numerical integration; Runge-Kutta; Euler; trapezoid; ballistic update; car-following model; intelligent driver model; traffic flow
A key element of microscopic traffic flow simulation is the so-called car-following model, describing the way in which a typical driver interacts with other vehicles on the road. This model is typically continuous and traffic micro-simulator updates its vehicle positions by a numerical integration scheme. While increasing the order of the scheme should lead to more accurate results, most micro-simulators employ the simplest Euler rule. In our contribution, inspired by , we will provide some additional details that have to be addressed when implementing higher-order numerical integration schemes for CFMs and we will show that the theoretical gain of higher-order methods is unfortunately masked out by the stochastic nature of real-world traffic flow.