Avijit Mukherjee

A Dynamic Stochastic Model for the Single Airport Ground Holding Problem

In this paper, we present a dynamic stochastic integer programming (IP) model for the single airport ground holding problem, in which ground delays assigned to flights can be revised during different decision stages, based on weather forecasts. The performance gain from our model is particularly significant in the following cases: (1) under stringent ground holding policy, (2) when an early ground delay program (GDP) cancellation is likely, and (3) for airports where the ratio between adverse and fair weather capacities is lower. The choice of ground delay cost component in the objective function strongly affects the allocation policy. When it is linear, the optimal solution involves releasing the long-haul flights at or near their scheduled departure times and using the short-haul flights to absorb delays if low-capacity scenarios eventuate. This policy resembles the current practice of exempting long-distance flights during ground delay programs. For certain convex ground delay cost functions, the spread of ground delay is more or less uniform across all categories of flights, which makes the overall delay assignment more equitable. Finally, we also present a methodology that could enable intra-airline flight substitutions by airlines after our model has been executed and scenario-specific slots have been assigned to all flights, and hence to the airlines that operate them. This makes our model applicable under the collaborative decision making (CDM) paradigm by allowing airlines to perform cancellations and substitutions and hence reoptimize their internal delay cost functions.

Modeling and Optimization in Traffic Flow Management

Traffic flow management (TFM) allocates the various airport, airspace, and other resources to maintain an efficient traffic flow consistent with safety. TFM is a complex area of research involving the disciplines of operations research, guidance and control, human factors, and software engineering. Hundreds of human operators make TFM decisions that involve tens of thousands of aircraft, en route air traffic control centers, the Federal Aviation Administrations System Command Center, and many airline operation centers. This paper provides an overview of how TFM decisions are made today and challenges facing the system in the future, and reviews modeling and optimization approaches for facilitating system-wide modeling, performance assessments, and system-level optimization of the national airspace system in the presence of both en route and airport capacity constraints.

Ground Delay Program Planning Under Uncertainty Based on the Ration-by-Distance Principle

This paper presents ration-by-distance (RBD), a new allocation method to be used in planning ground delay programs (GDPs) for traffic flow management. It is shown that RBD minimizes total expected delay, under certain assumptions related to the manner in which GDPs are dynamically controlled. On the other hand, RBD taken to the extreme has poor characteristics with respect to the equity of the allocation it produces. To address this issue, we propose a constrained version of RBD as a practical alternative to allocation procedures used in operations today. It is shown that this algorithm has superior overall performance in terms of efficiency and equity relative to existing procedures.

Sequential Traffic Flow Optimization with Tactical Flight Control Heuristics

‡A sequential optimization method is applied to manage air traffic flow under uncertainty in airspace capacity and demand. To support its testing, a decision support system is developed by integrating a deterministic integer programming model for assigning delays to aircraft under en route capacity constraints to reactively account for system uncertainties. To reduce computational complexity, the model assigns only departure controls, while a tactical control loop consisting of a shortest path routing algorithm and an airborne holding algorithm refines the strategic plan to keep flights from deviating into capacity constrained airspace. This integrated approach is used to conduct thirty-two, 6-hour fast-time simulation experiments to explore variations in the number and severity of departure controls, tactical reroutes, and airborne holding controls. Three feasible types of traffic flow controls emerged. The first type relied primarily on departure controls and strategic reroutes on the 300 to 400 nmi look-ahead horizon and worked best when rerouting occurred at a frequency of 10 to 15 minutes. The second type generated more tactical reroutes on the 200 ‐ 300 nmi look-ahead horizon and required little airborne holding or pre-departure control when rerouting occurred at a frequency of 5 minutes. The last type relied heavily on airborne holding controls and infrequent updates to the weather avoidance reroutes. This last type was the least desirable solution due to the impact of its airborne holding on airspace complexity and airspace users.

Air Traffic Flow Management

Air transportation systems are some of the most complex logistical systems imaginable. The world’s airlines transported over 2.2 billion passengers in 2008, and transported approximately 40% of world trade (measured by value). There are nearly 2,000 airlines worldwide, which have a total fleet of nearly 23,000 aircraft and serve some 3,750 airports through a route network of several million miles managed by around 160 air navigation service providers.

Central East Pacific Flight Scheduling

*† ‡ This paper examines the implications of strategically scheduling flights on user-preferred routes in the Central East Pacific to reduce trajectory crossing points. After first casting the flight scheduling problem in terms of a job shop scheduling problem, a 0-1 integer programming model is used to calculate the optimal departure and en route controls required to generate feasible flight schedules. To enhance the solution, a ration-by-schedule based heuristic is introduced to transform the original model into a subset of problems. By varying attributes of the machines in the job shop scheduling formation, two distinct types of feasible schedules are obtained. The first type of schedules are highly restrictive yet but free of all four-dimensional trajectory crossing points, while the second type are less restrictive but may require limited tactical flight separation maneuvers to alleviate residual crossing points. The average adjusted time savings per flight varied between 1.8 minutes and 4.6 minutes per flight when allowing for both strategic flight scheduling and user-preferred flight routing.

Design and Evaluation of a Dynamic Programming Flight Routing Algorithm Using the Convective Weather Avoidance Model

The optimization of tra! c flows in congested airspace with varying convective weather is a challenging problem. One approach is to generate shortest routes between origins and destinations while meeting airspace capacity constraint in the presence of uncertainties, such as weather and airspace demand. This study focuses on development of an optimal flight path search algorithm that optimizes national airspace system throughput and e! ciency in the presence of uncertainties. The algorithm is based on dynamic programming and utilizes the predicted probability that an aircraft will deviate around convective weather. It is shown that the running time of the algorithm increases linearly with the total number of links between all stages. The optimal routes minimize a combination of fuel cost and expected cost of route deviation due to convective weather. They are considered as alternatives to the set of coded departure routes which are predefined by FAA to reroute pre-departure flights around weather or air tra! c constraints. A formula, which calculates predicted probability of deviation from a given flight path, is also derived. The predicted probability of deviation is calculated for all path candidates. Routes with the best probability are selected as optimal. The predicted probability of deviation serves as a computable measure of reliability in pre-departure rerouting. The algorithm can also be extended to automatically adjust its design parameters to satisfy the desired level of reliability.

Classification of Days Using Weather Impacted Traffic in the National Airspace System

Classification of days based on weather impact on the National Airspace System is essential to evaluate the effectiveness of traffic management decisions in the past, which ultimately can improve the operational readiness when similar events occur in the future. To achieve this goal, this paper presents a methodology to classify days based on severe weather impact on traffic. A daily index of the impact of severe weather on scheduled traffic flow, termed as the Weather Impacted Traffic Index, is used as an input to perform the classification. First, a factor analysis is performed to identify the dominant weather patterns that occur on various days. Six major weather factors are identified based on this analysis. Factor scores are obtained for each day based on the day’s weather location and severity. Days are clustered using Ward’s minimum-variance method applied to the daily factor scores. The outcome of the analysis is a set of 21 clusters and days within each cluster. While the weather and traffic in the days belonging to a common cluster are similar, they are not completely identical. Following the classification of days, the reroute advisories are analyzed to identify the frequently used routes on days belonging to various clusters. It is observed that the most frequently used reroutes on days that belong to a particular cluster exhibit similarity to the National Playbook routes designed to mitigate weather impact on those days, which is an intuitive result that is supported by data analysis. I. INTRODUCTION dverse weather reduces the capacity of the National Airspace System (NAS) by partially or completely blocking routes, waypoints, and airports. During such conditions, traffic managers at the FAA’s Air Traffic Control System Command Center (ATCSCC) and dispatchers at various Airlines’ Operations Center (AOC) collaborate to mitigate the demand-capacity imbalance caused by weather. The end result is the implementation of a set of Traffic Flow Management (TFM) initiatives such as ground delay programs, reroute advisories, flow metering, and ground stops. The performance of the TFM control actions is measured using a set of metrics such as total delay, cancellations, diversions, additional flying time, airborne holding time, loss of predictability of operations, etc. These performance metrics vary from day-to-day based on the severity, location, and characteristics of weather as well as the effectiveness of TFM control actions. If a particular day can be characterized as being similar, in terms of weather and traffic, to a few days in the past, then the TFM control actions from those days could serve as a basis for strategizing TFM on the current day of operation. A thorough post-operational evaluation of TFM actions in the past can reveal the potential areas of improvement, if possible. Doing so will better equip the NAS users (i.e., airlines) and the service provider (i.e., ATCSCC) with information to mitigate weather impact, and hence, improve the operational readiness. It will also improve the predictability of TFM control actions if the weather forecasts are reasonably accurate on a given day. A successful classification of days is necessary to evaluate the effectiveness of TFM actions on days that are similar. This paper presents a methodology to classify days based on weather and traffic pattern and to cluster them into groups. Days belonging to the same cluster may not be identical, but are statistically close enough. The Weather Impacted Traffic Index (WITI) measures the location and severity of weather and its impact on traffic.

Similar Days in the NAS: an Airport Perspective

‡On any given day, constraints in the National Airspace System, for instance weather, necessitate the implementation of Traffic Flow Management initiatives, such as Ground Delay Programs. The parameters associated with these initiatives, for example the location, scope, duration, etc., are typically left to human decision makers, who must rely on intuition, past experience, and weather and traffic forecasts. Although the decisions of these traffic flow specialists are recorded on a daily basis, few studies have attempted to apply data mining techniques to these archives in an attempt to identify patterns and past decisions that could ultimately be used to influence future decision-making. The goal of this study is to take a preliminary step towards informing future decision-making by proposing a technique for identifying similar days in the National Airspace System in terms of the Ground Delay Programs that were operationally implemented. Hence an airport perspective is being taken to identify these similar days, as opposed to considering possible airspace features. A modified k-means clustering algorithm is applied to all days in 2011, resulting in the identification of 18 clusters that represent unique combinations of Ground Delay Program that were historically implemented. A given day was described in terms of the presence or absence of 33 features that were a combination of Ground Delay Program locations and causes. By far the largest cluster that was identified consisted of 73 days on which low ceiling related Ground Delay Programs impacted San Francisco International Airport. In an attempt to verify the stated cause of the Ground Delay Programs, an Expectation Maximization clustering algorithm was applied to the 8,760 hourly Meteorological Aerodrome Reports, scheduled arrival rate and Ground Delay Program start and end time records for 2011. In general, clusters were identified that corroborated the stated causes of the Ground Delay Programs. However, these clusters often contained a significant number of members for which a Ground Delay Program did not occur. Findings from this initial study indicate that it is possible to identify similar days under which the National Airspace System operates, and clustering techniques appear to be promising methods for identifying the major causes of Ground Delay Programs.

Predicting Ground Delay Program at an Airport Based on Meteorological Conditions

In this paper, we present two supervised-learning models, logistic regression and decision tree, to predict occurrence of a ground delay program at an airport based on meteorological conditions and scheduled traffic demand. Predicting the occurrence of ground delay programs can help the Federal Aviation Administration traffic managers and airline dispatchers prepare mitigation strategies to reduce impact of adverse weather. The models are developed for two major U.S. airports: Newark Liberty and San Francisco International airports. The logistic regression model estimates the probability that a ground delay program will occur during a given hour. The decision tree model, on the other hand, classifies whether or not a ground delay program is likely during an hour based on the input variables. Results indicate both models perform significantly better than a purely random prediction of ground delay program occurrence at the two airports. The degree to which various input variables impact the probability of ground delay program vary between the two airports. While the enroute convective weather is a dominant factor causing ground delay programs at Newark Liberty Intl. airport, poor visibility and low cloud ceiling caused by marine stratus are major drivers of ground delay program occurrence at San Francisco Intl. airport.