Modeling

Dynamic traffic assignment (DTA) models are capable of capturing traffic dynamics and are well-known as a critical tool in controlling and predicting the traffic situation Ameli (2019). DTA simulation allows us to measure the results of deploying different technologies and applying different policies along with real experiments Ameli et al. (2020); Chen et al. (2021); Balzer et al. (2023). One of the crucial steps to achieve realistic results from simulation tools is calibration. It aims to determine the DTA model’s input such that the output represents traffic scenarios with a reliable...

This article proves the existence and uniqueness of a weak solution to a scalar conservation law on a bounded domain. A weak formulation of hybrid boundary conditions is needed for the problem to be well posed. The boundary conditions are represented by a hybrid automaton with switches between the modes determined by the direction of characteristics of the system at the boundary. The existence of the solution results from the convergence of a Godunov scheme derived in this article. This weak formulation is written explicitly in the context of a strictly concave flux function (relevant for...

This article develops a model of air traffic flow using an Eulerian description with hyperbolic partial differential equations. Existence and uniqueness (well-posedness) of a solution to the system of partial differential equations on a network is established. Subsequently, an optimal control problem is studied with the junction coefficients as control variables. We use a continuous adjoint approach and we implement it on a network with 16 links and 5 junctions, demonstrating the computational efficiency of this method

Four Eulerian network models are implemented to model high altitude air traffic flow. Three of the models use the framework of discrete time dynamical systems, while the fourth consists of a network of partial differential equations. The construction of these models is done using one year of air traffic data. The four models are applied to high altitude traffic for six Air Route Traffic Control Centers in the National Airspace System and surrounding airspace. Simulations are carried out for a full day of data for each of the models, to assess their predictive capabilities. The models’...