Overall Influence of Dedicated Lanes for Connected and Autonomous Vehicles on Freeway Heterogeneous Traffic Flow

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Introduction
With the continuous and rapid growth of travel demand, the growth of the total freeway mileage is relatively slow due to limited land available [1]. is difference leads to the imbalance between the supply and the demand of freeways, the decrease in road capacity, and the increase in travel time [2].
ere is an increasing demand to improve the operating efficiency of freeway traffic flow and reduce vehicle exhaust emissions.
In the past few decades, researchers have been committed to using intelligent transportation systems (ITS) to improve traffic operating efficiency [3][4][5][6], ensure traffic safety [7][8][9][10], and reduce vehicle exhaust emissions [11][12][13][14]. In recent years, with the rapid development of artificial intelligence, sensor, and communication technology, due to the characteristics of autonomous driving, vehicle-to-vehicle (V2V) communication, and vehicle-to-infrastructure (V2I) communication, CAVs have been widely regarded as an effective way to alleviate the traffic problems [15]. However, it is worth noting that the application of CAVs is thought to be a long and slow process [16,17]. CAVs and MVs will coexist on roads for a long time.
e existing literature contains many contributions made in studying the influence of CAVs on traffic flow under the heterogeneous traffic flow conditions [18][19][20][21]. Ioannou and Stefanovic [22] found that adaptive cruise control vehicles could reduce the interference between vehicles, which was beneficial to the environment. Liu et al. [23] studied the influence of the autonomous vehicle (AV) penetration rate on heterogeneous traffic flow. e results indicated that AVs could considerably improve the traffic condition, and the level of improvement increased with the AV penetration rate. e research also found that the influence of AVs on the heterogeneous traffic flow characteristics was mainly related to the car-following and lane-changing behaviors. Morando et al. [24] estimated the impact of AVs on traffic safety and found that AVs significantly improved traffic safety and reduced the number of conflicts with high AV penetration rates. Gong and Du [25] found that CAVs could stabilize the traffic flow effectively and dampen traffic oscillation propagation. Ye and Yamamoto [26] proposed a heterogeneous traffic flow model including CAVs and MVs. e results showed that, with the increase of the CAV penetration rate, road capacity also increased. Liu et al. [27] studied the influence of cooperative adaptive cruise control (CACC) vehicles on the capacity of the freeway merge bottleneck area. e simulation results indicated that the freeway merge bottleneck area capacity increases quadratically as the penetration rate of CACC vehicles increases. Chen et al. [28] established a heterogeneous traffic flow model of MVs and AVs. e results showed that when the AV penetration rate increases, the critical vehicle density also increases. Zheng et al. [29] studied the stability of heterogeneous traffic flow and found that AVs are able to not only stabilize the traffic flow but also increase the average speed of vehicles effectively. Festa et al. [30] compared the macrosimulation model and the microsimulation model and verified model performances. After that, they [31] proposed an adaptive traffic signal control scheme. Connected vehicles provided their own positions to the control system, and the control system stored the vehicle positions on the network. Meanwhile, new vehicle trajectories were generated based on a map matching algorithm, and a new traffic signal plan was generated. e results showed that the scheme could effectively reduce the average travel time and pollution emissions. Wu et al. [32] established a two-lane lane-changing model and studied the control strategy at the freeway work area under the heterogeneous traffic flow. eir study disclosed that when the CAV penetration rate is high, the combination of the early lane-changing control strategy and the variable speed limits strategy is the optimal choice. Jiang et al. [33] established a heterogeneous traffic flow model based on the analysis of platoon behavior. e results showed that, with the increase of the CAV penetration rate, the road capacity was significantly improved.
Inspired by the managed lane strategy, the CAV dedicated lane strategy is considered to effectively separate CAVs from MVs, realize the local homogeneity of CAVs, and maximize the advantages of CAVs. e managed lane strategy can improve traffic conditions by setting up dedicated lanes for specific vehicles. Bus lanes, high-occupancy vehicle (HOV) lanes, and high-occupancy toll (HOT) lanes are all based on similar concepts and have proven their feasibility through practices [34][35][36]. Due to the limitations of technologies, studies on the CAV dedicated lane are still at the theoretical level and have not been put into practice.
Mohajerpoor and Ramezani [37] analyzed the total delay of a one-way two-lane road under the heterogeneous traffic flow for different lane allocation strategies. Ghiasi et al. [38] proposed a lane management model for the heterogeneous traffic flow based on the Markov chain method. Based on the condition of providing dedicated lanes for AVs to traffic intersections, Rey and Levin [39] proposed a new traffic signal control strategy. Some scholars have studied the CAV dedicated lane from the perspective of macroscopic network optimization. Chen et al. [40] proposed a mathematical model to optimize the deployment plan of CAV dedicated lanes in the heterogeneous traffic flow network based on time. On the basis of considering the user equilibrium route choice, Melson et al. [41] introduced CACC into the link transmission model (LTM) and found that CACC-dedicated lanes could reduce freeway congestion. By deploying dedicated lanes for AVs and subsidizing people who buy AVs, Chen et al. [42] formulated the AVs incentive program design problem as a stochastic programming model with equilibrium constraints. Some scholars have also studied the influence of CAV dedicated lanes on the traffic flow through microsimulation. Ye and Yamamoto [43] studied the influence of the number of CAV dedicated lanes on the traffic flow throughput. Zhang et al. [44] studied the influence of CAV dedicated lanes on the freeway heterogeneous traffic flow from the perspective of traffic safety. Hua et al. [45] studied the influence of different dedicated lane strategies on the heterogeneous traffic flow. e results showed that the CAV dedicated lanes could improve the freeway capacity, but dedicated lanes for MVs had little impact on the improvement of the freeway capacity.
However, it is worth noting that few researchers have studied the influence of the CAV dedicated lane strategy on vehicle exhaust emissions. is paper aims to evaluate the overall influence of different CAV dedicated lane strategies on the operating efficiency of the freeway traffic flow and vehicle exhaust emissions. We designed three different lane strategies and conducted the simulation under different densities with different CAV penetration rates. e remainder of this paper is organized as follows. In Section 2, the microsimulation models for CAVs and MVs are established, respectively. In Section 3, different lane strategies are introduced. In Section 4, the simulation results are analyzed, and the optimal ranges of different lane strategies are obtained. Finally, conclusions are obtained with an outline for the future research.

Model
e cellular automata model is one of the most widely used micro traffic simulation models [46]. Its advantages of simplicity and flexibility in adapting to the complex characteristics of real traffic flow have been proved in many previous studies. Some typical cellular automata models, including NS model [46], STCA model [47], VDR model [48], KKW model [49,50], MCD model [51], TS model [52], and TSM model [53], have been proposed. e TSM model can reproduce the metastable state, traffic oscillations, phase transitions, and other real traffic flow dynamics, with significant advantages compared with the other existing models. In this paper, an improved cellular automata model is proposed based on the TSM model to model the behaviors of MVs. Based on the characteristics of CAVs, the behaviors of CAVs are modeled.

e Steps Involved in the TSM Model.
Step 1: Deterministic speed update where v n (t) is the speed of vehicle n at time step t, v max is the maximum speed of the vehicle, d anti represents the anticipated space gap, v safe denotes the safe speed, d n (t) is the space gap between vehicle n and its preceding vehicle n + 1 at time step t, v anti is the expected speed of the preceding vehicle n + 1 at the next time step t + 1, d n+1 (t) represents the space gap between vehicle n + 1 and its preceding vehicle at time step t, and v n+1 (t) is the speed of vehicle n + 1 at time step t. In addition, g safety , b max , and a are model parameters, where a and b max represent vehicle acceleration and maximum deceleration, respectively. [x] denotes the value rounded to its nearest integer.
Step 2: Stochastic deceleration v n (t + 1) � max v n ′ (t + 1) − b rand , 0 with probability p v n ′ (t + 1)otherwise where b defense , T, p a , p b , and p c are model parameters.
x can return the maximum integer which is not greater than argument x. Probability p defense is represented by the logistic function, and β and v c represent the steepness and midpoint of the logistic function, respectively.
Step 3: Position update where x n (t) is the position of vehicle n at time step t.

Car-Following Model for MVs.
To ensure the deceleration within a reasonable range at the next step, we revised the TSM model by replacing d anti with d anti /T at the deterministic speed update step. Meanwhile, in order to make the model more realistic, we introduced t n,h (t) ≤ 1 as one of the conditions for selecting the random probability p, and t n,h (t) � d n (t)/v n (t) is the time interval for vehicle n to reach the tail of its preceding vehicle n + 1.
Using the new rules, the model is modified as follows: Step Step 2: Stochastic deceleration Step 3: Position update Journal of Advanced Transportation

Car-Following Model for CAVs.
Based on the TSM model and the characteristics of CAVs, the car-following model based on the autonomous driving and communication technology is established.
where a n (t) is the acceleration of vehicle n at time step t, which is defined by the adaptive cruise control model [54].
where a max , T ACC , K 1 , and K 2 are model parameters. T ACC represents the desired net time gap of vehicle n relative to its preceding vehicle, and a max represents the maximum acceleration of the vehicle. When the preceding vehicle n + 1 is an MV, since the speed of vehicle n + 1 at the next time step t + 1 cannot be accurately obtained, the anticipated space gap d anti of the current vehicle n is defined as When the preceding vehicle n + 1 is a CAV, the anticipated space gap d anti of the current vehicle n is defined as where v n+1 (t + 1) is the anticipated speed of the preceding vehicle n + 1 at the next time step t + 1, since vehicle n can effectively obtain the driving information of vehicle n + 1, and v n+1 (t + 1) can be expressed as where a n+1 (t), v n+1 safe , and d n+1 anti are the acceleration, the safe speed, and the anticipated space gap of vehicle n + 1 at time step t, respectively. e calculation for d n+1 anti is similar to that of d anti . e iteration continues until an MV appears. If i vehicles in front of the current vehicle n are all CAVs, the anticipated speed of the i th vehicle in front of vehicle n at the next time step t + 1 is where v n+i (t) represents the speed of vehicle n + i at the time step t, a n+i (t) represents the acceleration of vehicle n + i at the time step t, d n+i anti represents the anticipated space gap of vehicle n + i, d n+i (t) is the space gap between vehicle n + i and its preceding vehicle n + i + 1 at the time step t, and v n+i safe is the safe speed of vehicle n + i.
For CAVs, since their reaction time is assumed to be 0, the safe speed can be defined as Finally, the position of vehicle n is updated as follows: Step 1: e motivational conditions Journal of Advanced Transportation Step 2: e safety condition where d other (t) is the anticipated space gap between vehicle n and the preceding vehicle on the target lane at the time step t, d other n (t) is the space gap between vehicle n and the preceding vehicle on the target lane at the time step t, and d back other (t) is the space gap between vehicle n and the rear vehicle on the target lane at the time step t.

Lane-Changing Model for
CAVs. When the following conditions are met, a CAV will move onto the target lane with a probability of p CAV lc .
Step 1: e motivational conditions When the preceding vehicle on the current lane is a CAV, d anti can be de ned as When the preceding vehicle on the current lane is an MV, d anti can be de ned as

Journal of Advanced Transportation
When the preceding vehicle on the target lane is a CAV, d other (t) can be de ned as where v other n+1 (t + 1) represents the anticipated speed of the preceding vehicle on the target lane at the next time step t + 1. When the preceding vehicle on the target lane is an MV, d other (t) can be de ned as Step 2: e safety condition When the rear vehicle on the target lane is a CAV, the safety condition is as follows: where v other n−1 (t + 1) represents the anticipated speed of the rear vehicle on the target lane at the next time step t + 1.
When the rear vehicle on the target lane is an MV, the safety condition is as follows: where E 0 represents the lower limit of vehicle emissions corresponding to the speci ed emission type and f 1 to f 6 represent the parameters corresponding to each vehicle type and emission type, respectively. v n (t) and a n (t) represent the instantaneous speed and acceleration of vehicle n at time step t, respectively. e model parameters are shown in Table 1 [55].

Scenarios
In this paper, the cellular automata model is used to establish the simulation environment for a one-way three-lane freeway segment. e parameter values of the heterogeneous tra c ow model are shown in Table 2 [26,28,53]. e length of the cell is set to be 0.5 m. Each lane is represented by 5000 cells; that is, the lane length is 2500 m. e length of the vehicle is set as 7.5 m; in other words, each vehicle occupies 15 cells. e boundary condition is set as the periodical boundary condition. Each simulation runs 5600 time steps: the rst 2000 time steps will be deleted and only the last 3600 time steps will be retained, representing about a 60-minute run. e simulation results will be analyzed in Section 4.

e Basic Scenario.
In the basic scenario, there is no CAV dedicated lane on the freeway, and CAVs and MVs can travel along all lanes, as shown in Figure 1.

One CAV Dedicated Lane Scenario.
In the initial stage, with the increase of the CAV penetration rate, the innermost lane will be transformed into a CAV dedicated lane, as shown in Figure 2. On the CAV dedicated lane, since there is no interference from MVs, the adjacent CAVs can exchange their speed and position information to maintain a high average speed.

Two CAV Dedicated Lanes Scenario.
With the further increase of the CAV penetration rate, two CAV dedicated lanes will be set up, as shown in Figure 3. is strategy will further increase the right of way of CAVs, reduce the interference of the heterogeneous tra c ow on CAVs, and maximize the advantages of CAVs.

The Simulation Results
is section discusses the situations where di erent CAV dedicated lane strategies are best suitable for ve aspects: ow, speed, CO 2 emissions, NO X emissions, and VOC emissions. Under the condition of the same density, the number of vehicles on the freeway is the same no matter whether the CAV dedicated lane is set up on the freeway or not, and therefore the average exhaust emission of vehicles is used instead of exhaust emission value as the evaluation index.  Figure 4 shows the relationship between ow and density under di erent CAV penetration rates in the three scenarios. From Figure 4( Figure 6: Flow-density diagrams under di erent CAV penetration rates.

Journal of Advanced Transportation
Meanwhile, the higher road capacity can be maintained in a wider density range with the increase of CAV penetration rate. As shown in Figures 4(b) and 4(c), under the conditions of low CAV penetration rates, freeways with one or two CAV dedicated lanes have lower road capacity. is is mainly due to the fact that there are few CAVs on the freeway; setting up CAV dedicated lanes at this time causes the imbalance in the distribution of road resources.
erefore, under the conditions of low CAV penetration rates, it is inappropriate to set up CAV dedicated lanes on the freeway.
As can be seen from Figures 5(a) and 5(b), under the conditions of low densities and low CAV penetration rates, the average capacity of the CAV dedicated lanes is less than that of general lanes. is is because vehicles are in the state of free ow under the low-density conditions. At this time, due to the low CAV penetration rate, the number of vehicles on the CAV dedicated lanes is too small and therefore the capacity is small. As the density and the CAV penetration rate increase, the average capacity of the CAV dedicated lanes increases and exceeds that of general lanes. e maximum average capacity di erence can exceed 2000 veh/h. is shows that setting up the CAV dedicated lanes can signi cantly improve the capacity of the CAV dedicated lanes, but its negative impact on general lanes also should not be ignored. Setting up the CAV dedicated lanes will compress the road space for MVs and reduce the capacity of the general lanes. In order to evaluate the in uence of the CAV dedicated lanes on the freeway tra c ow, we should consider not only the improvement of tra c conditions of the CAV dedicated lanes but also the improvement of the overall tra c ow. erefore, we illustrate the owdensity relationship under the di erent CAV penetration rates in Figure 6.
As can be seen from Figure 6, the tra c ow under di erent lane strategies is signi cantly di erent. When the CAV penetration rate is 10%, on the whole, the strategy that does not set up the CAV dedicated lanes on the freeway is most bene cial to tra c ow. When the CAV penetration rate is 20% and the density exceeds 40 veh/km/lane, the tra c ow of the freeway with one CAV dedicated lane is higher than that of the freeway without the CAV dedicated lanes. However, the maximum tra c ow of the freeway with one CAV dedicated lane is lower than that of the freeway without the CAV  dedicated lanes. When the CAV penetration rate is 30%, on the whole, the strategy that sets up one CAV dedicated lane on the freeway is most bene cial to tra c ow. However, due to the low CAV penetration rate, when the density is not less than 120 veh/km/lane, it is impossible to set up one CAV dedicated lane on the freeway, because this will cause the general lanes to be unable to accommodate all MVs. When the CAV penetration rate exceeds 30% and the density is not less than 30 veh/km/lane, the overall tra c ow performance of the freeway with one CAV dedicated lane is better than that of the freeway without the CAV dedicated lanes. Similarly, when the CAV penetration rate exceeds 60% and the density is not less than 40 veh/km/lane, the overall tra c ow performance of the freeway with two CAV dedicated lanes is best. Meanwhile, with the increase of the CAV penetration rate, the variation of tra c ow resulting from di erent lane strategies decreases. is shows that, under the conditions of high CAV penetration rates, the heterogeneous tra c ow has little interference to CAVs and the in uence of CAV dedicated lanes on tra c ow is weakened.    conducive to maximizing the advantages of CAVs, reducing the frequent acceleration and deceleration, and consequently reducing NO X and VOC emissions. Specifically, when the CAV penetration rate exceeds 30%, on the whole, the emissions of NO X and VOC of the freeway with one CAV dedicated lane are lower than those of the freeway with no CAV dedicated lane. Similarly, when the CAV penetration rate exceeds 60%, the emissions of NO X and VOC of the freeway with two CAV dedicated lanes are the lowest.

Conclusions
In this paper, a heterogeneous traffic flow model is established to study the overall influence of the CAV dedicated lane on the freeway traffic flow. e model is mainly improved from the two following points: one is that MVs should be decelerated by a realistic amplitude and the other is that CAVs can accurately predict the speed of its preceding and rear CAVs at the next time step. Under different densities and CAV penetration rates, we studied the flow, speed, CO 2 emissions, NO X emissions, and VOC emissions under different lane strategies by a set of numerical simulations. e simulation results show that the density and the CAV penetration rate have significant impacts on the performance of the CAV dedicated lane strategy. Under the conditions with low CAV penetration rates, setting up the CAV dedicated lanes has negative impacts on the operating efficiency of traffic flow and vehicle exhaust emissions. When the density is not less than 30 veh/km/lane and the CAV penetration rate is 40%-60%, the lane strategy to set up one CAV dedicated lane is the best choice. When the density is not less than 40 veh/km/lane and the CAV penetration rate exceeds 60%, the lane strategy to set up two CAV dedicated lanes is the best choice. is paper investigates the effect of the traffic density and the CAV penetration rate on the performance of lane-setting strategies. e results are helpful to determine the optimal number of CAV dedicated lanes under different traffic conditions. e established model can be easily extended to other specific scenarios and thus there is significance of the application in the research field of the CAV dedicated lane management strategies in the future. However, there are still some shortcomings in this paper. e influence of CAV dedicated lanes on the merging and diverging area of freeways needs to be studied and analyzed in the future.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.