Stochastic Modelling of Aircraft Queues: A Review

In this paper we consider the modelling and optimal control of queues of aircraft waiting to use the runway(s) at airports, and present a review of the related literature. We discuss the formulation of aircraft queues as nonstationary queueing systems and examine the common assumptions made in the literature regarding the random distributions for inter-arrival and service times. These depend on various operational factors, including the expected level of precision in meeting pre-scheduled operation times and the inherent uncertainty in airport capacity due to weather and wind variations. We also discuss strategic and tactical methods for managing congestion at airports, including the use of slot controls, ground holding programs, runway configuration changes and aircraft sequencing policies

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

Air traffic flow management at airports : a unified optimization approach

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 137-140).The cost of air traffic delays is well documented, and furthermore, it is known that the significant proportion of delays is incurred at airports. Much of the air traffic flow management literature focuses on traffic flows between airports in a network, and when studies have focused on optimizing airport operations, they have focused largely on a single aspect at a time. In this thesis, we fill an important gap in the literature by proposing unified approaches, on both strategic and tactical levels, to optimizing the traffic flowing through an airport. In particular, we consider the entirety of key problems faced at an airport: a) selecting a runway configuration sequence; b) determining the balance of arrivals and departures to be served; c) assigning flights to runways and determining their sequence; d) determining the gate-holding duration of departures and speedcontrol of arrivals; and e) routing flights to their assigned runway and onwards within the terminal area. In the first part, we propose an optimization approach to solve in a unified manner the strategic problems (a) and (b) above, which are addressed manually today, despite their importance. We extend the model to consider a group of neighboring airports where operations at different airports impact each other due to shared airspace. We then consider a more tactical, flight-by-flight, level of optimization, and present a novel approach to optimizing the entire Airport Operations Optimization Problem, made up of subproblems (a) - (e) above. Until present, these have been studied mainly in isolation, but we present a framework which is both unified and tractable, allowing the possibility of system-optimal solutions in a practical amount of time. Finally, we extend the models to consider the key uncertainties in a practical implementation of our methodologies, using robust and stochastic optimization. Notable uncertainties are the availability of runways for use, and flights' earliest possible touchdown/takeoff times. We then analyze the inherent trade-off between robustness and optimality. Computational experience using historic and manufactured datasets demonstrates that our approaches are computationally tractable in a practical sense, and could result in cost benefits of at least 10% over current practice.by Michael Joseph Frankovich.Ph.D

A Hybrid Tabu/Scatter Search Algorithm for Simulation-Based Optimization of Multi-Objective Runway Operations Scheduling

As air traffic continues to increase, air traffic flow management is becoming more challenging to effectively and efficiently utilize airport capacity without compromising safety, environmental and economic requirements. Since runways are often the primary limiting factor in airport capacity, runway operations scheduling emerge as an important problem to be solved to alleviate flight delays and air traffic congestion while reducing unnecessary fuel consumption and negative environmental impacts. However, even a moderately sized real-life runway operations scheduling problem tends to be too complex to be solved by analytical methods, where all mathematical models for this problem belong to the complexity class of NP-Hard in a strong sense due to combinatorial nature of the problem. Therefore, it is only possible to solve practical runway operations scheduling problem by making a large number of simplifications and assumptions in a deterministic context. As a result, most analytical models proposed in the literature suffer from too much abstraction, avoid uncertainties and, in turn, have little applicability in practice. On the other hand, simulation-based methods have the capability to characterize complex and stochastic real-life runway operations in detail, and to cope with several constraints and stakeholders’ preferences, which are commonly considered as important factors in practice. This dissertation proposes a simulation-based optimization (SbO) approach for multi-objective runway operations scheduling problem. The SbO approach utilizes a discrete-event simulation model for accounting for uncertain conditions, and an optimization component for finding the best known Pareto set of solutions. This approach explicitly considers uncertainty to decrease the real operational cost of the runway operations as well as fairness among aircraft as part of the optimization process. Due to the problem’s large, complex and unstructured search space, a hybrid Tabu/Scatter Search algorithm is developed to find solutions by using an elitist strategy to preserve non-dominated solutions, a dynamic update mechanism to produce high-quality solutions and a rebuilding strategy to promote solution diversity. The proposed algorithm is applied to bi-objective (i.e., maximizing runway utilization and fairness) runway operations schedule optimization as the optimization component of the SbO framework, where the developed simulation model acts as an external function evaluator. To the best of our knowledge, this is the first SbO approach that explicitly considers uncertainties in the development of schedules for runway operations as well as considers fairness as a secondary objective. In addition, computational experiments are conducted using real-life datasets for a major US airport to demonstrate that the proposed approach is effective and computationally tractable in a practical sense. In the experimental design, statistical design of experiments method is employed to analyze the impacts of parameters on the simulation as well as on the optimization component’s performance, and to identify the appropriate parameter levels. The results show that the implementation of the proposed SbO approach provides operational benefits when compared to First-Come-First-Served (FCFS) and deterministic approaches without compromising schedule fairness. It is also shown that proposed algorithm is capable of generating a set of solutions that represent the inherent trade-offs between the objectives that are considered. The proposed decision-making algorithm might be used as part of decision support tools to aid air traffic controllers in solving the real-life runway operations scheduling problem

Incorporating declared capacity uncertainty in optimizing airport slot allocation

Slot allocation is the mechanism used to allocate capacity at congested airports. A number of models have been introduced in the literature aiming to produce airport schedules that optimize the allocation of slot requests to the available airport capacity. A critical parameter affecting the outcome of the slot allocation process is the airport’s declared capacity. Existing airport slot allocation models treat declared capacity as an exogenously defined deterministic parameter. In this presentation we propose a new robust optimization formulation based on the concept of stability radius. The proposed formulation considers endogenously the airport’s declared capacity and expresses it as a function of its throughput. We present results from the application of the proposed approach to a congested airport and we discuss the trade-off between the declared capacity of the airport and the efficiency of the slot allocation process

Stochastic Runway Scheduling using Simheuristics

Runway scheduling (also known as “aircraft sequencing”) problems involve micromanaging the sequences of landings and take-offs at an airport in order to reduce costly flight delays. The earliest versions of these problems were both static and deterministic, with all relevant information assumed known and unchanging. Under such assumptions one obtains an NP-hard combinatorial optimisation problem, in which the optimal runway sequences depend on required time separations between different aircraft weight classes. In reality, though, the problem is both stochastic and dynamic, as air traffic controllers make decisions based on the latest estimated times of arrival (ETA) for enroute aircraft, weather conditions and other factors that evolve in unpredictable ways over time. In recent years, some progress has been made in applying stochastic programming methods to these problems, but even these methods are usually based on highly simplified problem formulations. In this talk we consider a new problem formulation in which the “system state” at any given time includes hundreds of variables evolving via continuous-time stochastic processes. With conventional dynamic programming methods being out of the question, we consider an approach based on the emerging field of “simheuristics” and demonstrate the advantages of using this approach as opposed to an alternative based on deterministic forecasts

A New Simheuristic Approach for Stochastic Runway Scheduling

We consider a stochastic, dynamic runway scheduling problem involving aircraft landings on a single runway. Sequencing decisions are made with knowledge of the estimated arrival times (ETAs) of all aircraft due to arrive at the airport, and these ETAs vary according to continuous-time stochastic processes. Time separations between consecutive runway landings are modeled via sequence dependent Erlang distributions and are affected by weather conditions, which also evolve continuously over time. The resulting multi-stage optimization problem is intractable using exact methods and we propose a novel simheuristic approach, based on the application of methods analogous to variable neighborhood search (VNS) in a high-dimensional stochastic environment. Our model is calibrated using flight tracking data for over 98,000 arrivals at Heathrow Airport. Results from numerical experiments indicate that our proposed simheuristic algorithm outperforms an alternative based on deterministic forecasts under a wide range of parameter values, with the largest benefits being seen when the underlying stochastic processes become more volatile and also when the on-time requirements of individual flights are given greater weight in the objective function

Stochastic programming methods for scheduling of airport runway operations under uncertainty

Runway systems at airports have been identified as a major source of delay in the aviation system and efficient runway operations are, therefore, important to maintain and/or increase the capacity of the entire aviation system. The goal of the airport runway scheduling problem is to schedule a set of aircraft and minimize a given objective while maintaining separation requirements and enforcing other operational constraints. Uncertain factors such as weather, surrounding traffic and pilot behavior affect when aircraft can be scheduled, and these factors need to be considered in planning models. In this thesis we propose two stochastic programs to address the stochastic airport runway scheduling problem and similarly structured machine scheduling problems. In the first part, we develop a two-stage stochastic integer programming model and analyze it by developing alternative formulations and solution methods. As part of our analysis, we first show that a restricted version of the stochastic runway scheduling problem is equivalent to a machine scheduling problem on a single machine with sequence dependent setup times and stochastic due dates. We then extend this restricted model by considering characteristics specific to the runway scheduling problem and present two different stochastic integer programming models. We derive some tight valid inequalities for these formulations, and we propose a solution methodology based on sample average approximation and Lagrangian based scenario decomposition. Realistic data sets are then used to perform a detailed computational study involving implementations and analyses of several different configurations of the models. The results from the computational tests indicate that practically implementable truncated versions of the proposed solution algorithm almost always produce very high quality solutions. In the second part, we propose a sampling based stochastic program for a general machine scheduling problem with similar characteristics as the airport runway scheduling problem. The sampling based approach allows us to capture more detailed aspects of the problem, such as taxiway operations crossing active runways. The model is based on the stochastic branch and bound algorithm with several enhancements to improve the computational performance. More specifically, we incorporate a method to dynamically update the sample sizes in various parts of the branching tree, effectively decreasing the runtime without worsening the solution quality. When applied to runway scheduling, the algorithm is able to produce schedules with makespans that are 5% to 7% shorter than those obtained by optimal deterministic methods. Additional contributions in this thesis include the development of a global cost function, capturing all relevant costs in airport runway scheduling and trading off different, sometimes conflicting, objectives. We also analyze the impact of including environmental factors in the scheduling process.PhDCommittee Chair: Clarke, John-Paul; Committee Co-Chair: Johnson, Ellis; Committee Member: Ahmed, Shabbir; Committee Member: Sokol, Joel; Committee Member: Solak, Sena

A Simheuristic Method for Airport Runway Scheduling

Runway scheduling (also known as aircraft sequencing) involves controlling the sequence of aircraft landings on a runway in order to optimise delay-related performance measures. In practice, air traffic controllers might use a ‘first-come-first-served’ policy so that aircraft land in the same order that they arrive in the terminal area, but this is not always the most efficient approach, as the separation requirements between consecutive aircraft pairs also depend on aircraft weight classes – with larger gaps usually required if the leading aircraft is in the ‘heavy’ class. In the academic literature, this type of problem has been formulated as a multi-objective combinatorial optimisation problem. Some classical formulations assume that the problem is both static (i.e. the landing sequence only needs to be determined once, without any subsequent updating) and deterministic (i.e. all relevant information is known, without any uncertainty). However, in reality, the problem is both dynamic and stochastic. In this talk we consider a dynamic, stochastic runway scheduling problem in which the system state at any point in time is high-dimensional and includes the latest estimated times of arrival (ETAs) of planes due to land at the airport, the latest positions of aircraft that have already been ‘queued’ for landing, and also the weather conditions and latest forecast. The ETAs and weather forecasts vary according to continuous-time stochastic processes. The problem is too complicated to be solved using exact methods and we therefore introduce a novel simheuristic method, which involves continuously simulating the performances of various possible landing sequences and using a ranking and selection method to update the hypothesised ‘optimal’ sequence. Preliminary results suggest that our simheuristic method can outperform alternative heuristics that use ‘expected value’ estimates based on the latest system information and treat the problem as if it were deterministic