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

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.