A Comparison of a Cellular Automaton and a Macroscopic Model

TL;DR

This paper explores the relationship between a microscopic stochastic cellular automaton traffic model and a macroscopic continuum model, explicitly integrating stochasticity into the macroscopic model's fundamental diagram for improved comparison.

Contribution

It introduces a novel method to incorporate stochasticity from cellular automaton models into the macroscopic LWR model's fundamental diagram.

Findings

The models show comparable tempo-spatial behavior in simulations.

Explicit stochasticity integration improves model alignment.

Analytical results support the simulation findings.

Abstract

In this paper we describe a relation between a microscopic stochastic traffic cellular automaton model (i.e., the STCA) and the macroscopic first-order continuum model (i.e., the LWR model). The innovative aspect is that we explicitly incorporate the STCA's stochasticity in the construction of the fundamental diagram used by the LWR model. We apply our methodology to a small case study, giving a comparison of both models, based on simulations, numerical, and analytical calculations of their tempo-spatial behavior.