Control of departure processes

In the realm of air traffic flow management, there is a class of alternative models to the ones that do aircraft-based optimization. These models, called Eulerian models, are concerned with the optimal control of the flow of aircraft, rather than the trajectory of individual aircraft. Eulerian models only deal with aircraft counts in specific control volumes of airspace rather individual aircraft trajectories, and are more tractable for the purpose of control [74, 101]. However, these dynamic control approaches have not been applied to the aircraft flow on the surface of the airport.

An airport congestion control strategy in its simplest form would be a state-dependent pushback policy aiming at reducing congestion on the ground. One such approach is the N-Control strategy.

N-Control is one implementation of the virtual queue concept described in the Departure Planner [47] and variants of it have been extensively studied [16, 19, 20, 92]. The main idea behind N-Control is an observation of the performance of the departure throughput of US airports: As more aircraft pushback from their gates onto the taxiway system, the throughput of the departure

runway initially increases because more aircraft are available in the departure queue. However, as this number, denoted N , exceeds a threshold, the departure runway capacity becomes the limiting factor, and there is no additional increase in throughput. We denote this threshold as N^∗. The dependence of the departure throughput on the number of aircraft taxiing out is illustrated in Figure 1-3 using ASPM data from 2011 for runway configuration (VMC; 31 | 4) of LGA. Beyond the threshold N^∗, any additional aircraft that pushback simply incur taxi-out delays without increasing the airport throughput [107].

0 5 10 15 20 25 30 35 40

0 2 4 6 8 10 12

Aircraft taxiing out

Departure throughput (AC/15 min) data mean

data median

N^*

Figure 1-3: Departure throughput as a function of the number of aircraft taxiing out, for the (VMC;

31 | 4) configuration at LGA

The policy is effectively a simple threshold heuristic: If the total number of departing aircraft on the ground exceeds a certain threshold, N_ctrl, where N_ctrl ≥ N^∗ , stop dispatching aircraft requesting pushback until the number of aircraft on the ground drops below the threshold. While the choice of N_ctrl must be large enough to maintain runway utilization, too large a value will be overly conservative, and result in a loss of benefits from the control strategy. Such a policy aims at preventing excessive congestion and is already heuristically in use by air traffic controllers [25]

during excessively congested situations.

The N-Control policy is also closely related to the constant work-in-process (CONWIP) policy in manufacturing systems. The main benefits of CONWIP systems are their simplicity, imple-mentability and controllability [118]. This approach presents an efficient way to control congestion

by accepting an adjustable risk of capacity loss. The N-Control strategy has been shown through several simulation studies to have similar properties.

More complex policies which attempt to attain some optimization objective have not been considered for surface traffic until recently. In 2009, Burgain et al. used more advanced modeling and optimization tools for the characterization of optimal pushback policies. More specifically, they modeled the airport surface with a state space model, and characterized optimal pushback policies as a function of the state of the system, and not just the total number of aircraft on the ground [17].

The optimal policies considered were full-state feedback policies, which faced some implementation issues [15]. This control protocol was a generalization of the N-Control strategy, in which, at each minute, the state of the surface was mapped to an on-off input signal.

All the above policies (Control, CONWIP systems, and Burgain et al.’s refinements of N-Control) can be classified as token-based, or surplus-based policies [48]. In these approaches, every state transition generates a token, an action or a signal, which is applied at the input to the system (the pushback process). Equivalently, every state transition translates to a new surplus level (or lack thereof) at different buffers of the system, which implies a different flow of input into the system. More general approaches can be found in the literature on the dynamic control of queuing systems.

There has been much prior research on the optimal control of a variety of queuing systems, considering different decision variables and control objectives [29, 78, 80, 119, 120]. In the modeling framework of Low [80] and Lippman [78] , the state of the system is the number of customers in the system. A holding cost hi is incurred per unit time that the system is in state i and a reward (or entrance fee) pλ is received (paid) whenever a customer enters the system at a point in time when the arrival rate is λ. hi is assumed to be convex and non-decreasing. Then, it can be shown that the optimal λ is a non-decreasing function of the state i. This formulation can be easily modified so as to yield optimal policies with respect to performance measures such as throughput, congestion, or a combination of the two.

Several challenges remain when attempting to apply results from queuing, manufacturing and inventory control in the context of controlling the departure process. Firstly, on-off or event-driven control policies for controlling the pushback process are difficult to implement in practice. Both the air traffic controllers and the airlines would prefer a state-dependent pushback rate that would be valid for a predefined time period, after which it would be updated. Air traffic controllers prefer such periodically updated pushback rate recommendations for workload and procedural reasons,

and airlines prefer them because of their predictability, which is essential for planning ground crews.

Secondly, the control input is applied at the gates during pushback, whereas the main bottleneck is the runway. The control strategy cannot be applied directly at the runway queue, but instead has to accommodate stochastic taxi-out times between the gate and the runway. Factors that contribute to the stochasticity of taxi-out times include the pushback process, flight checklists, communication delays, and variable taxi speeds.

For all of the above reasons, the N-Control strategy has not been applied as such in the airport context. Researchers have developed several heuristic modifications of it for field-testing customized for different airport environments and requirements. Characteristic examples of these efforts are the metering of departures at New York JFK airport by PASSUR Aerospace, Inc. [86], the field evaluation of the Collaborative Departure Queue Management concept at Memphis (MEM) airport [14], the human-in-the-loop simulations of the Spot and Runway Departure Advisor (SARDA) con-cept at DFW airport [66] and the trials of the Departure Manager (DMAN) concon-cept [13] in Athens International airport (ATH) [103]. During summer of 2010, we also developed and successfully tested such a heuristic, the Pushback Rate Control protocol (henceforth referred to as PRC v1.0) [110]. However, none of these efforts, which are essentially different variants of N-Control [85], have explicitly estimated the stochasticity of the underlying processes, and developed algorithms that explicitly attain certain objectives.

Finally, when applying results from queuing theory to congestion control, another critical issue is that the service times are not exponentially distributed [55, 107, 113]. Researchers have considered modeling them as time-dependent Erlang distributions [55, 94, 113], time-dependent deterministic distributions [73, 89], binomial [91], or multinomial distributions [15, 107]. However, to the best of our knowledge, empirical service times have not been extracted to date from operational data.