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This approach geometry (which is referred to as the “trombone maneuver”) is advantageous to air traffic controllers as it allows them great flexibility in spacing aircraft by adjusting the length of the downwind leg (hence the name trombone).
4.2 Simulation procedure
A necessary step in the implementation of the MCMC algorithm is the extraction of the ˜
Xj for a
given value of ω. In the ATC case studies this corresponds to the extraction of aircraft trajectories for a given airspace configuration (current aircraft positions and given flight plans). The extraction of multiple such trajectories (J to be precise) will be necessary in the algorithm implementation. The trajectories will be in general different from one another because of the uncertainty that enters the process (due to wind, aircraft parameters unknown to ATC, etc.)
In earlier work we developed an air traffic simulator to simulate adequately the behavior of a set of aircraft from the point of view of ATC [8, 9, 10]. The simulator implements realistic models of current commercial aircraft described in the Base of Aircraft Data (BADA) [5]. The simulator contains also realistic stochastic models of the wind disturbance [3]. The aircraft models contain continuous dynamics, arising from the physical motion of the aircraft, discrete dynamics, arising from the logic embedded in the Flight Management System, and stochastic dynamics, arising from the effect of the wind and incomplete knowledge of physical parameters (for example, the aircraft mass, which depends on fuel, cargo and number of passengers). The simulator has been coded in Java and can be used in different operation modes, either to generate accurate data for validation of the performance of conflict detection and resolution algorithm, or to run faster simulations of simplified models. The nominal path for each aircraft is entered in the simulator as a sequence of way-points, either by reading data files, or manually. The simulator can also be used in a so called interactive mode, where the user is allowed to manipulate the flight plans on-line (move way-points, introduce new way points, etc.)
The actual trajectories of the aircraft generated by the simulator are a perturbed version of the flight plan that depends on the particular realizations of wind disturbances and uncertain parameters. The trajectories of the aircraft can be displayed on the screen (Figure 2) and/or stored in files for post-processing. The reader is referred to [9, 10] for a more detailed description of the simulator.
The air traffic simulator has been used to produce the examples presented in this section. The full accurate aircraft, FMS and wind models have been used both during the Monte Carlo optimization procedure and to obtain Monte Carlo estimates of post-resolution conflict probabilities. The simulator was invoked from Matlab on a Linux workstation with a Pentium 4 3GHz processor. Under these conditions the simulation of the flight of two aircraft for 30 minutes, which is approximately the horizon considered in the examples, took 0.2 seconds on the average. Notice that this simulation speed (5 simulations/sec) is quite low for a Monte Carlo framework. This is mainly due to the fact that no attempt has been made to optimize the code at this stage. For example, executing the Java simulator from a Matlab environment introduces unnecessary and substantial computational overhead. The reader is requested to evaluate the computation times reported in the following examples keeping this fact in mind.
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Monte Carlo Optimization for Conflict Resolution in Air Traffic Control(9)
