Density-feedback control in traffic and transport far from equilibrium

TL;DR

This paper investigates a density-feedback control mechanism in traffic flow, analyzing its effects on flow optimization through numerical and analytical methods, including the Burgers equation and TASEP simulations.

Contribution

It introduces and analyzes a simple density-feedback control model for traffic flow, combining analytical and simulation approaches to optimize flow.

Findings

Rich stationary phase diagram identified

Optimal threshold for maximum flow determined

Analytical results confirmed by microscopic simulations

Abstract

A bottleneck situation in one-lane traffic-flow is typically modelled with a constant demand of entering cars. However, in practice this demand may depend on the density of cars in the bottleneck. The present paper studies a simple bimodal realization of this mechanism to which we refer to as density-feedback control (DFC): If the actual density in the bottleneck is above a certain threshold, the reservoir density of possibly entering cars is reduced to a different constant value. By numerical solution of the discretized viscid Burgers equation a rich stationary phase diagram is found. In order to maximize the flow, which is the goal of typical traffic-management strategies, we find the optimal choice of the threshold. Analytical results are verified by computer simulations of the microscopic TASEP with DFC.