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Unmanned aircraft systems must demonstrate a capability to sense and avoid air traffic as part of a layered conflict management system to enable safe operations in the National Airspace System. During operations, an unmanned aircraft system should attempt to remain "well clear" to minimize the need for a collision avoidance action. Previously, a well-clear definition was adopted for large unmanned aircraft systems; however, this definition is not appropriate for small unmanned aircraft system weighing less than 55 lb operating at low altitudes. In response, this paper outlines research toward a definition of well clear for small unmanned aircraft systems, based on airborne collision risk, for midterm concepts of operations at low altitudes in nonterminal airspace.

In this paper, we consider the air-traffic conflictresolution problem and develop an optimization model to identify the required heading and speed changes of aircraft to avoid conflict such that fuel costs are minimized. Nonconvex fuel functions in the optimization problem are modeled through tight linear approximations, which enable the formulation of the problem as a mixed-integer linear program. The significance of the developed model is that fuel-optimal conflict-resolution maneuvers can be identified in near real time, even for conflicts involving a large number of aircraft. Computational tests based on realistic air-traffic scenarios demonstrate that conflicts involving up to 15 aircraft can be solved in less than 10 s with an optimality gap of around 0.02%.

With the forecast increase in air traffic demand over the next decades, it is imperative to develop tools to provide traffic flow managers with the information required to support decision making. In particular, decision-support tools for traffic flow management should aid in limiting controller workload and complexity, while supporting increases in air traffic throughput. Indeed, the growth of air transportation is conditioned on the ability to maintain acceptable safety. While many decision-support tools exist for short-term traffic planning, few have addressed the strategic needs for medium-and long-term planning for time horizons greater than 30 minutes. This paper seeks to address this gap through the introduction of 3D aircraft proximity maps that evaluate the future probability of presence of at least one or two aircraft at any given point of the airspace. Three types of proximity maps are presented: (i) presence maps that indicate the local density of traffic, (ii) conflict maps that determine locations of potential conflicts and their corresponding probabilities, and (iii) outlier proximity maps that show the probability of conflict due to aircraft not belonging to dominant traffic patterns. These maps provide traffic flow managers with information relating to the complexity and difficulty of managing an airspace. The intended purpose of the maps is to anticipate how aircraft flows interact, and how outliers impact the dominant traffic flow for a given time period. This formulation is able to predict which "critical" regions may be subject to conflicts between aircraft, thereby requiring careful monitoring and additional effort to manage the airspace. These probabilities are computed using a generative aircraft flow model. Time-varying flow characteristics, such as geometrical configuration, speed, and probability density function of aircraft spatial distribution within the flow, are determined from archived Enhanced Traffic Management System data, using a tailored clustering algorithm. Aircraft not belonging to flows are identified as outliers.

This paper considers the air traffic conflict resolution problem in the context of wind uncertainty. Aircraft are assigned changes in airspeed to prevent conflict. The goal is to determine the optimal maneuver to balance deviation costs (e.g., fuel costs) and the probability of conflict. A twostage recourse model is developed, in which new airspeeds are assigned in the first stage, based on expected costs due to possible corrective actions in the second stage. The second-stage considers the expected costs for any last-minute maneuvers to compensate wind modeling errors. The resulting model is solved in real-time via numerical methods, providing optimal airspeed values for the resolution of a conflict.

Deterministic air traffic flow management (TFM) decisions—the state of the art in terms of implementation—often result in unused airspace capacity. This is because the inherent uncertainties in weather predictions make it difficult to determine the number of aircraft that can be safely accommodated in a region of airspace during a given period. On the other hand, stochastic TFM algorithms are not amenable to implementation in practice due to the lack of valid stochastic mappings between weather forecasts and airspace capacity to serve as inputs to these algorithms. To fill this gap, we develop a fast simulation-based methodology to determine the stochastic capacity of a region of airspace using integrated weather-traffic models. The developed methodology consists of combining ensemble weather forecast information with an air traffic control algorithm to generate capacity maps over time. We demonstrate the overall methodology through a novel conflict resolution procedure and a simple weather scenario generation tool, and also discuss the potential use of ensemble weather forecasts. An operational study based on comparisons of the generated capacity distributions with observed impacts of weather events on air traffic is also presented.

Despite the existence of several automated air traffic conflict resolution algorithms, there is a need for formulations that account for air traffic controller workload. This paper presents such an algorithm with controller workload constraints modeled parametrically. To this end, we first develop an integer programming model for general conflict resolution, which emphasizes the minimization of fuel costs, and runs in near real-time. A parametric procedure based on this model is then developed to consider controller workload limitations. Two versions of the parametric approach are described, along with computational results. It is demonstrated that both formulations can be used to capture a broad range of possible controller actions.

American universities use a procedure based on a rolling six-year graduation rate to calculate statistics regarding their students’ final educational outcomes (graduating or not graduating). As an alternative to the six-year graduation rate method, many studies have applied absorbing Markov chains for estimating graduation rates. In both cases, a frequentist approach is used. For the standard six-year graduation rate method, the frequentist approach corresponds to counting the number of students who finished their program within six years and dividing by the number of students who entered that year. In the case of absorbing Markov chains, the frequentist approach is used to compute the underlying transition matrix, which is then used to estimate the graduation rate. In this paper, we apply a sensitivity analysis to compare the performance of the standard six-year graduation rate method with that of absorbing Markov chains. Through the analysis, we highlight significant limitations with regards to the estimation accuracy of both approaches when applied to small sample sizes or cohorts at a university. Additionally, we note that the Absorbing Markov chain method introduces a significant bias, which leads to an underestimation of the true graduation rate. To overcome both these challenges, we propose and evaluate the use of a regularly updating multi-level absorbing Markov chain (RUML-AMC) in which the transition matrix is updated year to year. We empirically demonstrate that the proposed RUML-AMC approach nearly eliminates estimation bias while reducing the estimation variation by more than 40%, especially for populations with small sample sizes.