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

## TL;DR

This paper analyzes how the number of predecessors in acceleration-based flow models affects stability, revealing non-monotonic relations and providing conditions for stability in microscopic pedestrian and car-following models.

## Contribution

It introduces a stability analysis considering multiple predecessors and uncovers unexpected non-monotonic effects on stability in flow models.

## Key findings

- Stability depends on small relaxation times.
- Non-monotonic relation between number of predecessors and stability.
- General conditions for linear stability on ring geometries.

## 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.