Impacts of Down-Up Hill Segment on the Threshold of Shock Formation of Ring Road Vehicular Flow

The study of impacts of down-up hill road segment on the density threshold of traffic shock formation in ring road vehicular flow is helpful to the deep understanding of sags' bottleneck effect. Sags are freeway segments along which the gradient increases gradually in the traffic direction. The main aim of this paper is to seek the density threshold of shock formation of vehicular flow in ring road with down-up hill segment, because down-up hill roadway segment is a source to cause capacity reduction that is an attractive topic in vehicular traffic science. To seek the density threshold numerically, a viscoelastic continuum model [1] is extended and used. To solve the model equations, a fifth-order weighted essentially non-oscillatory scheme for spatial discretization, and a 3rd order Runge-Kutta scheme for time partial derivative term are used. Validation by existing observation data and the Navier-Stokes like model [2] extended as EZM is done before conducting extensive numerical simulations. For ring road vehicular flow with three separated down-up hill segments, it is found that the density threshold of shock formation decreases monotonically with the relative difference of free flow speed, this variation can be simply fitted by a third order polynomial.

Automated summary

The study focuses on understanding the bottleneck effect of sags through analyzing the impacts of down-up hill road segments on the density threshold of traffic shock formation in ring road vehicular flow. A viscoelastic continuum model is used to numerically seek the density threshold, and validation is done using existing observation data and a Navier-Stokes like model. The results show a monotonic decrease in the density threshold with the relative difference of free flow speed in ring road vehicular flow with three separated down-up hill segments, which can be fitted by a third order polynomial.