Estimation of travel time through a composite ring road by a viscoelastic traffic flow model

Abstract

To estimate travel time through a composite ring road, a viscoelastic traffic flow model is developed by assuming traffic sound speed on empty road is just equal to free flow speed. Based on the viscoelastic model, numerical tests of traffic flows were conducted to provide node traffic speed for estimating travel time. The composite ring road with three ramp intersections has five parts, each part is composed of a tunnel, a horizontal, an uphill and a downhill segment. The length of uphill segment is the same as the length of downhill segment, both are 1km, while the tunnel length can be 1, 0.5, and 0.1km. To validate the reliability and feasibility of the viscoelastic traffic flow model, the Navier–Stokes like model Zhang (2003) is extended and adopted to provide the counterpart numerical results for comparison. It was found that in case without ramp effects any tunnel inlet becomes a starting point of traffic congestion region when initial density normalized by its jam value is not below 0.2. But in case with ramp effects, even if initial density is 0.15, downstream an on-ramp intersection, any tunnel inlet can also induce traffic shock when the tunnel is positioned upstream another off-ramp intersection. The off ramp flow can shorten mean travel time and increase its root mean square value significantly. The fitted expression of mean travel time has the form σtf=Aρ0m+bwhere A=8.9686, m=1.6260, b=0.8424, ρ0 is the initial density varying from 0.1 to 0.625.