Asymptotic dynamics of closed-boundary vehicular traffic

TL;DR

This paper analyzes the long-term behavior of traffic flow on a loop using a car-following model, deriving fundamental diagrams and examining speed correlations and noise effects.

Contribution

It provides a detailed steady-state analysis of single-cluster traffic and explores the impact of noise on vehicular dynamics, which is novel in the context of closed-loop traffic models.

Findings

Steady-state solutions for single-cluster traffic are derived.

Fundamental diagrams with two branches for jam entry and exit are presented.

Speed averages converge to a constant regardless of clustering state.

Abstract

We study the dynamics of vehicular traffic in a loop using a car-following model with the consideration of volume exclusions. In particular, we solve the steady state for the single-cluster case and derive fundamental diagrams, exhibiting two branches representative of entering and leaving the jam, respectively. By simulations we also observe that the speed average over all vehicles reaches the same constant at the steady states, regardless of the final clustering state. The autocorrelation functions for the overall speed average and single vehicle speed are investigated, each revealing a robust time scale. The effects of noises in vehicular acceleration are discussed.