Boundary effects on energy dissipation in a cellular automaton model

TL;DR

This study investigates how boundary conditions affect energy dissipation in a cellular automaton traffic model, revealing persistent dissipation and phase-dependent behaviors through numerical and theoretical analysis.

Contribution

It provides the first detailed analysis of boundary effects on energy dissipation in the NaSch model with open boundaries, including phase-specific results and contributions of different dissipation mechanisms.

Findings

Nonvanishing energy dissipation rate in all phases.

Critical extinction rate influences dissipation in deterministic models.

Energy dissipation relates directly to traffic phases.

Abstract

In this paper, we numerically study energy dissipation caused by traffic in the Nagel-Schreckenberg (NaSch) model with open boundary conditions (OBC). Numerical results show that there is a nonvanishing energy dissipation rate Ed, and no true free-flow phase exists in the deterministic and nondeterministic NaSch models with OBC. In the deterministic case, there is a critical value of the extinction rate $\beta{cd}$ below which Ed increases with increasing $\beta$, but above which Ed abruptly decreases in the case of the speed limit vmax>2. However, when vmax<3, no discontiguous change in Ed occurs. In the nondeterministic case, the dissipated energy has two different contributions: one coming from the randomization, and one from the interactions, which is the only reason for dissipating energy in the deterministic case. The relative contributions of the two dissipation mechanisms are presented in the stochastic NaSch model with OBC. Energy dissipation rate Ed is directly related to traffic phase. Theoretical analyses give an agreement with numerical results in three phases (low-density, high-density and maximum current phase) for the case vmax=1.