Methods for numerical calculation of parameters pertaining to the microscopic following-the-leader model of traffic flow: using the fast spline transformation

Abstract

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.