Analyzing work zone effects on vehicular flow on an annular freeway with a tunnel

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 1.5 km 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.