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An evaluation of lane management strategy for CAV priority in mixed traffic

An evaluation of lane management strategy for CAV priority in mixed traffic INTRODUCTIONConnected autonomous vehicles (CAVs) have seen rapid development in recent years in tandem with new developments in the Internet and other communication technologies [1]. These vehicles can enhance traffic safety by eliminating human error [2] and can increase the stability of traffic flow by decreasing traffic oscillations (the stop‐and‐go phenomenon) [3]. In addition, CAVs can play an important role in improving traffic flow efficiency due to their ability to follow each other at shorter distances [4, 5] and to reduce emissions through lower fuel consumption through more efficient driving [6, 7].However, mixed traffic flow (between CAVs and non CAVs) will still exist, and there will still be complex interactions between CAVs and human‐driven vehicles (HDVs) [8]. Therefore, the market penetration rate of CAVs has always been a concern with mixed traffic flow. Previous research has indicated that traffic flow stability can be improved, and mean spacing and speed variance can both be reduced by increasing the amount of CAVs on the road [9–11]. In addition, some other models have shown that road capacity may significantly increase at a high CAV penetration rate or even a full CAV scenario [12, 13]. For example, Liu et al. simulated CAVs in mixed traffic flow and found that freeway capacity at 100% market penetration was roughly 90% higher than at 0% [14]. However, the difference in capacity is not significant at low CAV penetration [15]. In addition, the benefits of additional CAVs may be offset by the interaction between HDVs and CAVs in practice. This is because a CAV must degrade into an Autonomous Vehicle (AV) (CAV degradation) or be taken over by humans when the preceding vehicle is an HDV. Hence, a decrease in road capacity may occur [16, 17].Managed lane strategies, especially CAV‐dedicated lanes, are considered to be one of the most effective solutions to this problem. Highways may effectively be able to improve traffic capacity, reduce the CAV degradation rate [18], promote longer CAV platoons [19], and enhance safety with dedicated CAV lanes [20]. Some research has found that CAV‐dedicated lanes are only beneficial at high penetration rates [21–24], however. For example, Talebpour et al. evaluated three strategies and found that the throughput can be significantly improved at penetration rates of more than 50% for a two‐lane highway and 30% for a four‐lane highway [25]. However, the deployment of dedicated lanes can also cause a waste of road resources and worsen traffic conditions when the CAV penetration rate is low [26, 27]. Hence, it may be best for dedicated lanes to be gradually deployed with an increase in CAV market penetration [28, 29].Other research suggested that mixed lanes or dedicated lanes for CAVs and high‐occupancy vehicles (HOVs) (driven by humans)can be set at low CAV penetration rates [30]. Liu and Song proposed autonomous vehicle/toll (AVT) lanes as an alternative to dedicated lanes during times when CAV penetration rate drops. The AVT allows AVs to enter for free but requires HDVs pay a toll to enter these lanes [31]. This is one example where road capacity might be further improved through effective lane management.Lane management (for example, using HOV lanes, dedicated bus lanes (DBLs), intermittent bus lanes (IBLs) etc.) is considered to be an effective traffic management measure under certain conditions. In addition, the provision of active lane management strategies can promote the development of CAVs, provide better driving experiences for CAVs, and improve overall traffic capacity. Researchers have investigated different lane management strategies by building theoretical models or using simulation software and have found that appropriate lane management strategies can further increase road capacity at different penetration rates [32–34]. Zhong and Lee even proposed managed lane score matrices to assess the overall suitability of each lane management strategy [35].In general, appropriate lane management strategies may be able to further improve lane utilization and can increase road capacity. However, intermittent CAV priority lane management has yet to be considered. An intermittent CAV priority lane can greatly reduce the CAV degradation rate and optimize road resources through the real‐time allocation of right‐of‐way. However, frequent lane‐changing behaviour can lead to a decrease in road capacity, especially at high CAV market penetration rates and high traffic demand. Therefore, it is important to understand mixed traffic flow characteristics in determining appropriate lane management strategies for different scenarios under different traffic demands and CAV penetration rates.To this end, in this study, we analysed the characteristics of mixed traffic flow under different lane management strategies through theoretical and numerical study, and evaluated the performance of these lane management strategies. The contributions of this study are as follows: (1) Previous studies mainly focus on deploying of dedicated lanes. In this study, a new lane management strategy that considers the deployment of the CAV priority lane is proposed, simulated, and evaluated to find the possibility of further improving road performance. (2) A theoretical model is proposed to evaluate the capacity under different lane management strategies. Numerical simulation demonstrates that the road capacity can be further increased through appropriate lane management. (3) Three different lane management strategies for a two‐lane road with mixed traffic are proposed based on theoretical analysis. These strategies are evaluated by simulation software, under different scenarios with different traffic demands and CAV penetration rates. The simulation results cross‐validate the results of the theoretical model in terms of traffic capacity and further prove that the appropriate lane management strategy can further improve the performance of travel time and speed.The remainder of this paper is organized as follows. Section 2 proposes a capacity model for mixed traffic under different lane management strategies. A simulation environment is established to evaluate three different lane strategies under different CAV penetration rates and traffic demand scenarios based on the Simulation of Urban Mobility (SUMO) framework in Section 3. Then, our simulation results are analysed in Section 4. Finally, our conclusions and a discussion of future work are presented in Section 5.CAPACITY FORMULATIONSIn this paper, it is assumed that vehicles travel at the optimal speed v until they reach their corresponding minimum headways when traffic flow reaches the capacity. Note that the physical lane capacity is determined at the beginning of the road design, and is independent of the lane policy. In this section, traffic capacity is defined as the maximum sustainable flow for given proportions of CAVs and HDVs in traffic streams. The capacity models under three different lane management strategies are established by us based on this assumption. The notations for all models are listed in Table 1, and the capacity formulas for mixed lanes, dedicated lanes, and priority lanes are proposed in Sections 2.1, 2.2, and 2.3, respectively.1TABLENomenclature listNotionsDefinitionshsc${h}_{sc}$spacing of CAVshsh${h}_{sh}$spacing of HDVshsch${h}_{sch}$spacing of AVsh¯s${\bar{h}}_s$average spacing of all vehiclesλc${\lambda }_c$spacing coefficient of CAVs in a platoonλch${\lambda }_{ch}$spacing coefficient of AVsvfree‐flow speedαr${\alpha }_r$CAV penetration rate in the regular laneαd${\alpha }_d$CAV penetration rate in the dedicated laneαp${\alpha }_p$CAV penetration rate in the priority laneC0traffic capacity with only HDVsCr${C}_r$traffic capacity of the regular laneCm${C}_m$traffic capacity of the mixed laneCe${C}_e$traffic capacity of the dedicated laneCp${C}_p$traffic capacity of the priority laneQtraffic flow of all lanesqr${q}_r$traffic flow of the regular laneqe${q}_e$traffic flow of the dedicated laneqp${q}_p$traffic flow of the priority lanepCAV penetration ratepCAV${p}_{CAV}$CAVs in a platoon penetration ratepAV${p}_{AV}$AV penetration ratepHDV${p}_{HDV}$HDV penetration ratep0CAV critical penetration rate when the CAV dedicated lane is just saturatedpp${p}_p$CAV critical penetration rate when the CAV priority lane is just saturatedlclear${l}_{clear}$clear distanceCapacity of the mixed lane policyThe mixed lane management strategy (No Managed Lane (NML)) is where CAVs and HDVs are mixed in the lane, as shown in Figure 1. In a connected environment, CAVs can keep driving with a smaller spacing than HDVs when the preceding vehicle is a CAV. Therefore, the spacing of CAVs can be expressed by λc(1>λc>0)${\lambda }_c( {1 &gt; {\lambda }_c &gt; 0} )$:1hsc=λchsh\begin{equation}{h}_{sc} = {\lambda }_c{h}_{sh}\end{equation}where hsc${h}_{sc}$ and hsh${h}_{sh}$ are the spacing of CAVs and HDVs, respectively. The CAV degrades into an AV when the preceding vehicle is an HDV. Therefore, the spacing coefficient of AVs is smaller than that of CAVs. The spacing of AVs can be expressed by λch(1>λch>λc>0)${\lambda }_{ch}( {1 &gt; {\lambda }_{ch} &gt; {\lambda }_c &gt; 0} )$:2hsch=λchhsh\begin{equation}{h}_{sch} = {\lambda }_{ch}{h}_{sh}\end{equation}where hsch${h}_{sch}$ is the spacing of AVs. The variable p represents the proportion of CAVs in the entire traffic flow, and pCAV${p}_{CAV}$, pAV${p}_{AV}$, and pHDV${p}_{HDV}$ represent the proportion of CAVs (the preceding vehicle is a CAV), AVs (the preceding vehicle is an HDV), and HDVs, respectively. Thus the pCAV=p2${p}_{CAV} = {p}^2\ $, pAV=p(1−p)${p}_{AV} = \ p( {1 - p} )$ and pHDV=1−p${p}_{HDV} = \ 1 - p$ can be obtained, therefore,3p=p2+p1−p\begin{equation}p = {p}^2 + p\left( {1 - p} \right)\end{equation}1FIGUREIllustration of the mixed laneThe change in the proportion of different vehicle types under different penetration rates p is shown in Figure 2.2FIGUREThe proportion of vehicle type changes with PThe average headway of all vehicles on a single‐lane h¯s${\bar{h}}_s\ $can be expressed by Equation (4) below.4h¯s=hsc·pCAV+hsch·pAV+hsh·pHDV=hsc·p2+hsch·p1−p+hsh·1−p\begin{equation} \def\eqcellsep{&}\begin{array}{l} {\overline h }_s = {h}_{sc} \cdot {p}_{CAV} + {h}_{sch} \cdot {p}_{AV} + {h}_{sh} \cdot {p}_{HDV}\\[6pt] \!\quad\mathop {}\nolimits = {h}_{sc} \cdot {p}^2 + {h}_{sch} \cdot p\left( {1 - p} \right) + {h}_{sh} \cdot \left( {1 - p} \right) \end{array} \end{equation}Substituting Equations (1) and (2) into Equation (4) gives us:5h¯s=λchsh·p2+λchhsh·p1−p+hsh·1−p\begin{equation}{\overline h }_s = {\lambda }_c{h}_{sh} \cdot {p}^2 + {\lambda }_{ch}{h}_{sh} \cdot p\left( {1 - p} \right) + {h}_{sh} \cdot \left( {1 - p} \right)\end{equation}Additionally, the traffic flow capacity of mixed traffic flow is expressed by Equation (6).6Cm=1h¯s/v=vhsc·p2+hsch·p1−p+hsh·1−p=vhshλc·p2+λch·p1−p+1−p=C0λc·p2+λch·p1−p+1−p\begin{equation} \def\eqcellsep{&}\begin{array}{l} {C}_m = \dfrac{1}{{{{\overline h }}_s/v}} = \dfrac{v}{{{h}_{sc} \cdot {p}^2 + {h}_{sch} \cdot p\left( {1 - p} \right) + {h}_{sh} \cdot \left( {1 - p} \right)}}\\[12pt] \quad\mathop {}\nolimits = \dfrac{v}{{{h}_{sh}\left( {{\lambda }_c \cdot {p}^2 + {\lambda }_{ch} \cdot p\left( {1 - p} \right) + \left( {1 - p} \right)} \right)}}\\[12pt] \quad\mathop {}\nolimits = \dfrac{{{C}_0}}{{{\lambda }_c \cdot {p}^2 + {\lambda }_{ch} \cdot p\left( {1 - p} \right) + \left( {1 - p} \right)}} \end{array} \end{equation}where αr${\alpha }_r$ denotes the CAV penetration rate on the regular lane. Therefore, the traffic flow capacity in the regular lane can be expressed by Equation (7).7Cr=C0λc·αr2+λch·αr1−αr+1−αr\begin{equation}{C}_r = \frac{{{C}_0}}{{{\lambda }_c \cdot {\alpha }_r^2 + {\lambda }_{ch} \cdot {\alpha }_r\left( {1 - {\alpha }_r} \right) + \left( {1 - {\alpha }_r} \right)}}\end{equation}Using Equation (7), Figure 3 shows the impact of parameters λc${\lambda }_c\ $and λch${\lambda }_{ch}$ on capacity gain under different CAV penetration rates.3FIGURE(a) Capacity gain changes with various p(λch=${\bm{p }}({\bm \lambda }_{{{\bm ch}}} = \ $0.8); (b) Capacity gain changes with various p(λch=${\bm{p }}({\bm \lambda }_{\bm ch} = \ $0.6)As shown in Figure 3, capacity gain increases with increasing CAV penetration rates and decreasing λc${\lambda }_c$ and λch${\lambda }_{ch}$, but capacity gain has a non‐linear relationship with penetration rate. The capacity gain increases faster as λc${\lambda }_c$ decreases as can be seen in Figure 3a. This means that changes in road capacity are influenced by the development of CAVs. Furthermore, at different λch${\lambda }_{ch}$, the capacity gain increases concavely with the penetration rate can be seen in Figure 3b. Initially, the traffic capacity rapidly increases with an increasing number of CAVs in the traffic flow. After that, however, the number of HDVs in the traffic flow becomes less and less as penetration rate increase further. Therefore, the probability of a CAV following an HDV becomes lower, and the growth rate of traffic capacity slows down. Note that the traffic flow is composed entirely of CAVs when the penetration rate is 1. In other words, traffic capacity is not affected by the value of λch${\lambda }_{ch}$ in this case due to the absence of any CAVs following HDVs.Capacity of the dedicated lane policyThe dedicated lane management strategy (DL policy) is where CAVs and HDVs are mixed in regular lanes but only CAVs are allowed to drive in the CAV‐dedicated lanes, as shown in Figure 4. The traffic capacity of the CAV dedicated lane is shown in Equation (8).8Ce=C0λc\begin{equation}{C}_e = \frac{{{C}_0}}{{{\lambda }_c}}\end{equation}4FIGUREIllustration of the CAV dedicated laneThe variables qe${q}_e$ and qr${q}_r$ represent the traffic flow on the dedicated lane and regular lane, respectively, and Q denotes the traffic flow of all lanes. The flow conservation equation is shown in Equations (9) and (10).9Q=qe+qr\begin{equation}Q = {q}_e + {q}_r\end{equation}10p·Q=αeqe+αrqr\begin{equation}p \cdot Q = {\alpha }_e{q}_e + {\alpha }_r{q}_r\end{equation}where p is CAV penetration rate, αe${\alpha }_e$ is the CAV penetration rate in the CAV dedicated lane, and αr${\alpha }_r$ is the CAV penetration rate in the regular lane. Only CAVs are allowed to drive in the CAV dedicated lane, so αe=1${\alpha }_e = \ 1$, and Equation (10) can be rewritten as:11p·Q=qe+αrqr\begin{equation}p \cdot Q = {q}_e + {\alpha }_r{q}_r\end{equation}Assuming that CAVs will only enter the regular lane when the capacity of the CAV dedicated lane reaches saturation, the CAV dedicated lane is just saturated when:12p0=qeqe+qr\begin{equation}{p}_0 = \frac{{{q}_e}}{{{q}_e + {q}_r}}\end{equation}Substituting Equation (8) into Equation (12) gives:13p0=11+λc\begin{equation}{p}_0 = \frac{1}{{1 + {\lambda }_c}}\end{equation}As shown in Figure 5, the critical penetration rate can be obtained at a smaller penetration as λc${\lambda }_c$ increases. This is because CAVs can travel with smaller spacing that increases the capacity of CAV‐dedicated lanes.5FIGUREp0 and αr change with λc and p, respectively (λc=0.6${{\bm{\lambda }}}_{\bm{c}} = {\bm{\ }}0.6$)When p<p0$p &lt; {p}_0$, the CAV‐dedicated lane is not saturated, and there are no CAVs in the regular lane. At this moment, αr=0${\alpha }_r = \ 0$, p·Q=qe$p \cdot Q\ = {q}_e\ $, and the road flow is given by:14Q=p·Q+qr\begin{equation}Q = p \cdot Q + {q}_r\end{equation}Rewriting Equation (14) yields:15Q=qr1−p=Cr1−p=C01−p\begin{equation}Q = \frac{{{q}_r}}{{1 - p}} = \frac{{{C}_r}}{{1 - p}} = \frac{{{C}_0}}{{1 - p}}\end{equation}The CAV‐dedicated lane reaches a saturated state when p≥p0$p \ge {p}_0$. Therefore, more CAVs enter the regular lane with an increase in p. The CAV penetration rate can thus be expressed as Equation (16).16p=qe+αrqrqe+qr\begin{equation}p = \frac{{{q}_e + {\alpha }_r{q}_r}}{{{q}_e + {q}_r}}\end{equation}Under this condition, the road flow is:17p·Q=qe+αrqr=Q−qr+αrqr\begin{equation}p \cdot Q = {q}_e + {\alpha }_r{q}_r = \left( {Q - {q}_r} \right) + {\alpha }_r{q}_r\end{equation}and rewriting Equation (17) gives us:18Q=qr1−αr1−p=Cr1−αr1−p\begin{equation}Q = \frac{{{q}_r\left( {1 - {\alpha }_r} \right)}}{{1 - p}} = \frac{{{C}_r\left( {1 - {\alpha }_r} \right)}}{{1 - p}}\end{equation}In summary, the traffic capacity of the DL policy at different CAV penetration rates is expressed as Equation (19).19Q=C01−p,ifp<p0Q=Cr1−αr1−p,ifp>p0\begin{equation}\left\{ \def\eqcellsep{&}\begin{array}{l} Q = \dfrac{{{C}_0}}{{1 - p}},\quad i\!{f}p &lt; {p}_0\\[12pt] Q = \dfrac{{{C}_r\left( {1 - {\alpha }_r} \right)}}{{1 - p}},\quad i\!{f}p &gt; {p}_0 \end{array} \right.\end{equation}The changes in the capacity gain for DL policy with various p that is calculated from Equation (19) are shown in Figure 6. The CAV‐dedicated lane is not saturated and the capacity gain is less than 1 when the penetration rate is less than 50%. This is because the regular lane is saturated, but the number of CAVs on the dedicated lane is insufficient, resulting in a serious waste of road resources. Therefore, the CAV‐dedicated lane cannot improve road capacity under these conditions. The traffic capacity starts to increase due to the fact that the capacity gain is greater than 1 when the penetration rate exceeds 50%, and the CAV‐dedicated lane is just saturated when the penetration rate reaches the critical penetration rate p0 (p0=0.625${p}_0 = \ 0.625$ when λc=0.6${\lambda }_c = \ 0.6$). Here, the CAVs enter the regular lane, as the penetration rate further increases, and the penetration rate αr${\alpha }_r$ of the CAVs in the regular lane gradually increases as well.6FIGURECapacity gain of DL policy changes with various p (λc=0.6,λch=0.8${{\bm{\lambda }}}_{\bm{c}} = {\bm{\ }}0.6,\ \ {{\bm{\lambda }}}_{{\bm{ch}}} = {\bm{\ }}0.8$)Capacity of the priority lane policyThe priority lane management strategy (PL policy) is shown in Figure 7. In this scenario, all HDVs are equipped with information receiving equipment that can receive lane change commands from CAVs or Road Side Units (RSUs). As a CAV progresses along the priority lane, the HDVs in the lane ahead of it can receive V2X information to determine if they need to leave the lane. The distance between the CAV and the downstream vehicles that must exit is defined as “Clear Distance”.7FIGUREIllustration of CAV priority laneHDVs that are behind a CAV are allowed to enter the priority lane at any time in this scenario. The average headway of all vehicles in the priority lane can be expressed by Equation (20).20h¯s=hsc·P2+lclear·P1−P+hsh·1−P=λrhsc·P2+λclearhsh·P1−P+hsh·1−P\begin{equation} \def\eqcellsep{&}\begin{array}{l} {\overline h }_s = {h}_{sc} \cdot {P}^2 + {l}_{clear} \cdot P\left( {1 - P} \right) + {h}_{sh} \cdot \left( {1 - P} \right)\\[6pt] \quad\mathop {}\nolimits = {\lambda }_r{h}_{sc} \cdot {P}^2 + {\lambda }_{clear}{h}_{sh} \cdot P\left( {1 - P} \right) + {h}_{sh} \cdot \left( {1 - P} \right) \end{array} \end{equation}where lclear${l}_{clear}$ is clear distance, lclear=λclearhsh${l}_{clear} = {\lambda }_{clear}\ {h}_{sh}$, and λclear(>1)${\lambda }_{clear}( &gt; 1)$. The variable αp${\alpha }_p$ denotes the CAV penetration rate in the priority lane. The mixed traffic flow capacity of the CAV priority lane can be expressed by Equation (21).21CP=C0λc·αp2+λclear·αp1−αp+1−αp\begin{equation}{C}_P = \frac{{{C}_0}}{{{\lambda }_c \cdot {\alpha }_p^2 + {\lambda }_{clear} \cdot {\alpha }_p\left( {1 - {\alpha }_p} \right) + \left( {1 - {\alpha }_p} \right)}}\end{equation}The variables qp${q}_p\ $andqr$\ {q}_r$ represent the flow in the priority lane and regular lane, respectively. The traffic conservation equations can be expressed as Equations (22) and (23).22Q=qp+qr\begin{equation}Q = {q}_p + {q}_r\end{equation}23p·Q=αpqp+αrqr\begin{equation}p \cdot Q = {\alpha }_p{q}_p + {\alpha }_r{q}_r\end{equation}It is once again assumed that CAVs will only enter the regular lane when the capacity of the CAV priority lane reaches saturation, and let the critical CAV penetration rate be pp${p}_p$ when the CAV priority lane is just saturated.When p<pp$p &lt; {p}_p$, the CAV priority lane is not saturated, and there are no CAVs in the regular lane. At this moment, αr=0${\alpha }_r = \ 0$, p·Q=αpqp$p \cdot Q\ = {\alpha }_p{q}_p\ $, and the following conditions are met:24p=αrqpqp+qr\begin{equation}p = \frac{{{\alpha }_r{q}_p}}{{{q}_p + {q}_r}}\end{equation}and25p·Q=αpqp\begin{equation}p \cdot Q = {\alpha }_p{q}_p\end{equation}Rewriting Equation (25) yields:26Q=αpqpp\begin{equation}Q = \frac{{{\alpha }_p{q}_p}}{p}\end{equation}When p>pp$p &gt; {p}_p$, the CAV priority lane reaches the saturation state, which is equivalent to the CAV‐dedicated lane scenario from the previous section. In summary, the traffic capacity of the PL policy is expressed as Equation (27) at different penetration rates.27Q=Cpαpp,ifp<ppQ=Cr1−αr1−p,ifp>pp\begin{equation}\left\{ \def\eqcellsep{&}\begin{array}{l} Q = \dfrac{{{C}_p{\alpha }_p}}{p},\mathop {}\nolimits i{f}p &lt; {p}_p\\[11pt] Q = \dfrac{{{C}_r\left( {1 - {\alpha }_r} \right)}}{{1 - p}},\mathop {}\nolimits i{f}p &gt; {p}_p \end{array} \right.\end{equation}When more CAVs enter the priority lane, the penetration rate further increases, and the penetration rate αp${\alpha }_p$ of the CAVs in the priority lane gradually increases, as shown in Figure 8. The priority lane is saturated when the critical penetration rate is reached. The probability of a CAV following an HDV increases and then decreases when the penetration rate increases (Figure 2‐Blue line), therefore the capacity of the priority lane shows the same behaviour.8FIGURECapacity gain of PL policy changes with various p (λc=0.6,λclear${{\bm{\lambda }}}_{\bm{c}} = \ 0.6,\ {{\bm{\lambda }}}_{{\bm{clear}}}$= 6)As shown in Figure 9, the capacity of the priority lane management strategy decreases with an increase in CAVs because of the limitation of clear distance when the penetration rate is less than 20%. The opposite situation occurs when the penetration rate is greater than 20%. Hence PL policy performs better than DL policy until the critical penetration rate pp${p}_p$ is reached. This is because up until this point the priority lane is not saturated, and the priority lane allows HDV to enter. Since the CAV priority lane is saturated when the penetration rate reaches the critical penetration rate pp${p}_p$ (pp=0.625${p}_p = \ 0.625$), after that it necessarily becomes the same as the dedicated lane. Therefore, the total capacity of DL policy and PL policy is the same when the penetration rate reaches the critical penetration rate.9FIGUREComparison of DL policy and PL policy (λc=0.6,λclear${{\bm{\lambda }}}_{\bm{c}} = \ 0.6,\ {{\bm{\lambda }}}_{{\bm{clear}}}$= 6)Determining the true critical penetration rate is difficult because of the complexity of the priority lane. The influence of lane‐changing behaviour is not easy account for in the theoretical model. Therefore, the traffic characteristics of different lane management strategies are further studied with micro‐simulation software, which can overcome the difficulty of the proposed theoretical model and cross‐validate its results with numerical analysis.SIMULATIONDifferent lane management strategies under different penetration rates and demands will be evaluated in this section. First, the SUMO [36] simulation framework is introduced in Section 3.1. Second, the car‐following models and lane change model are introduced in Sections 3.2 and 3.3, and 3.4, respectively. Finally, the simulation scenarios are listed in Section 3.5.Simulation frameworkThe SUMO framework is open source micro‐simulation software that is widely used in the field of CAV simulation [37]. Through its TraCI (Traffic Control Interface) interface secondary development and real‐time control of vehicles can be realized with the help of Python. In addition, SUMO has a large number of built‐in vehicles following models, and the parameters of these models are easy to adjust. For our purposes, the Krauss model and CACC (Cooperative Adaptive Cruise Control) model are selected as the car‐following models of HDVs and CAVs, respectively, and the model parameters are shown in Table 2. The real‐time simulation of priority lanes is performed using Python through the TraCI interface, and the operational logic in each simulation step is shown in Figure 10.2TABLEParameters in the simulationParameterDescriptionValuetauThe driver's desired (minimum) time headway1.4 s (HDV)0.6 s (CAV)accelthe acceleration ability of vehicles2.6 m/s2decelthe deceleration ability of vehicles4.5 m/s210FIGUREFlowchart of each simulation time stepsHDV car‐followingThe Krauss model [38] was used to model HDVs, which is also the default car‐following model of SUMO. The Krauss model allows a vehicle to go as fast as possible while maintaining safety. This means that collisions can always be avoided if the leader brakes within the maximum acceleration range. Therefore, the vehicle speed is always less than its safe speed, and its safe speed calculation equation is:28vsafe=vp+g−vτvp+v/2b+τ\begin{equation}{v}_{safe} = {v}_p + \frac{{g - v\tau }}{{\left( {{v}_p + v} \right)/2b + \tau }}\end{equation}where vp${v}_p$ is the speed of the preceding vehicle, g is the distance between vehicles, v is the current vehicle speed, b is the maximum deceleration, and τ is the driver's reaction time. The Krauss model is expressed in Equations (29) and (30):29vd=minvt+a,vmax,vsafe\begin{equation}{v}_d = min\left( {{v}_t + a,{v}_{max},{v}_{safe}} \right)\end{equation}30vt+1=max0,randvd−εa,vd\begin{equation}{v}_{t + 1} = max\left[ {0,rand\left( {{v}_d - \varepsilon a,{v}_d} \right)} \right]\end{equation}where vd${v}_d$ is vehicle desired speed, vt${v}_t$ is speed at time t, a is the maximum speed, vmax${v}_{max}$ is the maximum limit vehicle speed on the road, ε is the error caused by the driver's imperfect driving whose value is set to 0.5, and vt+1${v}_{t + 1}$ is speed at time t+1.CAV car‐followingMany CACC models were widely used for CAV simulations. The integrated CACC car‐following model is based on the work of Milanés, Xiao and Wang [39–41] in SUMO. The CACC model is divided into three control modes:Speed control modeThis mode will keep the vehicle at the preset desired speed if there is no leader in front of the vehicle or if the time gap is greater than 2 s.31ai,k=k0·vd−vi,k−1\begin{equation}{a}_{i,k} = {k}_0 \cdot \left( {{v}_d - {v}_{i,k - 1}} \right)\end{equation}Here vd${v}_d$ is the driver's desired speed, and k0 is control gain to determine the rate of speed error for acceleration, with value 0.4 s−1.Gap control modeThis mode is designed to maintain a constant time gap between the vehicle and the leader when the vehicle is in the following state. This mode is activated when gap and speed deviations are concurrently smaller than 0.2 m and 0.1 m/s, respectively.32vi,k=vi,k−1+kp·ei,k−1+kd·ei,k−1−ei,k−2Δt\begin{equation}{v}_{i,k} = {v}_{i,k - 1} + {k}_p \cdot {e}_{i,k - 1} + {k}_d \cdot \frac{{\left( {{e}_{i,k - 1} - {e}_{i,k - 2}} \right)}}{{\Delta t}}\end{equation}The variable ei,k−1${e}_{i,k - 1}$ is the gap error of vehicle i at time step k−1 (Equation (33)), and kp${k}_p$ and kd${k}_d$ are 0.45 s−1 and 0.0125, respectively. In addition,33ei,k=xi−1,k−1−xi,k−1−L−td·vi,k−1−d0\begin{equation}{e}_{i,k} = {x}_{i - 1,k - 1} - {x}_{i,k - 1} - L - {t}_d \cdot {v}_{i,k - 1} - {d}_0\end{equation}where xi−1,k−1−xi,k−1${x}_{i - 1,k - 1} - {x}_{i,k - 1}$ is inter‐vehicle spacing at time step k−1, td${t}_d$ is the desired time gap, L is vehicle length, and d0 is spacing margin, determined by Equation (34).34d0=fx=0,v≥10m/s−0.125v,v<10m/s\begin{equation}{d}_0 = f\left( x \right) = \left\{ \def\eqcellsep{&}\begin{array}{l} 0,\qquad\quad \mathop {}\nolimits v \ge 10{\rm{ m/s}}\\[6pt] - 0.125v,\mathop {}\nolimits\quad v &lt; 10{\rm{ m/s}} \end{array} \right.\end{equation}Gap‐closing control modeA smooth transition from speed control mode to gap control mode can be achieved by this mode when the time gap is less than 1.5 s. The vehicle retains the previous control mode when the time gap is between 1.5 and 2 s. The feedback gain on speed error and gap error in Equation (32) is adjusted to kp${k}_p$ and kd${k}_d$, which are 0.005 s–1 and 0.05, respectively in order to reduce the speed difference and gap more safely.Lane change modelThe LC2013 lane change model in SUMO was used for the simulation in this paper [42]. In this model, vehicle lane changes are determined by the 4‐layered hierarchy of motivations: strategic change, cooperative change, tactical change, and regulatory change. The following sub‐steps are executed for every vehicle during each simulation step.Calculation of preferred successor lanes;Calculation of safe speed under the assumption of staying in the current lane and integration with the speed request related to the lane change in the previous simulation step;Lane‐changing model calculation of change request (left, right, stay);Performance of lane change or calculation of speed request for the next simulation step.Simulation scenarioNowadays, the simulation scenario is established with a road length of 1000 m, 2 lanes, and a speed limit of 33.3 m/s. The simulation time step for CAVs and HDVs are 0.1 and 1 s, respectively, and the simulation lasted for 3800 s. The first 100 s and the last 100 s are discarded for more accurate data collection. In the initial state, vehicles are inserted into the road network at equal intervals, and a safe distance must be kept from any leading vehicle according to its following model. Furthermore, in each simulation, vehicles are loaded by setting the number of vehicles per hour. The time interval between vehicles entering the simulation is different, so the vehicle distribution is also different, which ensures the randomness of vehicle distribution to a certain extent. For this two‐lane highway, there are three lane management strategies:No managed lane (NML): There is no additional management strategy for the lanes, and CAVs and HDVs are mixed in the lanes;One dedicated lane (DL): The leftmost lane is a CAV‐dedicated lane, and only CAVs are allowed to use it;One priority lane (PL): The leftmost lane is the CAV priority lane. By clearing the HDVs within a certain distance, CAVs can be guaranteed to pass first.To study the performance of each lane management strategy under different traffic conditions, penetration rates and traffic demand are selected by us as variables, from 0–100% with 10% intervals and from 2000–8000 veh/h with 500 veh/h intervals, respectively. Then, the three lane management strategies are simulated and the simulation results are analysed by combining these two variables. A full experiment was run 429 (3×13×11) times for different variable combinations. The simulation seed of each simulation was generated by SUMO based on the current system time to eliminate random errors. Performance data (throughput, travel time, and speed) are collected for each simulation run.ANALYSIS OF SIMULATION RESULTSThe raw data of each time step in three scenarios were collected and analysed for throughput, travel time, and speed.ThroughputThe simulation results of three lane management strategies are shown in Figure 11. The other lane management strategies can further improve road capacity beyond that of NML.11FIGUREComparison of three lane management strategiesHowever, the effect of improvement is affected by traffic demand and penetration rate. Four scenarios at demands of 3000, 4500, 6000 and 7500 veh /h were selected to further analyse the performance of different lane management strategies. Simulation results as shown in Figure 12.12FIGURESimulation result under four demandsAs shown in Figure 12a, the throughput of the three lane management strategies has similar performance when the penetration rate is higher than 40%. Moreover, the traffic demand is less than the road capacity and all scenarios can reach their maximum traffic demand. However, DL reduces road performance when the penetration rate is lower than 40%. This is because when the dedicated lane is not saturated, the road utilization rate is reduced since the HDVs cannot use the dedicated lane. In addition, road capacity can be further increased with PL compared with DL when the penetration rate is lower than 40%. This is because PL increases lane usage by allowing HDVs to use priority lanes.When the penetration rate is less than 50%, the performance of PL is lower than NML as shown in Figure 12b. This is because a certain amount of road space is idle due to the existence of clear distance. However, DL and PL can improve road capacity compared with NML when the penetration rate is between 50% and 80%. Furthermore, DL can satisfy traffic demands faster (at 60%) than NML and PL (at 80%).The lane management strategy can further improve road capacity, as shown in Figure 12c. Here the critical point of improving traffic capacity is advanced with the increase in traffic demand can be seen by comparison with Figure 12a,b. In Figure 12d, it can be observed that the results of all three lane management strategies are consistent with our analytical results from Section 2. In summary, the following characteristics of lane management strategies can be concluded:For NML, the road capacity increases concavely with penetration rates;For DL, the rate of increase in road capacity slows down at high penetration rates;For PL, it is similar to NML at low penetration rates and similar to DL for middle and high penetration rates (see below).Travel timeThe results of two scenarios are discussed with respect to traffic demand and penetration rates for comparative analysis. In the first scenario, the travel time is calculated as the average of the total travel time under the corresponding traffic demand. Penetration rates are divided into low penetration (10–30%), middle penetration (40–60%), and high penetration (70–90%), as shown in Figure 13a. In general, vehicle travel time increases as traffic demand increases. The travel time for both lane management strategies is significantly less than that for no management strategies. In the case of low penetration and low traffic demand, it is clear waste of travel time to implement the CAV dedicated lane.13FIGURETravel time. (a) Travel time under different penetration. (b) Travel time under different demandIn the second scenario, the travel time is calculated as the average of the total travel time under the corresponding penetration rate. Traffic demands are divided into low demand (2000–3500 veh/h), middle demand (4000–5500 veh/h), and high demand (6000–8000 veh/h), as shown in Figure 13b. As penetration rate increases, CAVs play a positive role in significantly reducing vehicle travel times. The travel times for the three lane management strategies become more similar as the penetration rate increased as well. Moreover, the threshold points of wasted travel time caused by DL shift from the middle point to lower points with increasing traffic demand.SpeedThe average speed of vehicles at each penetration rate is plotted in Figure 14. For all three strategies, the average speed increases as the penetration increases, and DL is more affected by the penetration rate. In addition, the average speed distribution of DL and PL are more concentrated, which means that the traffic flow is more stable with less speed changes. Due to the low penetration rate of CAVs, conflicts between CAVs and HDVs are not prominent, which give PL better performance, and the DL and PL speed distributions are quite similar at high penetration rates.14FIGUREAverage speedSummaryIn terms of throughput, DL is not ideal when the penetration rate is lower than 20%, but DL had the best performance when the penetration rate is greater than 50%. Furthermore, between 20% and 40%, the critical penetration rate for using DL decreases as traffic demand increases. In the rest of the cases, the mixed lane strategy is similar to the priority lane strategy. Although there is no significant improvement in throughput, PL had better performance in terms of user experience (travel time, speed). Even if PL cannot significantly improve the performance of the transportation network, it can encourage greater use of CAVs and thereby promote their development. Therefore, PL can be used as a lane management strategy up until the mass popularization of CAVs.Hence, DL is the optimal choice when the penetration rate is greater than 50%, and PL is better when the penetration rate is 30–50%. When the penetration rate is below 20%, the performance of PL and NML is almost the same. However, as just mentioned the use of PL may encourage the use of CAVs.CONCLUSIONThe effects of different lane management strategies on traffic performance under mixed traffic flow were studied in this paper. First, a theoretical model of capacity gain was established based on the spacing characteristics of different vehicle types and average vehicle speed, and then it was extended to derive a theoretical formula of capacity under different lane management strategies. Then, a simulation experiment was implemented using SUMO because of the limitations of our theoretical model (the impact of lane‐changing behaviour could not be reflected, and the time‐varying traffic demand could not be considered). The Krauss model and CACC model were selected for HDV and CAV, respectively, to analyse the management strategies further. Through the above research, the central conclusions of this paper are as follows.Regardless of the lane management strategy from this study, the capacity increases as penetration rate increases can be found. Appropriate lane management strategies can therefore further improve road capacity, and the threshold point for improving the capacity advances with an increase in traffic demand. It can also be found that travel time is directly proportional to penetration rate and inversely proportional to traffic demand and that appropriate lane management strategies can significantly reduce travel time. In addition, the introduction of CAVs can increase the average speed of vehicles, even when no managed lane policy is in place. Finally, the speed distribution of the two‐lane management strategies that have a priority system for CAVs has a lower variance, indicating that traffic flow is more stable with less speed changes.Additionally, our formulation assumes the uniform distribution of CAVs in the traffic. In reality, it may be dynamic and random. Capacity formulation considering random and dynamic P will study in future research. And the impact of other factors on the results of our lane management strategies will be explored in our future research, such as dynamic speed limits, lane settings in weaving areas, and others. In addition, the more refined settings of lane management measures (multi‐lane management and lane deployment location) should not be overlooked since the innermost lane is usually used as the managed lane in current practices, and this can lead to additional lane changing needs. The deployment of the right‐most lane as the managed lane might be a good option [43] in some cases. What is more interesting is to further study the performance of setting different numbers of special lanes in a multi‐lane highway scenario. Lastly, the interactions between CAVs and HDVs should also be considered, especially the restriction of HDVs by implementing active management strategies for CAVs.AUTHOR CONTRIBUTIONSZ.W.: Conceptualization; Methodology; Project administration; Resources; Supervision. Q.M.: Formal analysis; Investigation; Software; Validation; Visualization; Writing ‐ original draft; Writing ‐ review & editing. J.X.: Investigation; Methodology; Validation; Writing ‐ original draft; Writing ‐ review & editing. Z.Z.: Software, Validation. J.T.: SupervisionACKNOWLEDGEMENTSNational Natural Science Foundation of China (No. 52172339); Project of HuNan Provincial Science and Technology Department (2020SK2098 and 2020RC4048); Project of the Education Department of Hunan Province (20A023); Postgraduate Scientific Research Innovation Project of Hunan Province (CX2021SS111).CONFLICT OF INTERESTThe authors declare that there are no conflicts of interest regarding the publication of this paper.DATA AVAILABILITY STATEMENTThe data that support the findings of this study are available from the corresponding author upon reasonable request.REFERENCESShladover, S.E.: Connected and automated vehicle systems: Introduction and overview. J. Intell. Transp. 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An evaluation of lane management strategy for CAV priority in mixed traffic

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Abstract

INTRODUCTIONConnected autonomous vehicles (CAVs) have seen rapid development in recent years in tandem with new developments in the Internet and other communication technologies [1]. These vehicles can enhance traffic safety by eliminating human error [2] and can increase the stability of traffic flow by decreasing traffic oscillations (the stop‐and‐go phenomenon) [3]. In addition, CAVs can play an important role in improving traffic flow efficiency due to their ability to follow each other at shorter distances [4, 5] and to reduce emissions through lower fuel consumption through more efficient driving [6, 7].However, mixed traffic flow (between CAVs and non CAVs) will still exist, and there will still be complex interactions between CAVs and human‐driven vehicles (HDVs) [8]. Therefore, the market penetration rate of CAVs has always been a concern with mixed traffic flow. Previous research has indicated that traffic flow stability can be improved, and mean spacing and speed variance can both be reduced by increasing the amount of CAVs on the road [9–11]. In addition, some other models have shown that road capacity may significantly increase at a high CAV penetration rate or even a full CAV scenario [12, 13]. For example, Liu et al. simulated CAVs in mixed traffic flow and found that freeway capacity at 100% market penetration was roughly 90% higher than at 0% [14]. However, the difference in capacity is not significant at low CAV penetration [15]. In addition, the benefits of additional CAVs may be offset by the interaction between HDVs and CAVs in practice. This is because a CAV must degrade into an Autonomous Vehicle (AV) (CAV degradation) or be taken over by humans when the preceding vehicle is an HDV. Hence, a decrease in road capacity may occur [16, 17].Managed lane strategies, especially CAV‐dedicated lanes, are considered to be one of the most effective solutions to this problem. Highways may effectively be able to improve traffic capacity, reduce the CAV degradation rate [18], promote longer CAV platoons [19], and enhance safety with dedicated CAV lanes [20]. Some research has found that CAV‐dedicated lanes are only beneficial at high penetration rates [21–24], however. For example, Talebpour et al. evaluated three strategies and found that the throughput can be significantly improved at penetration rates of more than 50% for a two‐lane highway and 30% for a four‐lane highway [25]. However, the deployment of dedicated lanes can also cause a waste of road resources and worsen traffic conditions when the CAV penetration rate is low [26, 27]. Hence, it may be best for dedicated lanes to be gradually deployed with an increase in CAV market penetration [28, 29].Other research suggested that mixed lanes or dedicated lanes for CAVs and high‐occupancy vehicles (HOVs) (driven by humans)can be set at low CAV penetration rates [30]. Liu and Song proposed autonomous vehicle/toll (AVT) lanes as an alternative to dedicated lanes during times when CAV penetration rate drops. The AVT allows AVs to enter for free but requires HDVs pay a toll to enter these lanes [31]. This is one example where road capacity might be further improved through effective lane management.Lane management (for example, using HOV lanes, dedicated bus lanes (DBLs), intermittent bus lanes (IBLs) etc.) is considered to be an effective traffic management measure under certain conditions. In addition, the provision of active lane management strategies can promote the development of CAVs, provide better driving experiences for CAVs, and improve overall traffic capacity. Researchers have investigated different lane management strategies by building theoretical models or using simulation software and have found that appropriate lane management strategies can further increase road capacity at different penetration rates [32–34]. Zhong and Lee even proposed managed lane score matrices to assess the overall suitability of each lane management strategy [35].In general, appropriate lane management strategies may be able to further improve lane utilization and can increase road capacity. However, intermittent CAV priority lane management has yet to be considered. An intermittent CAV priority lane can greatly reduce the CAV degradation rate and optimize road resources through the real‐time allocation of right‐of‐way. However, frequent lane‐changing behaviour can lead to a decrease in road capacity, especially at high CAV market penetration rates and high traffic demand. Therefore, it is important to understand mixed traffic flow characteristics in determining appropriate lane management strategies for different scenarios under different traffic demands and CAV penetration rates.To this end, in this study, we analysed the characteristics of mixed traffic flow under different lane management strategies through theoretical and numerical study, and evaluated the performance of these lane management strategies. The contributions of this study are as follows: (1) Previous studies mainly focus on deploying of dedicated lanes. In this study, a new lane management strategy that considers the deployment of the CAV priority lane is proposed, simulated, and evaluated to find the possibility of further improving road performance. (2) A theoretical model is proposed to evaluate the capacity under different lane management strategies. Numerical simulation demonstrates that the road capacity can be further increased through appropriate lane management. (3) Three different lane management strategies for a two‐lane road with mixed traffic are proposed based on theoretical analysis. These strategies are evaluated by simulation software, under different scenarios with different traffic demands and CAV penetration rates. The simulation results cross‐validate the results of the theoretical model in terms of traffic capacity and further prove that the appropriate lane management strategy can further improve the performance of travel time and speed.The remainder of this paper is organized as follows. Section 2 proposes a capacity model for mixed traffic under different lane management strategies. A simulation environment is established to evaluate three different lane strategies under different CAV penetration rates and traffic demand scenarios based on the Simulation of Urban Mobility (SUMO) framework in Section 3. Then, our simulation results are analysed in Section 4. Finally, our conclusions and a discussion of future work are presented in Section 5.CAPACITY FORMULATIONSIn this paper, it is assumed that vehicles travel at the optimal speed v until they reach their corresponding minimum headways when traffic flow reaches the capacity. Note that the physical lane capacity is determined at the beginning of the road design, and is independent of the lane policy. In this section, traffic capacity is defined as the maximum sustainable flow for given proportions of CAVs and HDVs in traffic streams. The capacity models under three different lane management strategies are established by us based on this assumption. The notations for all models are listed in Table 1, and the capacity formulas for mixed lanes, dedicated lanes, and priority lanes are proposed in Sections 2.1, 2.2, and 2.3, respectively.1TABLENomenclature listNotionsDefinitionshsc${h}_{sc}$spacing of CAVshsh${h}_{sh}$spacing of HDVshsch${h}_{sch}$spacing of AVsh¯s${\bar{h}}_s$average spacing of all vehiclesλc${\lambda }_c$spacing coefficient of CAVs in a platoonλch${\lambda }_{ch}$spacing coefficient of AVsvfree‐flow speedαr${\alpha }_r$CAV penetration rate in the regular laneαd${\alpha }_d$CAV penetration rate in the dedicated laneαp${\alpha }_p$CAV penetration rate in the priority laneC0traffic capacity with only HDVsCr${C}_r$traffic capacity of the regular laneCm${C}_m$traffic capacity of the mixed laneCe${C}_e$traffic capacity of the dedicated laneCp${C}_p$traffic capacity of the priority laneQtraffic flow of all lanesqr${q}_r$traffic flow of the regular laneqe${q}_e$traffic flow of the dedicated laneqp${q}_p$traffic flow of the priority lanepCAV penetration ratepCAV${p}_{CAV}$CAVs in a platoon penetration ratepAV${p}_{AV}$AV penetration ratepHDV${p}_{HDV}$HDV penetration ratep0CAV critical penetration rate when the CAV dedicated lane is just saturatedpp${p}_p$CAV critical penetration rate when the CAV priority lane is just saturatedlclear${l}_{clear}$clear distanceCapacity of the mixed lane policyThe mixed lane management strategy (No Managed Lane (NML)) is where CAVs and HDVs are mixed in the lane, as shown in Figure 1. In a connected environment, CAVs can keep driving with a smaller spacing than HDVs when the preceding vehicle is a CAV. Therefore, the spacing of CAVs can be expressed by λc(1>λc>0)${\lambda }_c( {1 &gt; {\lambda }_c &gt; 0} )$:1hsc=λchsh\begin{equation}{h}_{sc} = {\lambda }_c{h}_{sh}\end{equation}where hsc${h}_{sc}$ and hsh${h}_{sh}$ are the spacing of CAVs and HDVs, respectively. The CAV degrades into an AV when the preceding vehicle is an HDV. Therefore, the spacing coefficient of AVs is smaller than that of CAVs. The spacing of AVs can be expressed by λch(1>λch>λc>0)${\lambda }_{ch}( {1 &gt; {\lambda }_{ch} &gt; {\lambda }_c &gt; 0} )$:2hsch=λchhsh\begin{equation}{h}_{sch} = {\lambda }_{ch}{h}_{sh}\end{equation}where hsch${h}_{sch}$ is the spacing of AVs. The variable p represents the proportion of CAVs in the entire traffic flow, and pCAV${p}_{CAV}$, pAV${p}_{AV}$, and pHDV${p}_{HDV}$ represent the proportion of CAVs (the preceding vehicle is a CAV), AVs (the preceding vehicle is an HDV), and HDVs, respectively. Thus the pCAV=p2${p}_{CAV} = {p}^2\ $, pAV=p(1−p)${p}_{AV} = \ p( {1 - p} )$ and pHDV=1−p${p}_{HDV} = \ 1 - p$ can be obtained, therefore,3p=p2+p1−p\begin{equation}p = {p}^2 + p\left( {1 - p} \right)\end{equation}1FIGUREIllustration of the mixed laneThe change in the proportion of different vehicle types under different penetration rates p is shown in Figure 2.2FIGUREThe proportion of vehicle type changes with PThe average headway of all vehicles on a single‐lane h¯s${\bar{h}}_s\ $can be expressed by Equation (4) below.4h¯s=hsc·pCAV+hsch·pAV+hsh·pHDV=hsc·p2+hsch·p1−p+hsh·1−p\begin{equation} \def\eqcellsep{&}\begin{array}{l} {\overline h }_s = {h}_{sc} \cdot {p}_{CAV} + {h}_{sch} \cdot {p}_{AV} + {h}_{sh} \cdot {p}_{HDV}\\[6pt] \!\quad\mathop {}\nolimits = {h}_{sc} \cdot {p}^2 + {h}_{sch} \cdot p\left( {1 - p} \right) + {h}_{sh} \cdot \left( {1 - p} \right) \end{array} \end{equation}Substituting Equations (1) and (2) into Equation (4) gives us:5h¯s=λchsh·p2+λchhsh·p1−p+hsh·1−p\begin{equation}{\overline h }_s = {\lambda }_c{h}_{sh} \cdot {p}^2 + {\lambda }_{ch}{h}_{sh} \cdot p\left( {1 - p} \right) + {h}_{sh} \cdot \left( {1 - p} \right)\end{equation}Additionally, the traffic flow capacity of mixed traffic flow is expressed by Equation (6).6Cm=1h¯s/v=vhsc·p2+hsch·p1−p+hsh·1−p=vhshλc·p2+λch·p1−p+1−p=C0λc·p2+λch·p1−p+1−p\begin{equation} \def\eqcellsep{&}\begin{array}{l} {C}_m = \dfrac{1}{{{{\overline h }}_s/v}} = \dfrac{v}{{{h}_{sc} \cdot {p}^2 + {h}_{sch} \cdot p\left( {1 - p} \right) + {h}_{sh} \cdot \left( {1 - p} \right)}}\\[12pt] \quad\mathop {}\nolimits = \dfrac{v}{{{h}_{sh}\left( {{\lambda }_c \cdot {p}^2 + {\lambda }_{ch} \cdot p\left( {1 - p} \right) + \left( {1 - p} \right)} \right)}}\\[12pt] \quad\mathop {}\nolimits = \dfrac{{{C}_0}}{{{\lambda }_c \cdot {p}^2 + {\lambda }_{ch} \cdot p\left( {1 - p} \right) + \left( {1 - p} \right)}} \end{array} \end{equation}where αr${\alpha }_r$ denotes the CAV penetration rate on the regular lane. Therefore, the traffic flow capacity in the regular lane can be expressed by Equation (7).7Cr=C0λc·αr2+λch·αr1−αr+1−αr\begin{equation}{C}_r = \frac{{{C}_0}}{{{\lambda }_c \cdot {\alpha }_r^2 + {\lambda }_{ch} \cdot {\alpha }_r\left( {1 - {\alpha }_r} \right) + \left( {1 - {\alpha }_r} \right)}}\end{equation}Using Equation (7), Figure 3 shows the impact of parameters λc${\lambda }_c\ $and λch${\lambda }_{ch}$ on capacity gain under different CAV penetration rates.3FIGURE(a) Capacity gain changes with various p(λch=${\bm{p }}({\bm \lambda }_{{{\bm ch}}} = \ $0.8); (b) Capacity gain changes with various p(λch=${\bm{p }}({\bm \lambda }_{\bm ch} = \ $0.6)As shown in Figure 3, capacity gain increases with increasing CAV penetration rates and decreasing λc${\lambda }_c$ and λch${\lambda }_{ch}$, but capacity gain has a non‐linear relationship with penetration rate. The capacity gain increases faster as λc${\lambda }_c$ decreases as can be seen in Figure 3a. This means that changes in road capacity are influenced by the development of CAVs. Furthermore, at different λch${\lambda }_{ch}$, the capacity gain increases concavely with the penetration rate can be seen in Figure 3b. Initially, the traffic capacity rapidly increases with an increasing number of CAVs in the traffic flow. After that, however, the number of HDVs in the traffic flow becomes less and less as penetration rate increase further. Therefore, the probability of a CAV following an HDV becomes lower, and the growth rate of traffic capacity slows down. Note that the traffic flow is composed entirely of CAVs when the penetration rate is 1. In other words, traffic capacity is not affected by the value of λch${\lambda }_{ch}$ in this case due to the absence of any CAVs following HDVs.Capacity of the dedicated lane policyThe dedicated lane management strategy (DL policy) is where CAVs and HDVs are mixed in regular lanes but only CAVs are allowed to drive in the CAV‐dedicated lanes, as shown in Figure 4. The traffic capacity of the CAV dedicated lane is shown in Equation (8).8Ce=C0λc\begin{equation}{C}_e = \frac{{{C}_0}}{{{\lambda }_c}}\end{equation}4FIGUREIllustration of the CAV dedicated laneThe variables qe${q}_e$ and qr${q}_r$ represent the traffic flow on the dedicated lane and regular lane, respectively, and Q denotes the traffic flow of all lanes. The flow conservation equation is shown in Equations (9) and (10).9Q=qe+qr\begin{equation}Q = {q}_e + {q}_r\end{equation}10p·Q=αeqe+αrqr\begin{equation}p \cdot Q = {\alpha }_e{q}_e + {\alpha }_r{q}_r\end{equation}where p is CAV penetration rate, αe${\alpha }_e$ is the CAV penetration rate in the CAV dedicated lane, and αr${\alpha }_r$ is the CAV penetration rate in the regular lane. Only CAVs are allowed to drive in the CAV dedicated lane, so αe=1${\alpha }_e = \ 1$, and Equation (10) can be rewritten as:11p·Q=qe+αrqr\begin{equation}p \cdot Q = {q}_e + {\alpha }_r{q}_r\end{equation}Assuming that CAVs will only enter the regular lane when the capacity of the CAV dedicated lane reaches saturation, the CAV dedicated lane is just saturated when:12p0=qeqe+qr\begin{equation}{p}_0 = \frac{{{q}_e}}{{{q}_e + {q}_r}}\end{equation}Substituting Equation (8) into Equation (12) gives:13p0=11+λc\begin{equation}{p}_0 = \frac{1}{{1 + {\lambda }_c}}\end{equation}As shown in Figure 5, the critical penetration rate can be obtained at a smaller penetration as λc${\lambda }_c$ increases. This is because CAVs can travel with smaller spacing that increases the capacity of CAV‐dedicated lanes.5FIGUREp0 and αr change with λc and p, respectively (λc=0.6${{\bm{\lambda }}}_{\bm{c}} = {\bm{\ }}0.6$)When p<p0$p &lt; {p}_0$, the CAV‐dedicated lane is not saturated, and there are no CAVs in the regular lane. At this moment, αr=0${\alpha }_r = \ 0$, p·Q=qe$p \cdot Q\ = {q}_e\ $, and the road flow is given by:14Q=p·Q+qr\begin{equation}Q = p \cdot Q + {q}_r\end{equation}Rewriting Equation (14) yields:15Q=qr1−p=Cr1−p=C01−p\begin{equation}Q = \frac{{{q}_r}}{{1 - p}} = \frac{{{C}_r}}{{1 - p}} = \frac{{{C}_0}}{{1 - p}}\end{equation}The CAV‐dedicated lane reaches a saturated state when p≥p0$p \ge {p}_0$. Therefore, more CAVs enter the regular lane with an increase in p. The CAV penetration rate can thus be expressed as Equation (16).16p=qe+αrqrqe+qr\begin{equation}p = \frac{{{q}_e + {\alpha }_r{q}_r}}{{{q}_e + {q}_r}}\end{equation}Under this condition, the road flow is:17p·Q=qe+αrqr=Q−qr+αrqr\begin{equation}p \cdot Q = {q}_e + {\alpha }_r{q}_r = \left( {Q - {q}_r} \right) + {\alpha }_r{q}_r\end{equation}and rewriting Equation (17) gives us:18Q=qr1−αr1−p=Cr1−αr1−p\begin{equation}Q = \frac{{{q}_r\left( {1 - {\alpha }_r} \right)}}{{1 - p}} = \frac{{{C}_r\left( {1 - {\alpha }_r} \right)}}{{1 - p}}\end{equation}In summary, the traffic capacity of the DL policy at different CAV penetration rates is expressed as Equation (19).19Q=C01−p,ifp<p0Q=Cr1−αr1−p,ifp>p0\begin{equation}\left\{ \def\eqcellsep{&}\begin{array}{l} Q = \dfrac{{{C}_0}}{{1 - p}},\quad i\!{f}p &lt; {p}_0\\[12pt] Q = \dfrac{{{C}_r\left( {1 - {\alpha }_r} \right)}}{{1 - p}},\quad i\!{f}p &gt; {p}_0 \end{array} \right.\end{equation}The changes in the capacity gain for DL policy with various p that is calculated from Equation (19) are shown in Figure 6. The CAV‐dedicated lane is not saturated and the capacity gain is less than 1 when the penetration rate is less than 50%. This is because the regular lane is saturated, but the number of CAVs on the dedicated lane is insufficient, resulting in a serious waste of road resources. Therefore, the CAV‐dedicated lane cannot improve road capacity under these conditions. The traffic capacity starts to increase due to the fact that the capacity gain is greater than 1 when the penetration rate exceeds 50%, and the CAV‐dedicated lane is just saturated when the penetration rate reaches the critical penetration rate p0 (p0=0.625${p}_0 = \ 0.625$ when λc=0.6${\lambda }_c = \ 0.6$). Here, the CAVs enter the regular lane, as the penetration rate further increases, and the penetration rate αr${\alpha }_r$ of the CAVs in the regular lane gradually increases as well.6FIGURECapacity gain of DL policy changes with various p (λc=0.6,λch=0.8${{\bm{\lambda }}}_{\bm{c}} = {\bm{\ }}0.6,\ \ {{\bm{\lambda }}}_{{\bm{ch}}} = {\bm{\ }}0.8$)Capacity of the priority lane policyThe priority lane management strategy (PL policy) is shown in Figure 7. In this scenario, all HDVs are equipped with information receiving equipment that can receive lane change commands from CAVs or Road Side Units (RSUs). As a CAV progresses along the priority lane, the HDVs in the lane ahead of it can receive V2X information to determine if they need to leave the lane. The distance between the CAV and the downstream vehicles that must exit is defined as “Clear Distance”.7FIGUREIllustration of CAV priority laneHDVs that are behind a CAV are allowed to enter the priority lane at any time in this scenario. The average headway of all vehicles in the priority lane can be expressed by Equation (20).20h¯s=hsc·P2+lclear·P1−P+hsh·1−P=λrhsc·P2+λclearhsh·P1−P+hsh·1−P\begin{equation} \def\eqcellsep{&}\begin{array}{l} {\overline h }_s = {h}_{sc} \cdot {P}^2 + {l}_{clear} \cdot P\left( {1 - P} \right) + {h}_{sh} \cdot \left( {1 - P} \right)\\[6pt] \quad\mathop {}\nolimits = {\lambda }_r{h}_{sc} \cdot {P}^2 + {\lambda }_{clear}{h}_{sh} \cdot P\left( {1 - P} \right) + {h}_{sh} \cdot \left( {1 - P} \right) \end{array} \end{equation}where lclear${l}_{clear}$ is clear distance, lclear=λclearhsh${l}_{clear} = {\lambda }_{clear}\ {h}_{sh}$, and λclear(>1)${\lambda }_{clear}( &gt; 1)$. The variable αp${\alpha }_p$ denotes the CAV penetration rate in the priority lane. The mixed traffic flow capacity of the CAV priority lane can be expressed by Equation (21).21CP=C0λc·αp2+λclear·αp1−αp+1−αp\begin{equation}{C}_P = \frac{{{C}_0}}{{{\lambda }_c \cdot {\alpha }_p^2 + {\lambda }_{clear} \cdot {\alpha }_p\left( {1 - {\alpha }_p} \right) + \left( {1 - {\alpha }_p} \right)}}\end{equation}The variables qp${q}_p\ $andqr$\ {q}_r$ represent the flow in the priority lane and regular lane, respectively. The traffic conservation equations can be expressed as Equations (22) and (23).22Q=qp+qr\begin{equation}Q = {q}_p + {q}_r\end{equation}23p·Q=αpqp+αrqr\begin{equation}p \cdot Q = {\alpha }_p{q}_p + {\alpha }_r{q}_r\end{equation}It is once again assumed that CAVs will only enter the regular lane when the capacity of the CAV priority lane reaches saturation, and let the critical CAV penetration rate be pp${p}_p$ when the CAV priority lane is just saturated.When p<pp$p &lt; {p}_p$, the CAV priority lane is not saturated, and there are no CAVs in the regular lane. At this moment, αr=0${\alpha }_r = \ 0$, p·Q=αpqp$p \cdot Q\ = {\alpha }_p{q}_p\ $, and the following conditions are met:24p=αrqpqp+qr\begin{equation}p = \frac{{{\alpha }_r{q}_p}}{{{q}_p + {q}_r}}\end{equation}and25p·Q=αpqp\begin{equation}p \cdot Q = {\alpha }_p{q}_p\end{equation}Rewriting Equation (25) yields:26Q=αpqpp\begin{equation}Q = \frac{{{\alpha }_p{q}_p}}{p}\end{equation}When p>pp$p &gt; {p}_p$, the CAV priority lane reaches the saturation state, which is equivalent to the CAV‐dedicated lane scenario from the previous section. In summary, the traffic capacity of the PL policy is expressed as Equation (27) at different penetration rates.27Q=Cpαpp,ifp<ppQ=Cr1−αr1−p,ifp>pp\begin{equation}\left\{ \def\eqcellsep{&}\begin{array}{l} Q = \dfrac{{{C}_p{\alpha }_p}}{p},\mathop {}\nolimits i{f}p &lt; {p}_p\\[11pt] Q = \dfrac{{{C}_r\left( {1 - {\alpha }_r} \right)}}{{1 - p}},\mathop {}\nolimits i{f}p &gt; {p}_p \end{array} \right.\end{equation}When more CAVs enter the priority lane, the penetration rate further increases, and the penetration rate αp${\alpha }_p$ of the CAVs in the priority lane gradually increases, as shown in Figure 8. The priority lane is saturated when the critical penetration rate is reached. The probability of a CAV following an HDV increases and then decreases when the penetration rate increases (Figure 2‐Blue line), therefore the capacity of the priority lane shows the same behaviour.8FIGURECapacity gain of PL policy changes with various p (λc=0.6,λclear${{\bm{\lambda }}}_{\bm{c}} = \ 0.6,\ {{\bm{\lambda }}}_{{\bm{clear}}}$= 6)As shown in Figure 9, the capacity of the priority lane management strategy decreases with an increase in CAVs because of the limitation of clear distance when the penetration rate is less than 20%. The opposite situation occurs when the penetration rate is greater than 20%. Hence PL policy performs better than DL policy until the critical penetration rate pp${p}_p$ is reached. This is because up until this point the priority lane is not saturated, and the priority lane allows HDV to enter. Since the CAV priority lane is saturated when the penetration rate reaches the critical penetration rate pp${p}_p$ (pp=0.625${p}_p = \ 0.625$), after that it necessarily becomes the same as the dedicated lane. Therefore, the total capacity of DL policy and PL policy is the same when the penetration rate reaches the critical penetration rate.9FIGUREComparison of DL policy and PL policy (λc=0.6,λclear${{\bm{\lambda }}}_{\bm{c}} = \ 0.6,\ {{\bm{\lambda }}}_{{\bm{clear}}}$= 6)Determining the true critical penetration rate is difficult because of the complexity of the priority lane. The influence of lane‐changing behaviour is not easy account for in the theoretical model. Therefore, the traffic characteristics of different lane management strategies are further studied with micro‐simulation software, which can overcome the difficulty of the proposed theoretical model and cross‐validate its results with numerical analysis.SIMULATIONDifferent lane management strategies under different penetration rates and demands will be evaluated in this section. First, the SUMO [36] simulation framework is introduced in Section 3.1. Second, the car‐following models and lane change model are introduced in Sections 3.2 and 3.3, and 3.4, respectively. Finally, the simulation scenarios are listed in Section 3.5.Simulation frameworkThe SUMO framework is open source micro‐simulation software that is widely used in the field of CAV simulation [37]. Through its TraCI (Traffic Control Interface) interface secondary development and real‐time control of vehicles can be realized with the help of Python. In addition, SUMO has a large number of built‐in vehicles following models, and the parameters of these models are easy to adjust. For our purposes, the Krauss model and CACC (Cooperative Adaptive Cruise Control) model are selected as the car‐following models of HDVs and CAVs, respectively, and the model parameters are shown in Table 2. The real‐time simulation of priority lanes is performed using Python through the TraCI interface, and the operational logic in each simulation step is shown in Figure 10.2TABLEParameters in the simulationParameterDescriptionValuetauThe driver's desired (minimum) time headway1.4 s (HDV)0.6 s (CAV)accelthe acceleration ability of vehicles2.6 m/s2decelthe deceleration ability of vehicles4.5 m/s210FIGUREFlowchart of each simulation time stepsHDV car‐followingThe Krauss model [38] was used to model HDVs, which is also the default car‐following model of SUMO. The Krauss model allows a vehicle to go as fast as possible while maintaining safety. This means that collisions can always be avoided if the leader brakes within the maximum acceleration range. Therefore, the vehicle speed is always less than its safe speed, and its safe speed calculation equation is:28vsafe=vp+g−vτvp+v/2b+τ\begin{equation}{v}_{safe} = {v}_p + \frac{{g - v\tau }}{{\left( {{v}_p + v} \right)/2b + \tau }}\end{equation}where vp${v}_p$ is the speed of the preceding vehicle, g is the distance between vehicles, v is the current vehicle speed, b is the maximum deceleration, and τ is the driver's reaction time. The Krauss model is expressed in Equations (29) and (30):29vd=minvt+a,vmax,vsafe\begin{equation}{v}_d = min\left( {{v}_t + a,{v}_{max},{v}_{safe}} \right)\end{equation}30vt+1=max0,randvd−εa,vd\begin{equation}{v}_{t + 1} = max\left[ {0,rand\left( {{v}_d - \varepsilon a,{v}_d} \right)} \right]\end{equation}where vd${v}_d$ is vehicle desired speed, vt${v}_t$ is speed at time t, a is the maximum speed, vmax${v}_{max}$ is the maximum limit vehicle speed on the road, ε is the error caused by the driver's imperfect driving whose value is set to 0.5, and vt+1${v}_{t + 1}$ is speed at time t+1.CAV car‐followingMany CACC models were widely used for CAV simulations. The integrated CACC car‐following model is based on the work of Milanés, Xiao and Wang [39–41] in SUMO. The CACC model is divided into three control modes:Speed control modeThis mode will keep the vehicle at the preset desired speed if there is no leader in front of the vehicle or if the time gap is greater than 2 s.31ai,k=k0·vd−vi,k−1\begin{equation}{a}_{i,k} = {k}_0 \cdot \left( {{v}_d - {v}_{i,k - 1}} \right)\end{equation}Here vd${v}_d$ is the driver's desired speed, and k0 is control gain to determine the rate of speed error for acceleration, with value 0.4 s−1.Gap control modeThis mode is designed to maintain a constant time gap between the vehicle and the leader when the vehicle is in the following state. This mode is activated when gap and speed deviations are concurrently smaller than 0.2 m and 0.1 m/s, respectively.32vi,k=vi,k−1+kp·ei,k−1+kd·ei,k−1−ei,k−2Δt\begin{equation}{v}_{i,k} = {v}_{i,k - 1} + {k}_p \cdot {e}_{i,k - 1} + {k}_d \cdot \frac{{\left( {{e}_{i,k - 1} - {e}_{i,k - 2}} \right)}}{{\Delta t}}\end{equation}The variable ei,k−1${e}_{i,k - 1}$ is the gap error of vehicle i at time step k−1 (Equation (33)), and kp${k}_p$ and kd${k}_d$ are 0.45 s−1 and 0.0125, respectively. In addition,33ei,k=xi−1,k−1−xi,k−1−L−td·vi,k−1−d0\begin{equation}{e}_{i,k} = {x}_{i - 1,k - 1} - {x}_{i,k - 1} - L - {t}_d \cdot {v}_{i,k - 1} - {d}_0\end{equation}where xi−1,k−1−xi,k−1${x}_{i - 1,k - 1} - {x}_{i,k - 1}$ is inter‐vehicle spacing at time step k−1, td${t}_d$ is the desired time gap, L is vehicle length, and d0 is spacing margin, determined by Equation (34).34d0=fx=0,v≥10m/s−0.125v,v<10m/s\begin{equation}{d}_0 = f\left( x \right) = \left\{ \def\eqcellsep{&}\begin{array}{l} 0,\qquad\quad \mathop {}\nolimits v \ge 10{\rm{ m/s}}\\[6pt] - 0.125v,\mathop {}\nolimits\quad v &lt; 10{\rm{ m/s}} \end{array} \right.\end{equation}Gap‐closing control modeA smooth transition from speed control mode to gap control mode can be achieved by this mode when the time gap is less than 1.5 s. The vehicle retains the previous control mode when the time gap is between 1.5 and 2 s. The feedback gain on speed error and gap error in Equation (32) is adjusted to kp${k}_p$ and kd${k}_d$, which are 0.005 s–1 and 0.05, respectively in order to reduce the speed difference and gap more safely.Lane change modelThe LC2013 lane change model in SUMO was used for the simulation in this paper [42]. In this model, vehicle lane changes are determined by the 4‐layered hierarchy of motivations: strategic change, cooperative change, tactical change, and regulatory change. The following sub‐steps are executed for every vehicle during each simulation step.Calculation of preferred successor lanes;Calculation of safe speed under the assumption of staying in the current lane and integration with the speed request related to the lane change in the previous simulation step;Lane‐changing model calculation of change request (left, right, stay);Performance of lane change or calculation of speed request for the next simulation step.Simulation scenarioNowadays, the simulation scenario is established with a road length of 1000 m, 2 lanes, and a speed limit of 33.3 m/s. The simulation time step for CAVs and HDVs are 0.1 and 1 s, respectively, and the simulation lasted for 3800 s. The first 100 s and the last 100 s are discarded for more accurate data collection. In the initial state, vehicles are inserted into the road network at equal intervals, and a safe distance must be kept from any leading vehicle according to its following model. Furthermore, in each simulation, vehicles are loaded by setting the number of vehicles per hour. The time interval between vehicles entering the simulation is different, so the vehicle distribution is also different, which ensures the randomness of vehicle distribution to a certain extent. For this two‐lane highway, there are three lane management strategies:No managed lane (NML): There is no additional management strategy for the lanes, and CAVs and HDVs are mixed in the lanes;One dedicated lane (DL): The leftmost lane is a CAV‐dedicated lane, and only CAVs are allowed to use it;One priority lane (PL): The leftmost lane is the CAV priority lane. By clearing the HDVs within a certain distance, CAVs can be guaranteed to pass first.To study the performance of each lane management strategy under different traffic conditions, penetration rates and traffic demand are selected by us as variables, from 0–100% with 10% intervals and from 2000–8000 veh/h with 500 veh/h intervals, respectively. Then, the three lane management strategies are simulated and the simulation results are analysed by combining these two variables. A full experiment was run 429 (3×13×11) times for different variable combinations. The simulation seed of each simulation was generated by SUMO based on the current system time to eliminate random errors. Performance data (throughput, travel time, and speed) are collected for each simulation run.ANALYSIS OF SIMULATION RESULTSThe raw data of each time step in three scenarios were collected and analysed for throughput, travel time, and speed.ThroughputThe simulation results of three lane management strategies are shown in Figure 11. The other lane management strategies can further improve road capacity beyond that of NML.11FIGUREComparison of three lane management strategiesHowever, the effect of improvement is affected by traffic demand and penetration rate. Four scenarios at demands of 3000, 4500, 6000 and 7500 veh /h were selected to further analyse the performance of different lane management strategies. Simulation results as shown in Figure 12.12FIGURESimulation result under four demandsAs shown in Figure 12a, the throughput of the three lane management strategies has similar performance when the penetration rate is higher than 40%. Moreover, the traffic demand is less than the road capacity and all scenarios can reach their maximum traffic demand. However, DL reduces road performance when the penetration rate is lower than 40%. This is because when the dedicated lane is not saturated, the road utilization rate is reduced since the HDVs cannot use the dedicated lane. In addition, road capacity can be further increased with PL compared with DL when the penetration rate is lower than 40%. This is because PL increases lane usage by allowing HDVs to use priority lanes.When the penetration rate is less than 50%, the performance of PL is lower than NML as shown in Figure 12b. This is because a certain amount of road space is idle due to the existence of clear distance. However, DL and PL can improve road capacity compared with NML when the penetration rate is between 50% and 80%. Furthermore, DL can satisfy traffic demands faster (at 60%) than NML and PL (at 80%).The lane management strategy can further improve road capacity, as shown in Figure 12c. Here the critical point of improving traffic capacity is advanced with the increase in traffic demand can be seen by comparison with Figure 12a,b. In Figure 12d, it can be observed that the results of all three lane management strategies are consistent with our analytical results from Section 2. In summary, the following characteristics of lane management strategies can be concluded:For NML, the road capacity increases concavely with penetration rates;For DL, the rate of increase in road capacity slows down at high penetration rates;For PL, it is similar to NML at low penetration rates and similar to DL for middle and high penetration rates (see below).Travel timeThe results of two scenarios are discussed with respect to traffic demand and penetration rates for comparative analysis. In the first scenario, the travel time is calculated as the average of the total travel time under the corresponding traffic demand. Penetration rates are divided into low penetration (10–30%), middle penetration (40–60%), and high penetration (70–90%), as shown in Figure 13a. In general, vehicle travel time increases as traffic demand increases. The travel time for both lane management strategies is significantly less than that for no management strategies. In the case of low penetration and low traffic demand, it is clear waste of travel time to implement the CAV dedicated lane.13FIGURETravel time. (a) Travel time under different penetration. (b) Travel time under different demandIn the second scenario, the travel time is calculated as the average of the total travel time under the corresponding penetration rate. Traffic demands are divided into low demand (2000–3500 veh/h), middle demand (4000–5500 veh/h), and high demand (6000–8000 veh/h), as shown in Figure 13b. As penetration rate increases, CAVs play a positive role in significantly reducing vehicle travel times. The travel times for the three lane management strategies become more similar as the penetration rate increased as well. Moreover, the threshold points of wasted travel time caused by DL shift from the middle point to lower points with increasing traffic demand.SpeedThe average speed of vehicles at each penetration rate is plotted in Figure 14. For all three strategies, the average speed increases as the penetration increases, and DL is more affected by the penetration rate. In addition, the average speed distribution of DL and PL are more concentrated, which means that the traffic flow is more stable with less speed changes. Due to the low penetration rate of CAVs, conflicts between CAVs and HDVs are not prominent, which give PL better performance, and the DL and PL speed distributions are quite similar at high penetration rates.14FIGUREAverage speedSummaryIn terms of throughput, DL is not ideal when the penetration rate is lower than 20%, but DL had the best performance when the penetration rate is greater than 50%. Furthermore, between 20% and 40%, the critical penetration rate for using DL decreases as traffic demand increases. In the rest of the cases, the mixed lane strategy is similar to the priority lane strategy. Although there is no significant improvement in throughput, PL had better performance in terms of user experience (travel time, speed). Even if PL cannot significantly improve the performance of the transportation network, it can encourage greater use of CAVs and thereby promote their development. Therefore, PL can be used as a lane management strategy up until the mass popularization of CAVs.Hence, DL is the optimal choice when the penetration rate is greater than 50%, and PL is better when the penetration rate is 30–50%. When the penetration rate is below 20%, the performance of PL and NML is almost the same. However, as just mentioned the use of PL may encourage the use of CAVs.CONCLUSIONThe effects of different lane management strategies on traffic performance under mixed traffic flow were studied in this paper. First, a theoretical model of capacity gain was established based on the spacing characteristics of different vehicle types and average vehicle speed, and then it was extended to derive a theoretical formula of capacity under different lane management strategies. Then, a simulation experiment was implemented using SUMO because of the limitations of our theoretical model (the impact of lane‐changing behaviour could not be reflected, and the time‐varying traffic demand could not be considered). The Krauss model and CACC model were selected for HDV and CAV, respectively, to analyse the management strategies further. Through the above research, the central conclusions of this paper are as follows.Regardless of the lane management strategy from this study, the capacity increases as penetration rate increases can be found. Appropriate lane management strategies can therefore further improve road capacity, and the threshold point for improving the capacity advances with an increase in traffic demand. It can also be found that travel time is directly proportional to penetration rate and inversely proportional to traffic demand and that appropriate lane management strategies can significantly reduce travel time. In addition, the introduction of CAVs can increase the average speed of vehicles, even when no managed lane policy is in place. Finally, the speed distribution of the two‐lane management strategies that have a priority system for CAVs has a lower variance, indicating that traffic flow is more stable with less speed changes.Additionally, our formulation assumes the uniform distribution of CAVs in the traffic. In reality, it may be dynamic and random. Capacity formulation considering random and dynamic P will study in future research. And the impact of other factors on the results of our lane management strategies will be explored in our future research, such as dynamic speed limits, lane settings in weaving areas, and others. In addition, the more refined settings of lane management measures (multi‐lane management and lane deployment location) should not be overlooked since the innermost lane is usually used as the managed lane in current practices, and this can lead to additional lane changing needs. The deployment of the right‐most lane as the managed lane might be a good option [43] in some cases. What is more interesting is to further study the performance of setting different numbers of special lanes in a multi‐lane highway scenario. Lastly, the interactions between CAVs and HDVs should also be considered, especially the restriction of HDVs by implementing active management strategies for CAVs.AUTHOR CONTRIBUTIONSZ.W.: Conceptualization; Methodology; Project administration; Resources; Supervision. Q.M.: Formal analysis; Investigation; Software; Validation; Visualization; Writing ‐ original draft; Writing ‐ review & editing. J.X.: Investigation; Methodology; Validation; Writing ‐ original draft; Writing ‐ review & editing. Z.Z.: Software, Validation. J.T.: SupervisionACKNOWLEDGEMENTSNational Natural Science Foundation of China (No. 52172339); Project of HuNan Provincial Science and Technology Department (2020SK2098 and 2020RC4048); Project of the Education Department of Hunan Province (20A023); Postgraduate Scientific Research Innovation Project of Hunan Province (CX2021SS111).CONFLICT OF INTERESTThe authors declare that there are no conflicts of interest regarding the publication of this paper.DATA AVAILABILITY STATEMENTThe data that support the findings of this study are available from the corresponding author upon reasonable request.REFERENCESShladover, S.E.: Connected and automated vehicle systems: Introduction and overview. J. Intell. Transp. 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IET Intelligent Transport Systems – Wiley

Published: Oct 27, 2022

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