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Article

Přikryl, Jan ; Vaniš, Miroslav
Comparing numerical integration schemes for a car-following model with real-world data. (English). In: Chleboun, J., Kůs, P., Přikryl, P., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Janov nad Nisou, June 19-24, 2016. Institute of Mathematics CAS, Prague, 2017. pp. 89-96
MSC: 65L06, 65L07, 68Q17 | DOI: 10.21136/panm.2016.11
Keywords:
numerical integration; Runge-Kutta; Euler; trapezoid; ballistic update; car-following model; intelligent driver model; traffic flow
Summary:
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 [1], 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.
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