Exploring the effects of work zone on vehicular flow on ring freeways with a tunnel using a three-lane continuum model

Freeway work zone forms as a result of traffic crash or road rehabilitation. To ascertain the effects of work zone with lane II completely blocked on vehicular flow on ring freeways with a tunnel, a three-lane continuum model is put forward. The mandatory net lane-changing rate from lane II to lane I or III just upstream of the work zone is described by a random number model, with the random number being produced within a small range around a median based on a golden section analysis. The net-changing rate between adjacent lanes is described using a lane-changing time on the basis of an assumption: the time ratio to relaxation time equals infinity when the absolute value of traffic densities between the two adjacent lanes is less than 1 veh/km, implying that the net-changing rate is zero; otherwise, the time ratio is inversely proportional to the vehicular spatial headway, which is equal to unity for traffic flow at saturation state, but infinity when the traffic flow is completely jammed. It is assumed that the freeway is a three lane ring with a total length of 100 km, and has a tunnel with a speed limit of 60 km/h and a length of 1.6 km located downstream the work zone with a length of 0.16 km. The free flow speeds on lanes I, II, and III are 120 km/h, 100 km/h, and 85 km/h, respectively. For the vehicular flow on the ring freeway with a tunnel, numerical simulations based on the three-lane continuum model are carried out with a reliable numerical method of high accuracy. It is found that the vehicular flow has two thresholds of traffic jam formation, one depending upon the tunnel and the other upon the work zone. The tunnel triggers a traffic jam when the initial density normalized by jam density is equal to the first threshold 0.15, and the work zone originates another traffic jam when the normalized initial density equals the second threshold 0.19. The freeway tunnel plays a dominant role in the prediction of mean travel time as soon as the tunnel has generated a traffic jam at the tunnel entrance. For the vehicular flow at unsaturated state, the average speed through the tunnel is about 26.67 km/h. When the normalized initial density exceeds the second threshold 0.19, the mean travel time through every lane increases with the initial density linearly. Vehicle fuel consumption can be estimated by interpolation with the time averaged grid traffic speed and an assumed vehicle performance curve. It is found that the vehicle fuel consumption is lane number dependent, and distributes with the initial density concavely, as well as has a value in the range of 6.5 to 8.3 l.