Methods for numerical calculation of parameters pertaining to the microscopic following-the-leader model of traffic flow: using the fast spline transformation
Nina Kuzhel,
Andrii Bieliatynskyi,
Olegas Prentkovskis,
Iryna Klymenko,
Šarūnas Mikaliūnas,
Olena Kolganova,
Svitlana Kornienko,
Volodymyr Shutko
Affiliations
Nina Kuzhel
Dept of Air Transportation Management, National Aviation University, Kosmonavta Komarova ave 1, 03680 Kyiv, Ukraine
Andrii Bieliatynskyi
Dept of Airport Reconstruction and Automobile Roads, National Aviation University, Kosmonavta Komarova ave 1, 03680 Kyiv, Ukraine
Olegas Prentkovskis
Dept of Transport Technological Equipment, Vilnius Gediminas Technical University, Plytinės g. 27, LT-10105 Vilnius, Lithuania
Iryna Klymenko
Dept of Economics, National University of Transport, Suvorova str. 1, 01010 Kyiv, Ukraine 5Dept of Railway Transport, Vilnius Gediminas Technical University, J. Basanavičiaus g. 28, LT-03224 Vilnius, Lithuania
Šarūnas Mikaliūnas
Dept of Railway Transport, Vilnius Gediminas Technical University, J. Basanavičiaus g. 28, LT-03224 Vilnius, Lithuania
Olena Kolganova
Dept of Information Security, National Aviation University, Kosmonavta Komarova ave 1, 03680 Kyiv, Ukraine
Svitlana Kornienko
Dept of Aviation Radioelectronic Complexes, National Aviation University, Kosmonavta Komarova ave 1, 03680 Kyiv, Ukraine
Volodymyr Shutko
Dept of Electronics, National Aviation University, Kosmonavta Komarova ave 1, 03680 Kyiv, Ukraine
As known in transport engineering, civil engineering, transport planning and mathematics, traffic flow is the study of interactions between vehicles, drivers and infrastructure (including highways, signage and traffic control devices), with the aim of understanding and developing an optimal road network with efficient movement of traffic and minimal traffic congestion problems. The presented paper discusses a small part of a traffic flow study – the development of the methodology for assessing the speed and acceleration of a car during the column movement followingthe-leader, based on a new mathematical method. Two methods – (1) the numerical calculation of the first derivative, i.e. speed of the car movement; (2) the numerical calculation of the second derivative, i.e. acceleration of the car movement – were developed, using the fast spline transformation. In the future, parameters obtained with the help of two new methods, can be used to solve complex transportation problems, such as: (1) control of traffic flows; (2) organisation of harmonised work of traffic lights; (3) analysis of psycho-physiological condition of a driver, etc.
