Applications of stochastic modeling in air traffic management:Methods, challenges and opportunities for solving air traffic problems under uncertainty

In this paper we provide a wide-ranging review of the literature on stochastic modeling applications within aviation, with a particular focus on problems involving demand and capacity management and the mitigation of air traffic congestion. From an operations research perspective, the main techniques of interest include analytical queueing theory, stochastic optimal control, robust optimization and stochastic integer programming. Applications of these techniques include the prediction of operational delays at airports, pre-tactical control of aircraft departure times, dynamic control and allocation of scarce airport resources and various others. We provide a critical review of recent developments in the literature and identify promising research opportunities for stochastic modelers within air traffic management

Computational optimization of networks of dynamical systems under uncertainties: application to the air transportation system

To efficiently balance traffic demand and capacity, optimization of air traffic management relies on accurate predictions of future capacities, which are inherently uncertain due to weather forecast. This dissertation presents a novel computational efficient approach to address the uncertainties in air traffic system by using chance constrained optimization model. First, a chance constrained model for a single airport ground holding problem is proposed with the concept of service level, which provides a event-oriented performance criterion for uncertainty. With the validated advantage on robust optimal planning under uncertainty, the chance constrained model is developed for joint planning for multiple related airports. The probabilistic capacity constraints of airspace resources provide a quantized way to balance the solution’s robustness and potential cost, which is well validated against the classic stochastic scenario tree-based method. Following the similar idea, the chance constrained model is extended to formulate a traffic flow management problem under probabilistic sector capacities, which is derived from a previous deterministic linear model. The nonlinearity from the chance constraint makes this problem difficult to solve, especially for a large scale case. To address the computational efficiency problem, a novel convex approximation based approach is proposed based on the numerical properties of the Bernstein polynomial. By effectively controlling the approximation error for both the function value and gradient, a first-order algorithm can be adopted to obtain a satisfactory solution which is expected to be optimal. The convex approximation approach is evaluated to be reliable by comparing with a brute-force method.Finally, the specially designed architecture of the convex approximation provides massive independent internal approximation processes, which makes parallel computing to be suitable. A distributed computing framework is designed based on Spark, a big data cluster computing system, to further improve the computational efficiency. By taking the advantage of Spark, the distributed framework enables concurrent executions for the convex approximation processes. Evolved from a basic cloud computing package, Hadoop MapReduce, Spark provides advanced features on in-memory computing and dynamical task allocation. Performed on a small cluster of six workstations, these features are well demonstrated by comparing with MapReduce in solving the chance constrained model

Simulation-Free Runway Balancing Optimization Under Uncertainty Using Neural Network

International audienceThis paper proposes a new optimization scheme using neural network for runway balancing to minimize departure and arrival aircraft delay. While other researchers have proposed solutions to the runway balancing problem using a simulation-based technique to calculate aircraft delay, the proposed method replaces the simulation by a neural network model-based estimation using the actual operational data, thus providing the following two advantages. First, accurate estimation of aircraft delay can improve the solution of the runway balancing problem. Second, the simulation process is not required in the optimization. Although it is difficult to develop an accurate simulation model especially under uncertain environment, the neural network model can estimate the average delay without explicitly modeling uncertainty. In this paper, as a first step, the effectiveness of the proposed method is validated through simulations. First, simulations considering uncertainty are used to generate the data, which are then used to train the neural network. The neural network predicts the delay under the current traffic and only this predicted delay is used for the runway balancing optimization with simulated annealing. The simulation result shows that the result by neural network outperforms the one by the simulation-based method under uncertainty. This means that the neural network can accurately estimate the delay under uncertainty environment, and is applicable in the optimization process

Air Taxi Skyport Location Problem for Airport Access

Witnessing the rapid progress and accelerated commercialization made in recent years for the introduction of air taxi services in near future across metropolitan cities, our research focuses on one of the most important consideration for such services, i.e., infrastructure planning (also known as skyports). We consider design of skyport locations for air taxis accessing airports, where we present the skyport location problem as a modified single-allocation p-hub median location problem integrating choice-constrained user mode choice behavior into the decision process. Our approach focuses on two alternative objectives i.e., maximizing air taxi ridership and maximizing air taxi revenue. The proposed models in the study incorporate trade-offs between trip length and trip cost based on mode choice behavior of travelers to determine optimal choices of skyports in an urban city. We examine the sensitivity of skyport locations based on two objectives, three air taxi pricing strategies, and varying transfer times at skyports. A case study of New York City is conducted considering a network of 149 taxi zones and 3 airports with over 20 million for-hire-vehicles trip data to the airports to discuss insights around the choice of skyport locations in the city, and demand allocation to different skyports under various parameter settings. Results suggest that a minimum of 9 skyports located between Manhattan, Queens and Brooklyn can adequately accommodate the airport access travel needs and are sufficiently stable against transfer time increases. Findings from this study can help air taxi providers strategize infrastructure design options and investment decisions based on skyport location choices.Comment: 25 page

Resource-Constrained Airline Ground Operations: Optimizing Schedule Recovery under Uncertainty

Die zentrale europäische Verkehrsflusssteuerung (englisch: ATFM) und Luftverkehrsgesellschaften (englisch: Airlines) verwenden unterschiedliche Paradigmen für die Priorisierung von Flügen. Während ATFM jeden Flug als individuelle Einheit betrachtet, um die Kapazitätsauslastung aller Sektoren zu steuern, bewerten Airlines jeden Flug als Teilabschnitt eines Flugzeugumlaufes, eines Crew-Einsatzplanes bzw. einer Passagierroute. Infolgedessen sind ATFM-Zeitfenster für Flüge in Kapazitätsengpässen oft schlecht auf die Ressourcenabhängigkeiten innerhalb eines Airline-Netzwerks abgestimmt, sodass die Luftfahrzeug-Bodenabfertigung – als Verbindungselement bzw. Bruchstelle zwischen einzelnen Flügen im Netzwerk – als Hauptverursacher primärer und reaktionärer Verspätungen in Europa gilt. Diese Dissertation schließt die Lücke zwischen beiden Paradigmen, indem sie ein integriertes Optimierungsmodell für die Flugplanwiederherstellung entwickelt. Das Modell ermöglicht Airlines die Priorisierung zwischen Flügen, die von einem ATFM-Kapazitätsengpass betroffen sind, und berücksichtigt dabei die begrenzte Verfügbarkeit von Abfertigungsressourcen am Flughafen. Weiterhin werden verschiedene Methoden untersucht, um die errechneten Flugprioritäten vertraulich innerhalb von kooperativen Lösungsverfahren mit externen Stakeholdern austauschen zu können. Das integrierte Optimierungsmodell ist eine Erweiterung des Resource-Constrained Project Scheduling Problems und integriert das Bodenprozessmanagement von Luftfahrzeugen mit bestehenden Ansätzen für die Steuerung von Flugzeugumläufen, Crew-Einsatzplänen und Passagierrouten. Das Modell soll der Verkehrsleitzentrale einer Airline als taktische Entscheidungsunterstützung dienen und arbeitet dabei mit einer Vorlaufzeit von mehr als zwei Stunden bis zur nächsten planmäßigen Verkehrsspitze. Systemimmanente Unsicherheiten über Prozessabweichungen und mögliche zukünftige Störungen werden in der Optimierung in Form von stochastischen Prozesszeiten und mittels des neu-entwickelten Konzeptes stochastischer Verspätungskostenfunktionen berücksichtigt. Diese Funktionen schätzen die Kosten der Verspätungsausbreitung im Airline-Netzwerk flugspezifisch auf der Basis historischer Betriebsdaten ab, sodass knappe Abfertigungsressourcen am Drehkreuz der Airline den kritischsten Flugzeugumläufen zugeordnet werden können. Das Modell wird innerhalb einer Fallstudie angewendet, um die taktischen Kosten einer Airline in Folge von verschiedenen Flugplanstörungen zu minimieren. Die Analyseergebnisse zeigen, dass die optimale Lösung sehr sensitiv in Bezug auf die Art, den Umfang und die Intensität einer Störung reagiert und es folglich keine allgemeingültige optimale Flugplanwiederherstellung für verschiedene Störungen gibt. Umso dringender wird der Einsatz eines flexiblen und effizienten Optimierungsverfahrens empfohlen, welches die komplexen Ressourcenabhängigkeiten innerhalb eines Airline-Netzwerks berücksichtigt und kontextspezifische Lösungen generiert. Um die Effizienz eines solchen Optimierungsverfahrens zu bestimmen, sollte das damit gewonnene Steuerungspotenzial im Vergleich zu aktuell genutzten Verfahren über einen längeren Zeitraum untersucht werden. Aus den in dieser Dissertation analysierten Störungsszenarien kann geschlussfolgert werden, dass die flexible Standplatzvergabe, Passagier-Direkttransporte, beschleunigte Abfertigungsverfahren und die gezielte Verspätung von Abflügen sehr gute Steuerungsoptionen sind und während 95 Prozent der Saison Anwendung finden könnten, um geringe bis mittlere Verspätungen von Einzelflügen effizient aufzulösen. Bei Störungen, die zu hohen Verspätungen im gesamten Airline-Netzwerk führen, ist eine vollständige Integration aller in Betracht gezogenen Steuerungsoptionen erforderlich, um eine erhebliche Reduzierung der taktischen Kosten zu erreichen. Dabei ist insbesondere die Möglichkeit, Ankunfts- und Abflugzeitfenster zu tauschen, von hoher Bedeutung für eine Airline, um die ihr zugewiesenen ATFM-Verspätungen auf die Flugzeugumläufe zu verteilen, welche die geringsten Einschränkungen im weiteren Tagesverlauf aufweisen. Die Berücksichtigung von Unsicherheiten im nachgelagerten Airline-Netzwerk zeigt, dass eine Optimierung auf Basis deterministischer Verspätungskosten die taktischen Kosten für eine Airline überschätzen kann. Die optimale Flugplanwiederherstellung auf Basis stochastischer Verspätungskosten unterscheidet sich deutlich von der deterministischen Lösung und führt zu weniger Passagierumbuchungen am Drehkreuz. Darüber hinaus ist das vorgeschlagene Modell in der Lage, Flugprioritäten und Airline-interne Kostenwerte für ein zugewiesenes ATFM-Zeitfenster zu bestimmen. Die errechneten Flugprioritäten können dabei vertraulich in Form von optimalen Verspätungszeitfenstern pro Flug an das ATFM übermittelt werden, während die Definition von internen Kostenwerten für ATFM-Zeitfenster die Entwicklung von künftigen Handelsmechanismen zwischen Airlines unterstützen kann.:1 Introduction 2 Status Quo on Airline Operations Management 3 Schedule Recovery Optimization Approach with Constrained Resources 4 Implementation and Application 5 Case Study Analysis 6 ConclusionsAir Traffic Flow Management (ATFM) and airlines use different paradigms for the prioritisation of flights. While ATFM regards each flight as individual entity when it controls sector capacity utilization, airlines evaluate each flight as part of an aircraft rotation, crew pairing and passenger itinerary. As a result, ATFM slot regulations during capacity constraints are poorly coordinated with the resource interdependencies within an airline network, such that the aircraft turnaround -- as the connecting element or breaking point between individual flights in an airline schedule -- is the major contributor to primary and reactionary delays in Europe. This dissertation bridges the gap between both paradigms by developing an integrated schedule recovery model that enables airlines to define their optimal flight priorities for schedule disturbances arising from ATFM capacity constraints. These priorities consider constrained airport resources and different methods are studied how to communicate them confidentially to external stakeholders for the usage in collaborative solutions, such as the assignment of reserve resources or ATFM slot swapping. The integrated schedule recovery model is an extension of the Resource-Constrained Project Scheduling Problem and integrates aircraft turnaround operations with existing approaches for aircraft, crew and passenger recovery. The model is supposed to provide tactical decision support for airline operations controllers at look-ahead times of more than two hours prior to a scheduled hub bank. System-inherent uncertainties about process deviations and potential future disruptions are incorporated into the optimization via stochastic turnaround process times and the novel concept of stochastic delay cost functions. These functions estimate the costs of delay propagation and derive flight-specific downstream recovery capacities from historical operations data, such that scarce resources at the hub airport can be allocated to the most critical turnarounds. The model is applied to the case study of a network carrier that aims at minimizing its tactical costs from several disturbance scenarios. The case study analysis reveals that optimal recovery solutions are very sensitive to the type, scope and intensity of a disturbance, such that there is neither a general optimal solution for different types of disturbance nor for disturbances of the same kind. Thus, airlines require a flexible and efficient optimization method, which considers the complex interdependencies among their constrained resources and generates context-specific solutions. To determine the efficiency of such an optimization method, its achieved network resilience should be studied in comparison to current procedures over longer periods of operation. For the sample of analysed scenarios in this dissertation, it can be concluded that stand reallocation, ramp direct services, quick-turnaround procedures and flight retiming are very efficient recovery options when only a few flights obtain low and medium delays, i.e., 95% of the season. For disturbances which induce high delay into the entire airline network, a full integration of all considered recovery options is required to achieve a substantial reduction of tactical costs. Thereby, especially arrival and departure slot swapping are valuable options for the airline to redistribute its assigned ATFM delays onto those aircraft that have the least critical constraints in their downstream rotations. The consideration of uncertainties in the downstream airline network reveals that an optimization based on deterministic delay costs may overestimate the tactical costs for the airline. Optimal recovery solutions based on stochastic delay costs differ significantly from the deterministic approach and are observed to result in less passenger rebooking at the hub airport. Furthermore, the proposed schedule recovery model is able to define flight priorities and internal slot values for the airline. Results show that the priorities can be communicated confidentially to ATFM by using the concept of 'Flight Delay Margins', while slot values may support future inter-airline slot trading mechanisms.:1 Introduction 2 Status Quo on Airline Operations Management 3 Schedule Recovery Optimization Approach with Constrained Resources 4 Implementation and Application 5 Case Study Analysis 6 Conclusion

Attractiveness-based airline network models with embedded spill and recapture

Purpose: In airline revenue management, the modeling of the spill and recapture effects is essential for an accurate estimation of the passenger flow and the revenue in a flight network. However, as most current approaches toward spill and recapture involve either non-linearity or a tremendous amount of additional variables, it is computationally intractable to apply those techniques to the classical network design and capacity planning models. Design/methodology: We present a new framework that incorporates the spill and recapture effects, where the spill from an itinerary is recaptured by other itineraries based on their attractiveness. The presented framework distributes the accepted demand of an itinerary according to the currently available itineraries, without adding extra variables for the recaptured spill. Due to its compactness, we integrate the framework with the classical capacity planning and network design models. Findings: Our preliminary computational study shows an increase of 1.07% in profitability anda better utilization of the network capacity, on a medium-size North American airline provided by Sabre Airline Solutions. Originality/value: Our investigation leads to a holistic model that tackles the network design and capacity planning simultaneously with an accurate modeling of the spill and re- capture effects.Furthermore, the presented framework for spill and recapture is versatile and can be easily applied to other disciplines such as the hospitality industry and product line design (PLD) problems.Peer Reviewe