Influence of the number of predecessors in interaction within acceleration-based flow models

Abstract

In this paper, the stability of the uniform solutions is analysed for microscopic flow models in interaction with $K\ge1$ predecessors. We calculate general conditions for the linear stability on the ring geometry and explore the results with particular pedestrian and car-following models based on relaxation processes. The uniform solutions are stable if the relaxation times are sufficiently small. The analysis is focused on the relevance of the number of predecessors in the dynamics. Unexpected non-monotonic relations between $K$ and the stability are presented.