Robert L. Hoffman

A Stochastic Integer Program with Dual Network Structure and Its Application to the Ground-Holding Problem

In this paper, we analyze a generalization of a classic network-flow model. The generalization involves the replacement of deterministic demand with stochastic demand. While this generalization destroys the original network structure, we show that the matrix underlying the stochastic model is dual network. Thus, the integer program associated with the stochastic model can be solved efficiently using network-flow or linear-programming techniques. We also develop an application of this model to the ground-holding problem in air-traffic management. The use of this model for the ground-holding problem improves upon prior models by allowing for easy integration into the newly developed ground-delay program procedures based on the Collaborative Decision-Making paradigm.

Collaborative Decision Making in Air Traffic Management: Current and Future Research Directions

Collaborative Decision Making (CDM) embodies a new philosophy for managing air traffic. The initial implementation of CDM in the US has been aimed at Ground Delay Program Enhancements (GDP-E). However, the underlying concepts of CDM have the potential for much broader applicability. This paper reviews on-going and proposed CDM research streams. The topic areas discussed include: ground delay program enhancements; collaborative routing; performance monitoring and analysis; collaborative resource allocation mechanisms; game theory models for analyzing CDM procedures and information exchange; collaborative information collection and distribution.

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.

A Comparison of Formulations for the Single-Airport Ground-Holding Problem with Banking Constraints

Both the single-airport ground-holding problem (GH) and the multi-airport ground-holding problem can be extended by the addition of banking constraints to accommodate the hubbing operations of major airlines. These constraints enforce the desire of airlines to land certain groups of flights, called banks, within fixed time windows, thus preventing the propagation of delays throughout their entire operation. GH can be formulated as a transportation problem and readily solved. But in the presence of banking constraints, GH becomes a difficult integer programming problem. In this paper, we construct five different models of the single-airport ground-holding problem with banking constraints (GHB). The models are evaluated both computationally and analytically. For two of the models, we show that the banking constraints induce facets of the convex hull of the set of integer solutions. In addition, we explore a linear transformation of variables and a branching technique.

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.

The rate control index for traffic flow

The objective of air traffic flow management is to maintain safe and efficient use of airspace and airports by regulating the flow of traffic. We introduce a single-valued metric for post-operatively rating the performance of achieved traffic flow against targeted traffic flow. We provide variations on the metric, one of which factors out stochastic conditions upon which a plan is formulated, and show how these improve on current traffic control analysis techniques. The core of the metric is intuitive and simple, yet leads to an interesting optimization problem that can be efficiently solved via dynamic programming. Numerical results of the metric are given as well as a sample of the type of analysis that should follow a low rating by the metric. Although this metric was originally developed to rate the performance of ground delay programs, it is equally applicable to any setting in which the flow of discrete objects such as vehicles is controlled and later evaluated.

Design Challenges for a Shadow Mode Assessment Tool for Air Traffic Management (Invited)

Traditionally, the rate of acceptance of advanced concepts and technologies (C&T) for air traffic management in the National Airspace System (NAS) has been slow, primarily hampered by the inability to show compatibility with other C&T or with existing systems, processes, and procedures. NASA is developing a Shadow Mode Assessment using Realistic Technologies for the NAS (SMART NAS) technology that will allow for development, testing, and demonstration of novel C&T at the live, virtual, and constructive levels. SMART NAS will support a broad user base and may eventually become a community resource. We discuss challenges associated with development of a SMART NAS technology and describe a component-based architecture to address those challenges.