When is a bottleneck a bottleneck?

TL;DR

This paper investigates the critical strength of bottlenecks in traffic models, showing that even infinitesimally small defects can cause global effects, resolving previous conflicting simulation results.

Contribution

It demonstrates that the critical defect strength in the ASEP model is zero, clarifying the impact of weak bottlenecks on traffic flow.

Findings

Critical defect strength is zero, meaning any small bottleneck affects the system.

Reconciles previous simulation results with theoretical expectations.

Implications for analyzing empirical traffic data and numerical models.

Abstract

Bottlenecks, i.e. local reductions of capacity, are one of the most relevant scenarios of traffic systems. The asymmetric simple exclusion process (ASEP) with a defect is a minimal model for such a bottleneck scenario. One crucial question is "What is the critical strength of the defect that is required to create global effects, i.e. traffic jams localized at the defect position". Intuitively one would expect that already an arbitrarily small bottleneck strength leads to global effects in the system, e.g. a reduction of the maximal current. Therefore it came as a surprise when, based on computer simulations, it was claimed that the reaction of the system depends in non-continuous way on the defect strength and weak defects do not have a global influence on the system. Here we reconcile intuition and simulations by showing that indeed the critical defect strength is zero. We discuss the implications for the analysis of empirical and numerical data.