Dynamic network modelling and simulation for air traffic flow analysis - Domingues, Tiago Mendes (2011)
This dissertation describes the achievement of a set of equations in order to represent a discrete model for air traffic dynamics in terminal areas. Such a mathematical model could be used to investigate the occupation of a TMA‡ at a single instant and has the potential to be used on the prediction of a future occupation. There are safety and legal limits to how many aircraft should be inside a TMA at once. It could also be useful for an Air Traffic Controller to predict a future overoccupation and thus being able to prevent it. That is why there is an interest to know at each instant an estimate of how many aircraft are in a specific TMA. The idea behind it was to make a Control Theory approach so that the same classical tools used in other topics such as flight dynamics could be applied to this subject. In order for that to happen there were needed some Network notions along with navigation formulae. If an aircraft leaves one place we know a priori that he will follow a path and later enter a certain TMA, unless something goes wrong. That information is known even before lift off. It limits our monitoring window and we can now focus on the physical existence of an aircraft in or out a determined TMA. Every aircraft within a radius of several nautical miles, depending on each TMA, does belong to that TMA. A transition between areas is considered a control input. Knowing the initial amount of aircraft on the zero instant at a particular site we can calculate the following instant state by adding the arrivals and subtracting the departures. This system has mass conservation in a sense that aircraft don’t just disappear - instead they move around and the total number of aircraft on the system remains the same. Depending on the complexity of the system other separated states can be monitored and we could separate the grounded aircraft from the airborne aircraft; allow mid-flight decision change to go to a different TMA, etc. Data retrieved from the website www.localizatodo.com together with Octave Software allowed the validation of the model. On this website the captured transponder signals are transformed into several bits of information from which were retrieved the ones useful: Longitude, Latitude and time stamp. The equations performed as they should, making them applicable to a real scenario, since the utilized data are in fact coming themselves from a real scenario and they are not invented. The first two models are slightly different from the third. One concerns the TMA as if they were contiguous and another considers the paths among each other. They are steps towards an objective, rather than a final solution. The inclusion of a sigmoid function to the model was the latest work to be done. It has to do with the prediction and how much would an incoming airship weight on the eyes of the Air Traffic Controller. There is a need to remove abrupt changes inherent to the model in a way that an aircraft would gradually become present on the arriving TMA from the moment he lifted off the departing TMA, instead of just showing up on the arriving TMA and thus giving no anticipation opportunity to the air traffic controllers. In a future work an estimator, such as a Kalman Filter, should be added to this model or even an improved similar model, since it has the flexibility to incorporate new features in a simple way. There is an explanation on how to perform these additions. This work could be used as a foundation for the implementation of a warning to the Air Traffic Controllers of the occupation status. Not only that but it could be a module on a fully automatic Airspace Controller or even other applications yet to be considered. It could even be applied on the traffic of buses (coaches) and it can be extrapolated to many other fields.