Abstract: 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.

Key words: Mikusinskis operator, variable operator, convergence, lineardifference equation with variable coefficients, solution of seriesform, operator equation, viscoelastic modeling, distinguishing period for time averaging, spatial-temporal pattern, travel time, traffic jam