Multirate numerical scheme for large-scale vehicle traffic simulation

Abstract

In modeling vehicular traffic on large scales in large cities, the number of vehicles could reach tens of thousands, which, for the microscopic approach, corresponds to the solution of ordinary differential equations (ODEs) with large dimensions. The speed of changes in the size of the components of such systems usually lies in a wide range, as the dynamics and behavior of the vehicles can strongly differ. In this paper we introduce a multirate numerical scheme with a self-adjusting time stepping strategy. Instead of using a single step size for the whole system, the step size for each component is determined by estimating its own local variation. The stability analysis for the developed scheme is performed and the stability conditions are obtained. The presented multirate scheme provides a significant speed-up in the CPU times compared to the corresponding single-rate one. The use of multiple time steps allows parallel computing.