Travel time prediction with viscoelastic traffic model

Travel time through a ring road with a total length of 80 km has been predicted by a viscoelastic traffic model(VEM), which is developed in analogous to the non-Newtonian fluid flow. The VEM expresses a traffic pressure for the unfree flow case by space headway, ensuring that the pressure can be determined by the assumption that the relevant second critical sound speed is exactly equal to the disturbance propagation speed determined by the free flow speed and the braking distance measured by the average vehicular length. The VEM assumes that the sound speed for the free flow case depends on the traffic density in some specific aspects, which ensures that it is exactly identical to the free flow speed on an empty road. To make a comparison, the open Navier-Stokes type model developed by Zhang(ZHANG, H. M. Driver memory, traffic viscosity and a viscous vehicular traffic flow model. Transp. Res. Part B, 37, 27–41(2003)) is adopted to predict the travel time through the ring road for providing the counterpart results.When the traffic free flow speed is 80 km/h, the braking distance is supposed to be 45 m,with the jam density uniquely determined by the average length of vehicles l ≈ 5.8 m. To avoid possible singular points in travel time prediction, a distinguishing period for time averaging is pre-assigned to be 7.5 minutes. It is found that the travel time increases monotonically with the initial traffic density on the ring road. Without ramp effects, for the ring road with the initial density less than the second critical density, the travel time can be simply predicted by using the equilibrium speed. However, this simpler approach is unavailable for scenarios over the second critical.

Tunnel effects on ring road traffic flow based on an urgent-gentle class traffic model

To explore tunnel effects on ring road traffic flow,a macroscopic urgent-gentle class traffic model is put forward.The model identifies vehicles with urgent and gentle classes,chooses the tunnel speed limit as free flow speed to express the fundamental diagram in the tunnel,and adopts algebraic expressions to describe traffic pressure and sound speed.With two speed trajectories at the Kobotoke tunnel in Japan,the model is validated,with good agreement with observed data.Numerical results indicate that in the case of having no ramp effects,tunnel mean travel time is almost constant dependent on tunnel length.When initial density normalized by jam density is above a threshold of about 0.21,a traffic shock wave originates at the tunnel entrance and propagates backward.Such a threshold drops slightly as a result of on-ramp merging effect,the mean travel time drops as off-ramp diversion effect intensifies gradually.These findings deepen the understanding of tunnel effects on traffic flow in reality.

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.