Hamsa Balakrishnan

Scheduling Aircraft Landings under Constrained Position Shifting

Optimal scheduling of airport runway operations can play an important role in improving the safety and efficiency of the National Airspace System (NAS). Methods that compute the optimal landing sequence and landing times of aircraft must accommodate practical issues that affect the implementation of the schedule. One such practical consideration, known as Constrained Position Shifting (CPS), is the restriction that each aircraft must land within a pre-specified number of positions of its place in the First-Come-First-Served (FCFS) sequence. We consider the problem of scheduling landings of aircraft in a CPS environment in order to maximize runway throughput (minimize the completion time of the landing sequence), subject to operational constraints such as FAA-specified minimum inter-arrival spacing restrictions, precedence relationships among aircraft that arise either from airline preferences or air traffic control procedures that prevent overtaking, and time windows (representing possible control actions) during which each aircraft landing can occur. We present a Dynamic Programming-based approach that scales linearly in the number of aircraft, and describe our computational experience with a prototype implementation on realistic data for Denver International Airport.

Algorithms for Scheduling Runway Operations Under Constrained Position Shifting

The efficient operation of airports, and runways in particular, is critical to the throughput of the air transportation system as a whole. Scheduling arrivals and departures at runways is a complex problem that needs to address diverse and often competing considerations of efficiency, safety, and equity among airlines. One approach to runway scheduling that arises from operational and fairness considerations is that of constrained position shifting (CPS), which requires that an aircrafts position in the optimized sequence not deviate significantly from its position in the first-come-first-served sequence. This paper presents a class of scalable dynamic programming algorithms for runway scheduling under constrained position shifting and other system constraints. The results from a prototype implementation, which is fast enough to be used in real time, are also presented.

A Framework for Coordinated Surface Operations Planning at Dallas-Fort Worth International Airport

An Integer Programming formulation is developed for optimizing surface operations at Dallas-Fort Worth airport, with the goal of assessing the potential benefits of taxi route planning. The model is based on operations in the eastern half of the airport under the most frequently used configuration. The focus is on operational concepts that optimize taxi routes by utilizing dierent control points on the airport surface. The benefits of two dierent concepts for optimizing taxiway operations, namely controlled pushback and taxi reroutes are analyzed, for both current data and a projected data set with approximately twice the trac density. The analysis estimates that: (1) for current trac densities, controlled pushback would reduce the average departure taxi time by 17% without altering runway schedule conformance, while the benefits of taxi reroutes would be minimal; and (2) for high-density operations, controlled pushback would reduce the average departure taxi time by 18%, while incorporating taxi reroutes would reduce the average arrival taxi time by 14%. Other benefits analyzed for these control strategies include a decrease in the average time spent in runway crossing queues.

Queuing Models of Airport Departure Processes for Emissions Reduction

Aircraft taxiing on the surface contribute significantly to the fuel burn and emissions at airports. This paper investigates the possibility of reducing fuel burn and emissions from surface operations through a reduction of the taxi times of departing aircraft. A novel approach is proposed that models the aircraft departure process as a queuing system, and attempts to reduce taxi times and emissions through improved queue management strategies. The departure taxi (taxi-out) time of an aircraft is represented as a sum of three components, namely, the unimpeded taxi-out time, the time spent in the departure queue, and the congestion delay due to ramp and taxiway interactions. The dependence of the taxi-out time on these factors is analyzed and modeled. The performance of the model is validated through a comparison of its predictions with observed data at Boston’s Logan International Airport (BOS). The reductions in taxi-out times from the proposed queue management strategy are translated to reductions in fuel burn and emissions using ICAO engine models for the taxi phase of the flight profile.

Stability Analysis of Explicit Congestion Control Protocols

In the context of explicit congestion control protocols like XCP and RCP where the equilibrium queue lengths are zero, we show that the stability region derived from traditional Nyquist analysis is not an accurate representation of the actual stability region, and that the use of switched linear system models with time delay and new Lyapunov tools can provide sound sufficient stability conditions.

A Dynamic Programming Algorithm for Robust Runway Scheduling

An algorithm for generating schedules of airport runway operations that are robust to perturbations caused by system uncertainty is presented. The algorithm computes a tradeoff curve between runway throughput and the probability that random deviations of aircraft from the schedule violate system constraints and require intervention from air traffic controllers. The algorithm accommodates various operational constraints imposed by the terminal-area system such as minimum separation requirements between successive aircraft, earliest and latest times for each aircraft, precedence constraints among aircraft and the limited flexibility in deviating from the first-come-first-served (FCFS) order afforded to air traffic controllers (a concept known as Constrained Position Shifting). When the maximum allowable number of position shifts from the FCFS order is bounded by a constant, the complexity of the algorithm is O(n(L/isin)3), where n is the number of aircraft, L is largest difference between the latest and earliest arrival time over all aircraft, and e is the desired output accuracy.

Impact of Congestion on Taxi Times, Fuel Burn, and Emissions at Major Airports

Taxiing aircraft contribute significantly to fuel burn and emissions at airports. This paper provides a comprehensive assessment of the impact of surface congestion on taxi times, fuel burn, and emissions through analysis of the departing traffic data from four major U.S. airports. Several metrics based on airport throughput and taxi-out times are introduced and studied, including one that considers the number of flights that encounter a congested airport, a second metric that compares the observed taxi-out times with the unimpeded ones, and a third that evaluates them in conjunction with the airport throughput.

Polynomial approximation algorithms for belief matrix maintenance in identity management

Updating probabilistic belief matrices as new observations arrive, in the presence of noise, is a critical part of many algorithms for target tracking in sensor networks. These updates have to be carried out while preserving sum constraints, arising for example, from probabilities. This paper addresses the problem of updating belief matrices to satisfy sum constraints using scaling algorithms. We show that the convergence behavior of the Sinkhorn scaling process, used for scaling belief matrices, can vary dramatically depending on whether the prior unscaled matrix is exactly scalable or only almost scalable. We give an efficient polynomial-time algorithm based on the maximum-flow algorithm that determines whether a given matrix is exactly scalable, thus determining the convergence properties of the Sinkhorn scaling process. We prove that the Sinkhorn scaling process always provides a solution to the problem of minimizing the Kullback-Leibler distance of the physically feasible scaled matrix from the prior constraint-violating matrix, even when the matrices are not exactly scalable. We pose the scaling process as a linearly constrained convex optimization problem, and solve it using an interior-point method. We prove that even in cases in which the matrices are not exactly scalable, the problem can be solved to e-optimality in strongly polynomial time, improving the best known bound for the problem of scaling arbitrary nonnegative rectangular matrices to prescribed row and column sums.

A Study of Tradeoffs in Scheduling Terminal-Area Operations

The terminal area surrounding an airport is an important component of the air transportation system, and efficient terminal-area schedules are essential for accommodating the projected increase in air traffic demand. Aircraft arrival schedules are subject to a variety of operational constraints, such as minimum separation for safety, required arrival time-windows, limited deviation from a first-come first-served sequence, and precedence constraints. There is also a range of objectives associated with multiple stakeholders that could be optimized in these schedules; the associated tradeoffs are evaluated in this paper. A dynamic programming algorithm for determining the minimum cost arrival schedule, given aircraft-dependent delay costs, is presented. The proposed approach makes it possible to determine various tradeoffs in terminal-area operations. A comparison of maximum throughput and minimum average delay schedules shows that the benefit from maximizing throughput could be at the expense of an increase in average delay, and that minimizing delay is the more advantageous of the two objectives in most cases. A comprehensive analysis of the tradeoffs between throughput and fuel costs and throughput and operating costs is conducted, accounting for both the cost of delay (as reported by the airlines) and the cost of speeding up when possible (from models of aircraft performance).

Interaction of High-Speed Rail and Aviation: Exploring Air–Rail Connectivity

U.S. airports face significant congestion problems, particularly in major metropolitan areas with continued population and economic growth. In addition to growth in air travel demand, frequent short-haul flights on routes of less than 500 mi contribute to airport congestion. The potential for high-speed rail (HSR) to substitute for aviation on these short-haul routes is well documented; however, there is a need to explore how rail can serve in a complementary mode to relieve congestion at airports by providing short-haul services in support of longer-haul airline services. The primary objective of this research project is to examine the role of cooperation between HSR and aviation to improve the aviation system planning process. This study addresses the following key questions: (a) How have airports, airlines, and rail operators cooperated to enable airport–HSR connectivity? (b) What are the service characteristics of airport–HSR connectivity? (c) What are the unique challenges associated with airport–HSR connectivity? (d) How has the demand for air transportation evolved in the presence of airport–HSR connectivity?