# A combined first and second order model for a junction with ramp buffer

## TL;DR

This paper introduces a hybrid traffic flow model combining first and second order features to accurately simulate capacity drop effects at junctions with ramp buffers, supported by theoretical analysis and numerical experiments.

## Contribution

It proposes a novel combined model that captures capacity drop at junctions with ramp buffers, bridging the gap between first and second order models.

## Key findings

- The combined model reproduces capacity drop effects.
- Numerical results align with second order model outcomes.
- Theoretical analysis clarifies coupling condition differences.

## Abstract

Second order macroscopic traffic flow models are able to reproduce the so-called capacity drop effect, i.e., the phenomenon that the outflow of a congested region is substantially lower than the maximum achievable flow. Within this work, we propose a first order model for a junction with ramp buffer that is solely modified at the intersection so that the capacity drop is captured. Theoretical investigations motivate the new choice of coupling conditions and illustrate the difference to purely first and second order models. The numerical example considering the optimal control of the onramp merging into a main road highlights that the combined model generates similar results as the second order model.