Travel time through a ring road with a total length of 80 km has been predicted by a viscoelastic traffic model(VEM), which is developed in analogous to the non-Newtonian fluid flow. The VEM expresses a traffic pressu...Travel time through a ring road with a total length of 80 km has been predicted by a viscoelastic traffic model(VEM), which is developed in analogous to the non-Newtonian fluid flow. The VEM expresses a traffic pressure for the unfree flow case by space headway, ensuring that the pressure can be determined by the assumption that the relevant second critical sound speed is exactly equal to the disturbance propagation speed determined by the free flow speed and the braking distance measured by the average vehicular length. The VEM assumes that the sound speed for the free flow case depends on the traffic density in some specific aspects, which ensures that it is exactly identical to the free flow speed on an empty road. To make a comparison, the open Navier-Stokes type model developed by Zhang(ZHANG, H. M. Driver memory, traffic viscosity and a viscous vehicular traffic flow model. Transp. Res. Part B, 37, 27–41(2003)) is adopted to predict the travel time through the ring road for providing the counterpart results.When the traffic free flow speed is 80 km/h, the braking distance is supposed to be 45 m,with the jam density uniquely determined by the average length of vehicles l ≈ 5.8 m. To avoid possible singular points in travel time prediction, a distinguishing period for time averaging is pre-assigned to be 7.5 minutes. It is found that the travel time increases monotonically with the initial traffic density on the ring road. Without ramp effects, for the ring road with the initial density less than the second critical density, the travel time can be simply predicted by using the equilibrium speed. However, this simpler approach is unavailable for scenarios over the second critical.展开更多
To explore tunnel effects on ring road traffic flow,a macroscopic urgent-gentle class traffic model is put forward.The model identifies vehicles with urgent and gentle classes,chooses the tunnel speed limit as free fl...To explore tunnel effects on ring road traffic flow,a macroscopic urgent-gentle class traffic model is put forward.The model identifies vehicles with urgent and gentle classes,chooses the tunnel speed limit as free flow speed to express the fundamental diagram in the tunnel,and adopts algebraic expressions to describe traffic pressure and sound speed.With two speed trajectories at the Kobotoke tunnel in Japan,the model is validated,with good agreement with observed data.Numerical results indicate that in the case of having no ramp effects,tunnel mean travel time is almost constant dependent on tunnel length.When initial density normalized by jam density is above a threshold of about 0.21,a traffic shock wave originates at the tunnel entrance and propagates backward.Such a threshold drops slightly as a result of on-ramp merging effect,the mean travel time drops as off-ramp diversion effect intensifies gradually.These findings deepen the understanding of tunnel effects on traffic flow in reality.展开更多
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
The study of impacts of down-up hill road segment on the density threshold of traffic shock formation in ring road vehicular flow is helpful to the deep understanding of sags’bottleneck effect.Sags are freeway segmen...The study of impacts of down-up hill road segment on the density threshold of traffic shock formation in ring road vehicular flow is helpful to the deep understanding of sags’bottleneck effect.Sags are freeway segments along which the gradient increases gradually in the traffic direction.The main aim of this paper is to seek the density threshold of shock formation of vehicular flow in ring road with down-up hill segment,because down-up hill roadway segment is a source to cause capacity reduction that is an attractive topic in vehicular traffic science.To seek the density threshold numerically,a viscoelastic continuum model[1]is extended and used.To solve the model equations,a fifth-order weighted essentially non-oscillatory scheme for spatial discretization,and a 3rd order Runge-Kutta scheme for time partial derivative term are used.Validation by existing observation data and the Navier-Stokes like model[2]extended as EZM is done before conducting extensive numerical simulations.For ring road vehicular flow with three separated down-up hill segments,it is found that the density threshold of shock formation decreases monotonically with the relative difference of free flow speed,this variation can be simply fitted by a third order polynomial.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Project supported by the Russian Foundation for Basic Research(No.18-07-00518)the National Natural Science Foundation of China(No.10972212)
文摘Travel time through a ring road with a total length of 80 km has been predicted by a viscoelastic traffic model(VEM), which is developed in analogous to the non-Newtonian fluid flow. The VEM expresses a traffic pressure for the unfree flow case by space headway, ensuring that the pressure can be determined by the assumption that the relevant second critical sound speed is exactly equal to the disturbance propagation speed determined by the free flow speed and the braking distance measured by the average vehicular length. The VEM assumes that the sound speed for the free flow case depends on the traffic density in some specific aspects, which ensures that it is exactly identical to the free flow speed on an empty road. To make a comparison, the open Navier-Stokes type model developed by Zhang(ZHANG, H. M. Driver memory, traffic viscosity and a viscous vehicular traffic flow model. Transp. Res. Part B, 37, 27–41(2003)) is adopted to predict the travel time through the ring road for providing the counterpart results.When the traffic free flow speed is 80 km/h, the braking distance is supposed to be 45 m,with the jam density uniquely determined by the average length of vehicles l ≈ 5.8 m. To avoid possible singular points in travel time prediction, a distinguishing period for time averaging is pre-assigned to be 7.5 minutes. It is found that the travel time increases monotonically with the initial traffic density on the ring road. Without ramp effects, for the ring road with the initial density less than the second critical density, the travel time can be simply predicted by using the equilibrium speed. However, this simpler approach is unavailable for scenarios over the second critical.
基金This work is supported by the National Natural Science Foundation of China(Grant 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To explore tunnel effects on ring road traffic flow,a macroscopic urgent-gentle class traffic model is put forward.The model identifies vehicles with urgent and gentle classes,chooses the tunnel speed limit as free flow speed to express the fundamental diagram in the tunnel,and adopts algebraic expressions to describe traffic pressure and sound speed.With two speed trajectories at the Kobotoke tunnel in Japan,the model is validated,with good agreement with observed data.Numerical results indicate that in the case of having no ramp effects,tunnel mean travel time is almost constant dependent on tunnel length.When initial density normalized by jam density is above a threshold of about 0.21,a traffic shock wave originates at the tunnel entrance and propagates backward.Such a threshold drops slightly as a result of on-ramp merging effect,the mean travel time drops as off-ramp diversion effect intensifies gradually.These findings deepen the understanding of tunnel effects on traffic flow in reality.
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 National Natural Science Foundation of China(NSFC No.11972341)fundamental research project of Lomonosov Moscow State University’s Mathematical models for multi-phase media and wave processes in natural,technical and social systems.
文摘The study of impacts of down-up hill road segment on the density threshold of traffic shock formation in ring road vehicular flow is helpful to the deep understanding of sags’bottleneck effect.Sags are freeway segments along which the gradient increases gradually in the traffic direction.The main aim of this paper is to seek the density threshold of shock formation of vehicular flow in ring road with down-up hill segment,because down-up hill roadway segment is a source to cause capacity reduction that is an attractive topic in vehicular traffic science.To seek the density threshold numerically,a viscoelastic continuum model[1]is extended and used.To solve the model equations,a fifth-order weighted essentially non-oscillatory scheme for spatial discretization,and a 3rd order Runge-Kutta scheme for time partial derivative term are used.Validation by existing observation data and the Navier-Stokes like model[2]extended as EZM is done before conducting extensive numerical simulations.For ring road vehicular flow with three separated down-up hill segments,it is found that the density threshold of shock formation decreases monotonically with the relative difference of free flow speed,this variation can be simply fitted by a third order polynomial.
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.
