A Dynamic Stochastic Model for Converging Inbound Air Traffic

Weather accounts for the majority of congestion in the National Airspace System which highlights the importance of addressing weather uncertainty to mitigate delays, and this paper presents an effort in this direction. Firstly, a new dynamic stochastic 0-1 Integer Programming (IP) model is proposed, which models the Single Airport Ground Holding Problem (SAGHP) with respect to uncertainty in the separation between flights instead of Airport Acceptance Rate (AAR) or landing capacity. Uncertainty in separation according to different weather conditions is represented through the scenario tree by using stochastic linear programming. Considering time separation constraints instead of AAR constraints, our model is able to schedule a more accurate plan for the individual flight in minutes. Secondly, a converging inbound air traffic model is formulated based on our dynamic stochastic IP model. We address a problem involving two paths inbound air traffic merging into a single airport in which uncertainty in separation from Minute-In-Trail restrictions is considered. Although First Come, First Serve policy is still obeyed by flights on the same path, the experimentation has shown that, allowing flights on different paths to switch arrival orders can help reduce the total delays. Finally, in order to tackle the running time problem faced by the disaggregate integer model we built, we introduce dual decomposition method into the model to improve the computing efficiency. The original problem is decomposed scenario by scenario into several sub-problems based on the dual decomposition method; then a parallel computing algorithm is developed to handle these sub-problems. Such combination increases the model\u27s computational efficiency

COMPUTATIONALLY TRACTABLE STOCHASTIC INTEGER PROGRAMMING MODELS FOR AIR TRAFFIC FLOW MANAGEMENT

A primary objective of Air Traffic Flow Management (ATFM) is to ensure the orderly flow of aircraft through airspace, while minimizing the impact of delays and congestion on airspace users. A fundamental challenge of ATFM is the vulnerability of the airspace to changes in weather, which can lower the capacities of different regions of airspace. Considering this uncertainty along with the size of the airspace system, we arrive at a very complex problem. The development of efficient algorithms to solve ATFM problems is an important and active area of research. Responding to predictions of bad weather requires the solution of resource allocation problems that assign a combination of ground delay and route adjustments to many flights. Since there is much uncertainty associated with weather predictions, stochastic models are necessary. We address some of these problems using integer programming (IP). In general, IP models can be difficult to solve. However, if "strong" IP formulations can be found, then problems can be solved quickly by state of the art IP solvers. We start by describing a multi-period stochastic integer program for the single airport stochastic dynamic ground holding problem. We then show that the linear programming relaxation yields integer optimal solutions. This is a fairly unusual property for IP formulations that can significantly reduce the complexity of the corresponding problems. The proof is achieved by defining a new class of matrices with the Monge property and showing that the formulation presented belongs to this class. To further improve computation times, we develop alternative compact formulations. These formulations are extended to show that they can also be used to model different concepts of equity and fairness as well as efficiency. We explore simple rationing methods and other heuristics for these problems both to provide fast solution times, but also because these methods can embody inherent notions of fairness. The initial models address problems that seek to restrict flow into a single airport. These are extended to problems where stochastic weather affects en route traffic. Strong formulations and efficient solutions are obtained for these problems as well

On the statistical description of the inbound air traffic over Heathrow airport

We present a model to describe the inbound air traffic over a congested hub. We show that this model gives a very accurate description of the traffic by the comparison of our theoretical distribution of the queue with the actual distribution observed over Heathrow airport. We discuss also the robustness of our model

Real-time adaptive aircraft scheduling

One of the most important functions of any air traffic management system is the assignment of ground-holding times to flights, i.e., the determination of whether and by how much the take-off of a particular aircraft headed for a congested part of the air traffic control (ATC) system should be postponed in order to reduce the likelihood and extent of airborne delays. An analysis is presented for the fundamental case in which flights from many destinations must be scheduled for arrival at a single congested airport; the formulation is also useful in scheduling the landing of airborne flights within the extended terminal area. A set of approaches is described for addressing a deterministic and a probabilistic version of this problem. For the deterministic case, where airport capacities are known and fixed, several models were developed with associated low-order polynomial-time algorithms. For general delay cost functions, these algorithms find an optimal solution. Under a particular natural assumption regarding the delay cost function, an extremely fast (O(n ln n)) algorithm was developed. For the probabilistic case, using an estimated probability distribution of airport capacities, a model was developed with an associated low-order polynomial-time heuristic algorithm with useful properties

Dynamic Air Holding Program for Delay Assignment applied to Barcelona Airport Case

Nowadays, the aircraft is the most used transport to travel between two very distanced places since it is the fastest way. For these last years, the demand of flights has been increasing immensely, so the airports have been also suffering the same increase in workload. Congestion is the word for the imbalance between demand and capacity. After applying a Ground Holding Program (GHP) optimization process before departure to solve this problem in a previous work [1], in this project the Air Holding Program (AHP) is presented in order to minimize the economic costs once in the landing phase. The main goal of this final degree project is to implement a basic model of AHP to minimize the delay costs near the single destination airport, Barcelona-El Prat in this case. The model of AHP is based on a dynamic stochastic GHP. The problem is solved using Gurobi libraries. Firstly, a pre-tactical phase in [1] of GHP is applied to make flights wait on ground according to capacity constraints in the Barcelona Airport. Then, once the flights are already flying towards the destination and entering the analysed area (500 km from destination airport), these flights will perform a Free Route Airspace (FRA) route in order to make them fly a straight route trajectory to possibly shorten the flight duration, which will cause that the arrival queue be again disordered making the capacity constraint again violated. In order to minimize the air delay costs, a second optimization to assign air delay is applied called AHP. Once the flights are leaving this airspace, they will be communicated their final assigned holding. Finally when they are entering the landing phase, they should first pass through the holding procedure to hold the time needed according to the delay assigned. Some of the conclusions after this research is that if capacity is reduced in destination airport, firstly a GHP can be applied before departure [1]. Then, an AHP can be applied for a second optimization purpose. If traffic is directly taken to be applied an AHP, the capacity flexibility is very reduced, while using pre-tactical regulation the capacity could be as small as desired. This outlines the advantage of using GHP and AHP together. Furthermore, although the main objective is to minimize the delay costs, if the flights are arriving earlier than scheduled in the most optimal case, the delays could be negative values, which means that costs are saved

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

MODELS AND SOLUTION ALGORITHMS FOR EQUITABLE RESOURCE ALLOCATION IN AIR TRAFFIC FLOW MANAGEMENT

Population growth and economic development lead to increasing demand for travel and pose mobility challenges on capacity-limited air traffic networks. The U.S. National Airspace System (NAS) has been operated near the capacity, and air traffic congestion is expected to remain as a top concern for the related system operators, passengers and airlines. This dissertation develops a number of model reformulations and efficient solution algorithms to address resource allocation problems in air traffic flow management, while explicitly accounting for equitable objectives in order to encourage further collaborations by different stakeholders. This dissertation first develops a bi-criteria optimization model to offload excess demand from different competing airlines in the congested airspace when the predicted traffic demand is higher than available capacity. Computationally efficient network flow models with side constraints are developed and extensively tested using datasets obtained from the Enhanced Traffic Management System (ETMS) database (now known as the Traffic Flow Management System). Representative Pareto-optimal tradeoff frontiers are consequently generated to allow decision-makers to identify best-compromising solutions based on relative weights and systematical considerations of both efficiency and equity. This dissertation further models and solves an integrated flight re-routing problem on an airspace network. Given a network of airspace sectors with a set of waypoint entries and a set of flights belonging to different air carriers, the optimization model aims to minimize the total flight travel time subject to a set of flight routing equity, operational and safety requirements. A time-dependent network flow programming formulation is proposed with stochastic sector capacities and rerouting equity for each air carrier as side constraints. A Lagrangian relaxation based method is used to dualize these constraints and decompose the original complex problem into a sequence of single flight rerouting/scheduling problems. Finally, within a multi-objective utility maximization framework, the dissertation proposes several practically useful heuristic algorithms for the long-term airport slot assignment problem. Alternative models are constructed to decompose the complex model into a series of hourly assignment sub-problems. A new paired assignment heuristic algorithm is developed to adapt the round robin scheduling principle for improving fairness measures across different airlines. Computational results are presented to show the strength of each proposed modeling approach

다중공항에서 지상 지연 프로그램 발생시 지연전파를 고려한 항공사의 운항 일정 변경

학위논문(석사) -- 서울대학교대학원 : 공과대학 산업공학과, 2022. 8. 문일경.본 연구의 목적은 항공 교통을 제어하는 중요한 수단 중 하나인 지상 지연 프로그램(GDP)이 발생할 경우 공항의 변경된 수용력에 대응하도록 항공사의 관점에서 항공편을 재조정하는데 도움을 주는 것이다. 단일 공항이 아닌 다중 공항으로 확장하여 동일한 공항뿐 아니라 다른 공항으로부터의 지연 전파를 고려했으며, 항공기 및 승무원의 계획된 일정에서 발생하는 현실적인 비용을 포함했다. GDP가 발행되면 항공사들은 변경된 시간대에 맞춰 항공편을 재조정할 수 있는 짧은 시간이 주어진다. 각 공항에는 수용력이 있으며, 특히 들어오는 항공기를 수용할 수 있는 용량인 공항 수용률(AAR)이 있다. 이 연구에서 비행 스케줄을 재조정하기 위해 혼합 정수 선형 프로그래밍 모델을 세웠다. 또한, 미래의 불확실성을 다루기 위해, MILP의 두 가지 버전을 사용하였다. AAR이 어느 시점에 다시 바뀌는 시나리오를 만든 후, 각 시나리오 별로 총 관련 비용을 최소화하는 솔루션을 도출하는 최적 모델과 모든 시나리오 솔루션의 총 관련 비용의 기댓값을 최소화하는 솔루션을 도출하는 추계 모델을 제시하고 서로 비교하였다The purpose of this thesis is to reschedule flights from the airline company’s perspective to correspond to the airport’s changed capacity in the event of a ground delay program (GDP), one of the important means of controlling air traffic. We considered delay propagation not only within the same airport but within other airports by extending the setup to include several airports rather than a single airport. We also included realistic costs from planned schedules of the aircraft and crew. When a GDP is issued, airlines are given a short time to reschedule flights in time for the changed slot. Each airport has its own capacity, especially the airport acceptance rate (AAR), which is a capacity that can accommodate incoming aircraft. We formulated a mixed-integer linear programming (MILP) model to reschedule flights. To handle the uncertainty of future scheduling, two versions of the MILP model may be applied. With scenarios in which the AAR changes again, an optimal model that obtains a minimizing total relevant cost in each scenario solution and a stochastic model solution that obtains a minimizing expectation of the total relevant cost of all scenarios are presented and compared.Chapter 1 Introduction 1 Chapter 2 Literature review 3 Chapter 3 Mathematical model 5 3.0 Model description 5 3.1 Multi-airport Scenario-based Optimal Rescheduling Problem 10 3.2 Multi-airport Scenario-based Stochastic Rescheduling Problem 13 Chapter 4 Computational experiments 14 4.0 Settings 14 4.1 Experiment 1 16 4.2 Experiment 2 18 4.3 Experiment 3 19 4.4 Experiment 4 20 Chapter 5 Conclusions 25 Appendix 27 Appendix A. 27 Appendix B. 28 Bibliography 31 국문초록 35석

The single airport static stochastic ground holding problem

Thesis (M.S.)--Massachusetts Institute of Technology, Sloan School of Management, 1998.Includes bibliographical references (leaves 45-46).by Ryan M. Rikfin.M.S