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This paper develops a three lane continuum model to analyze the effects of a work zone on vehicular flow on an annular freeway with a tunnel. The model expresses the mandatory lane changing rate just upstream of the work zone in an explicit algebraic form with the relevant random parameter generated from golden section analysis, and describes the discretionary lane changing rate between adjacent lanes with a lane changing time depending on local traffic flow density and relaxation time. It is assumed that the annular freeway has three lanes, a work zone with a length of 0.2 km and lane II completely blocked, an upstream tunnel of 1.5km long, and an initial jam between the tunnel and work zone. The three lane continuum model is applied in vehicular flow simulation with a 3rd order accuracy numerical scheme. Numerical results also indicate that golden section application in the analysis of work zone effects is helpful in obtaining density thresholds of traffic jam formation, the time averaged traffic speed through the tunnel, dependencies of mean travel time, and vehicle fuel consumption on the initial density normalized by jam density. Numerical results reveal that there are two density thresholds of traffic jam formation, if both density thresholds are normalized by traffic jam density, the first threshold relating to the work zone is 0.14, while the second depending on the tunnel is 0.21. In the absence of a work zone, the mean travel time through lane I is slightly longer than that estimated for cases with a work zone. As soon as initial density is above the second threshold, the time averaged speed through the tunnel is 31.91 km/h, which agrees well with published data.

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 ofthe work zone with is described by a random number model, with the random number being produced within a small range around a median based on 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 vehicular spatial headway, which is equal to unity for traffic flow at saturation state, but to infinity for traffic flow 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, 100 and 85 km/h respectively. For vehicular flows 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 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 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 initial density concavely, as well as has a value in the range of 6.5 to 8.3 l.

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