Analyses and implications of higher order finite volume methods on first-order macroscopic traffic flow models

Abstract

Selection of suitable numerical scheme for solving macroscopic traffic flow models should be based on the numerical errors in various traffic parameters. Although such errors associated with state variables such as density are known to some extent, their implications to the derived parameters such as travel time and queue-length are not understood well. This paper proposes a general basis for selecting the spatial order of accuracy of a finite volume scheme for solving first-order traffic flow models. Four Measures of Accuracy that are especially relevant for traffic flow have been introduced. We illustrate that, although higher order schemes outperform the lower order ones in the quality of simulation in terms of resolution as well as computational cost, their superior performance is underestimated with the use of conventional error measures of state predictions. Localized parameters such as size and duration of the queue are more sensitive towards the order of the scheme, than domain aggregated parameters such as duration of congestion and travel time.