical efficiency-equity trade-off at flight level, which would use easily available data. 2) It then studies the impact on passengers metrics. 3) It finally aims at covering the gap of equity for passengers by suggesting a definition of passenger delay fairness and finally analyses the trade-offs existing between flight and passenger performance and fairness metrics. Note that, during real life operations, the impact of uncertainty would be very relevant as the planned optimisation performed pre-tactically is subject to degradation when tactically realised. This might impact the trade-off between indicators and affect the optimal assignment of slots focusing on the expected outcome, as done for example in (Glover and Ball, 2013). In this paper, however, the assignment of slots is optimised in a deterministic manner since the main objective consists in defining and presenting different metrics. Future work should research the impact of the system's stochasticity on the stability of the solutions.
Section 2 details the background on fairness on delay assignment with an analysis of literature when allocating resources from a fairness point of view. Section 3 first explains the optimisation model and objectives used in this work. It then considers how individual objectives are combined in a multi-objective problem and presents the optimisation cases analysed in the paper. Finally, the consideration of efficiency and fairness trade-off with the concepts of price of fairness and price of efficiency are described. Section 4 recalls the main hypothesis of the simulation of traffic that has been used as an example in this paper. The main results (for the multi-objective optimisation and for the performance-fairness trade-offs) and their discussion are reported in Section 5. The paper finalises with the conclusions and further work found in Section 6.
Section snippets
Background: fairness on delay assignment
When assigning delay to flights due to capacity-demand imbalances, even though commonly used, RBS is not the only possibility. Extensive research has been conducted to assign the required delay in a most cost-effective manner (Ball et al., 2007; Gilbo, 1993; Dell’Olmo and Lulli, 2003; Vranas et al., 1994; Montlaur and Delgado, 2017). As described in (Bertsimas et al., 2012), this type of resource allocation problems may be viewed as a utility allocation among different parties, which will lead
Delay and fairness optimisation models
This section introduces the mathematical model used in this paper for the optimisation and for the analysis of the trade-off between efficiency (delay generated in the system) and fairness (based on the delay experienced by stakeholders). A description of price of fairness and price of efficiency is provided as a tool to understand these trade-offs. The different objective functions considered are explored in detail with particular focus on the definition of metrics (and objectives functions)
Problem description
In order to test the previously defined metrics and to provide a testing environment for trade-offs between performance and fairness for flights and passengers, a specific traffic scenario is modelled. The arrival demand at Paris Charles de Gaulle (CDG) airport on September 12th, 2014 has been considered for all simulations. It was a busy Friday without any major disruption. Morning traffic, between 5.00 GMT and 11.00 GMT, is analysed. For the traffic scheduled, data from EUROCONTROL Demand
Results
We calculate the Pareto optimal points needed for computation of the Pareto extreme points required in Equations (11) and (12). These optimal points (lightly shaded boxes in Table 2) are defined as the points minimising each objective, that is, for , for . The darker boxes indicate the maximum of each function. Note that, as shown in Table 2, optimal and maximum values are calculated for the chosen optimisation case (Case 1 for flight-based, Case 2 for passenger-based).
Conclusions and further work
In this paper, arrival delay due to ATFM regulations has been assigned as the optimisation of a multi-objective problem considering system performance (total delay) and fairness (deviation with respect to RBS solution). This has been done considering the perspective of flights and passengers. Two optimisation cases have been discussed: one where flights metrics are considered and another one focused on passengers indicators. A new definition for passenger fair assignment of delay has been
Acknowledgment
This work has been partly financed thanks to the Agència de Gestió d'Ajuts Universitaris i de Recerca - Generalitat de Catalunya (Grant number 2017-SGR-1278).
References (30)
- et al.
Chapter 1 Air Transportation: Irregular Operations and Control, Volume 14 of Handbooks in Operations Research and Management Science
(2007) - et al.
Measuring the cost of resilience
J. Air Transp. Manag.
(2016) - et al.
Stochastic optimization models for ground delay program planning with equity–efficiency tradeoffs
Transp. Res. C Emerg. Technol.
(2013) Ground delay program planning: delay, equity, and computational complexity
Transp. Res. C Emerg. Technol.
(2013)- et al.
Analysis of performance and equity in ground delay programs
Transp. Res. C Emerg. Technol.
(2010) - et al.
Flight and passenger delay assignment optimization strategies
Transp. Res. C Emerg. Technol.
(2017) - et al.
Equitable and efficient coordination in traffic flow management
Transp. Sci.
(2012) - et al.
A simulation study to investigate runway capacity using TAAM
- et al.
The price of fairness
Oper. Res.
(2011) - et al.
On the efficiency-fairness trade-off
Manag. Sci.
(2012)