Optimization of congested traffic flow in systems with a localized periodic inhomogeneity

TL;DR

This paper investigates how controlling the frequency of localized periodic inhomogeneities, like traffic signals, can optimize traffic flow in congested systems by generalizing the fundamental diagram to include wavelength effects.

Contribution

It introduces a generalized fundamental diagram incorporating wavelength dependence and demonstrates how controlling inhomogeneity frequency optimizes traffic flow in congestion.

Findings

Traffic flow can be optimized by adjusting inhomogeneity frequency.

The fundamental diagram must include wavelength effects for stop-and-go traffic.

The generalized diagram predicts a 2D flux-density region similar to empirical observations.

Abstract

We study traffic flow on roads with a localized periodic inhomogeneity such as traffic signals, using a stochastic car-following model. We find that in cases of congestion, traffic flow can be optimized by controlling the inhomogeneity's frequency. By studying the wavelength dependence of the flux in stop-and-go traffic states, and exploring their stability, we are able to explain the optimization process. A general conclusion drawn from this study is, that the fundamental diagram of traffic (density flux relation) has to be generalized to include the influence of wavelength on the flux, for the stop-and-go traffic. Projecting the generalized fundamental diagram on the density-flux plane yields a 2D region, qualitatively similar to that found empirically [B. S. Kerner, Phys. Rev. Lett. {\bf 81}, 3797 (1998)] in synchronized flow.