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 wo...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.展开更多
Fluid flow throttling is common in industrial and building services engineering.Similar tunnel throttling of vehicular flow is caused by the abrupt number reduction of roadway lane,as the tunnel has a lower lane numbe...Fluid flow throttling is common in industrial and building services engineering.Similar tunnel throttling of vehicular flow is caused by the abrupt number reduction of roadway lane,as the tunnel has a lower lane number than in the roadway normal segment.To predict the effects of tunnel throttling of annular freeway vehicular flow,a three-lane continuum model is developed.LaneⅢof the tunnel is completely blocked due to the need of tunnel rehabilitation,etc.There exists mandatory net lane-changing rate from laneⅢto laneⅡjust upstream of the tunnel entrance,which is described by a model of random number generated through a golden section analysis.The net-changing rate between adjacent lanes is modeled using a lane-changing time expressed explicitly in algebraic form.This paper assumes that the annular freeway has a total length of 100 km,a two-lane tunnel of length 2 km with a speed limit of 80 km/h.The free flow speeds on lanesⅠ,ⅡandⅢare assumed to be 110,100 and 90 km/h respectively.Based on the three-lane continuum model,numerical simulations of vehicular flows on the annular freeway with such a tunnel are conducted with a reliable numerical method of 3rd-order accuracy.Numerical results reveal that the vehicular flow has a smaller threshold of traffic jam formation in comparison with the case without tunnel throttling.Vehicle fuel consumption can be estimated by interpolation with time averaged grid traffic speed and an assumed curve of vehicle performance.The vehicle fuel consumption is lane number dependent,distributes with initial density concavely,ranging from 5.56 to 8.00 L.Tunnel throttling leads to an earlier traffic jam formation in comparison with the case without tunnel throttling.展开更多
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...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 lanechanging 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.展开更多
基金supported by National Natural Science Foundation of China(11972341)fundamental research project of Lomonosov Moscow State University‘Mathematical models for multi-phase media and wave processes in natural,technical and social systems’.
文摘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.
基金supported by the project of National Natural Science Foundation of China“exploring the road condition effect of travel time using emergency mitigation traffic flow models”(grant 11972341)fundamental research project of Lomonosov Moscow State University“mathematical models for multi-phase media and wave processes in natural,technical and social systems”。
文摘Fluid flow throttling is common in industrial and building services engineering.Similar tunnel throttling of vehicular flow is caused by the abrupt number reduction of roadway lane,as the tunnel has a lower lane number than in the roadway normal segment.To predict the effects of tunnel throttling of annular freeway vehicular flow,a three-lane continuum model is developed.LaneⅢof the tunnel is completely blocked due to the need of tunnel rehabilitation,etc.There exists mandatory net lane-changing rate from laneⅢto laneⅡjust upstream of the tunnel entrance,which is described by a model of random number generated through a golden section analysis.The net-changing rate between adjacent lanes is modeled using a lane-changing time expressed explicitly in algebraic form.This paper assumes that the annular freeway has a total length of 100 km,a two-lane tunnel of length 2 km with a speed limit of 80 km/h.The free flow speeds on lanesⅠ,ⅡandⅢare assumed to be 110,100 and 90 km/h respectively.Based on the three-lane continuum model,numerical simulations of vehicular flows on the annular freeway with such a tunnel are conducted with a reliable numerical method of 3rd-order accuracy.Numerical results reveal that the vehicular flow has a smaller threshold of traffic jam formation in comparison with the case without tunnel throttling.Vehicle fuel consumption can be estimated by interpolation with time averaged grid traffic speed and an assumed curve of vehicle performance.The vehicle fuel consumption is lane number dependent,distributes with initial density concavely,ranging from 5.56 to 8.00 L.Tunnel throttling leads to an earlier traffic jam formation in comparison with the case without tunnel throttling.
基金supported by the National Natural Science Foundation of China(No.11972341)the fundamental research project of Lomonosov Moscow State University‘Mathematical models for multi-phase media and wave processes in natural,technical and social systems’.
文摘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 lanechanging 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.
