Impact of connected and autonomous vehicle dedicated lane on the freeway traffic efficiency

The imminent emergence of connected and autonomous vehicles (CAVs) highlights the need for preparing the road infrastructure for traffic flows mixed with CAVs and human-driven vehicles. A dedicated lane (DL) for CAVs is one of the practical and potential ways to upgrade the road infrastructure for the mixed traffic. This paper proposes a theoretical method to discuss the influence of implementing a CAV DL policy on the freeway traffic efficiency. In detail, the impact was measured by capacity and throughput. The calculation methods of these efficiency measurements under different CAV DL policies were proposed. Numerical experiments were conducted under various compositions of CAV DL policies and traffic conditions. More specifically, the relationship between the traffic conditions (i.e., traffic demand, market penetration rate (MPR) of CAVs, platoon intensity of CAVs, willingness of CAVs using the CAV DL) and the CAV DL policies (i.e., lane configuration, DL access control policy) were discussed. The results have led to some interesting findings, including the critical values of MPR that are valuable to guide an appropriate implementation of a CAV DL policy under a specific traffic condition.


Introduction
Connected and Autonomous Vehicles (CAVs) are expected to bring benefits to traffic efficiency, safety, and energy-saving [1,2]. And there will be a long transition period with the coexistence of CAVs and Human-driven Vehicles (HVs). This mixed traffic condition is one of the major challenges in future traffic because of its complexity. For instance, CAVs might have six automation levels identified by the Society of Automotive Engineers (SAE), which results in different driving behaviors. The unpredictable human driving behavior could cause confusion and potentially unsafe situations to the CAVs. As a result, the expected outstanding performance of CAVs might be affected, especially with a low market penetration rate (MPR) [3]. It urges some appropriate and effective management or control strategies for the mixed traffic condition.
Inspired by the lane management techniques, the researchers have considered to apply the dedicated-lane (DL) techniques to manage the mixed traffic [4]. The lane management techniques have been widely applied in practice, e.g. High Occupancy Vehicle lanes, High Occupancy Toll lanes, and dedicated bus lanes, which have achieved great success in improving the traffic efficiency of the traditional HV traffic [5]. Ideally, assigning one or more lanes to CAVs might bring several benefits. It could reduce the potential conflicts between CAVs and HVs by the physical separation, as well as avoid the subsequent legal disputes. Besides, it could guide the CAVs to drive in the same lane, increasing the probability of forming CAV platoons, which has been proven to be more efficient (D. [1,6]. To some extent, it seems that the lane management could make the introduction of CAVs on the road smoother, safer, faster and more acceptable.
Before the field application of a CAV DL policy, it is essential to evaluate its impact on the efficiency, safety, and equity. However, due to the unknown and complex future mixed traffic with the unformed high-automationlevel CAVs, it is still a challenging and on-going task to make an extensive validation of a CAV DL policy. As a start, this study will conduct an impact evaluation of different CAV DL policies on the traffic efficiency. Accordingly, the rest of this paper is organized as follows: second section summarizes the existing studies. Third section introduces the detailed methodologies about the CAV DL policies and the traffic-efficiency measures. Numerical experiments and analysis are presented in fourth section. Fifth section gives the main findings and the future works.

Literature review
A batch of studies have made efforts to explore the application of DL policy under the novel traffic flow mixed with CAVs and HVs. Razmi Rad et al. reviewed the existing studies that underpin their conceptual framework illustrating the relationship among (1) the design and operation of CAV dedicated lane, (2) driver behavior, and (3) the impact on environment, traffic efficiency, and safety (Solmaz Razmi [4]. Following their work, this study extends the review on the relationship between CAV DL policy and traffic efficiency. For a better comparison, Table 1 lists five perspectives of the state-of-theart studies, including the mixed traffic composition, main method, performance measures, discussed variables, and main results, which also inspires this study to some extent. Based on the scale of studied roadway, these existing studies are categorized into the network-based studies and the link-based studies. Those network-based studies would commonly use such methods as the network equilibrium and traffic assignment models. And the network-wide issues have been discussed, e.g., selecting out the road segments in the network fitting to implement the DL, and the optimal tolling rate for using the DL, etc. From a view of a road link/segment/corridor, the link-based studies have used different methods which are classified into the theoretical methods and the simulation methods. The simulation methods are based on the modeling of microscopic driving behaviors, while the theoretical methods derivate the traffic flow models using the mathematical or physical theory. Both these methods could generate the macroscopic traffic performance measures (e.g., capacity, flow), while it seems that the simulation methods could achieve additional measures (e.g., speed, travel time, etc.). Comparatively, the theoretical methods are more meso or macro, which derivate the macroscopic performance measures more directly. Besides, the theoretical methods are more convenient in modeling the multiple possibilities of future CAVs, instead of a heavy workload of different microscopic driving behavior modeling in the simulation methods. Therefore, this study decides to use the theoretical method for convenience at a primary stage of research. As the mostly used flow-related measures in the theoretical methods, the capacity and throughput are also selected as the performance measures in this study. And then, an updated theoretical method to derivate the performance measures will be proposed in the following. Table 1 indicates that the market penetration rate (MPR) of CAVs has been definitely discussed in these existing studies. Besides, headway distributions, number of DLs, traffic demand, CAV platooning intensity, segregation policy, access strategies, speed limit are partially discussed. To make a more comprehensive exploration, this study expands the research by discussing various combinations of traffic-condition-related variables and CAV-DL-policy-related variables.
As Table 1 shows, the headway-based method is the mostly explored theoretical method. A challenge is that the headway distribution of mixed traffic is not yet sufficient to be conclusive. A review of studies on the headway distribution are summarized in Table 2 which is updated based on the study of Ghiasi et al. [1]. A popular assumption is that a CAV could keep a shorter distance with the preceding vehicle compared with an HV. From a security standpoint, some researchers would argue CAVs should keep a larger distance with a preceding HV to adapt to the randomness of human driving behavior [19]. Table 2 also indicates that the simulation method is mostly used to study the mixed traffic. Therefore, it would be meaningful for this study to further explore the various possibilities of CAV headways with a theoretical method.

Dedicated lane policies
Three aspects of a DL policy are discussed in this study, including the eligibility, number of DL, access strategy. Firstly, for convenience of implementation, this study defines that a freeway CAV DL is one of the freeway lanes assigned to be used by CAVs in a full automation mode only. The mentioned CAV eligible to use the DL drives the car by itself, which approximately refers to SAE Level 3-5 under the automated driving mode. Those vehicles that are ineligible to use the DL include the CAVs in SAE Level 1-2 and human-driving mode of Level 3-4, as well as those pure manual driving vehicles, which are all called as HVs in the following study for convenience.
It should be noted that if a CAV changes its automated driving mode to the manual driving mode, then it is urged to leave the DL. Second, different possibilities of CAV DL number will be explored in the following study, which are valued from zero to the total number of lanes.
Third, two access control policies are proposed, i.e., mandatory use and optional use. Following the 'mandatory use' policy, CAVs are obligated to travel on the DL, which strictly separates CAVs from HVs. Under this policy, the lanes are divided and named as the CAV DL and the general-purpose lane (GPL). The 'optional use' policy allows the CAVs to choose either driving on a DL or the other lane. In this case, the other lane is named as the mixed lane (ML), which could be used by both CAVs and HVs. It should be noted that the on-or off-ramps and weaving sections are not in the scope of this study and these access control policies are not suitable to apply on these sections. An illustration of these two access control policies is shown in Fig. 1.

Efficiency measures 3.2.1 Capacity
Three types of lanes are involved in the different DL policies, i.e., DL, GPL, and ML. Obviously, the traffic on a DL and GPL can be regarded as two extreme cases on an ML. Therefore, the capacity calculation method of an ML is introduced as a representative. As an ML example in Fig. 2, there are four types of car-following behaviors corresponding to four types of time headways which are defined as: (1) h CC for a CAV follows another CAV, (2) h CH for a CAV follows an HV, (3) h HC for a HV follows a where n CC , n CH , n HC , and n HH are the number of CAVs following CAV, the number of CAVs following HV, the number of HVs following CAV, and the number of HVs following HV. N mix is the sum of n CC , n CH , n HC , and n HH , which approximately equals to the traffic volume on the lane. Similarly, N C = n CC + n CH is the total CAV volume on the lane, and the MPR of CAVs on a lane could be calculated by: Besides, the platooning intensity (PI) of CAVs is proposed to reflect the proportion of CAVs forming the platoons to all CAVs: Similarly, we have p H representing the percentage of HVs on a lane and p HH representing the ratio of HVs following HV to the total number of HVs. Based on the average time headway of a lane (in seconds), the capacity of a ML (in veh/h) could be inferred by: The independent variables in Eq. (4) include different types of headway, MPR of CAVs and HVs, PI of CAVs and HVs, which will jointly determine the capacity of a ML.
(1) h mix = n CC · h CC + n CH · h CH + n HC · h HC + n HH · h HH N mix Accordingly, the formulas for the capacity of a CAV DL and a GPL could be inferred as:

Throughput
The expectation of implementing a DL policy is to achieve a larger throughput of a freeway segment. Assuming that a studied freeway segment has L lanes in one direction, L DL lanes are assigned as the CAV DLs where L DL ∈ [0, L) , and the left L − L DL lanes are GPLs or MLs depending where F DL is the flow on the DLs; F GPL is the flow on the GPLs; f DLi is the flow of ith DL; f GPLj is the flow of jth GPL; C DL is the DL capacity; C GPL is the GPL capacity; L DL is the number of DLs; P CAV is MPR of CAVs in the segment.   where F mix is the flow on the MLs; f mixj is the flow on jth ML.

Experiment settings
The numerical experiments are set up as follows: (a) Lane configurations Three types of freeway segments, i.e., 2 lanes, 3 lanes, and 4 lanes in one direction, are tested. Table 3 shows the detailed lane configurations in each testing scenario. Table 2 indicates that the existing studies have adopted different headway distributions including fixed-value distribution, uniform distribution, and Gaussian distribution. Obviously, the former two distributions are mostly discussed. Although the fixed-value distribution ignores the heterogeneities of different vehicles, it takes advantage of a simple and fast calculation. The uniform distribution exhibits the heterogeneities to some extent but increases the computational efforts. Since the proposed methods use the average headways, the fixed-value distribution seems more suitable and convenient. Referring to Table 2 Table 2 assume that HVs maintain the same average headway either following another HV or a CAV. And this study adopts the same assumption, i.e.,h HC = h HH . Besides, it is assumed that the average time headway between two CAVs is the shortest among the four types of car-following behaviors. There will be an increase in the average time headway when CAV follows an HV. And two possibilities of the increase will be explored. One possibility is that the increase is not that large and h CH is still smaller than h HH . Another possibility is h CH grows over h HH . Accordingly, there will be four kinds of CAV driving modes which are named as aggressive mode, neutral mode, conservative mode, and safe mode. In the former three modes, the relationship among different types of average headways is that h CC < h CH < h HC = h HH . In the safe mode, the relationship is h CC < h HC = h HH < h CH . The average time headways in each mode are valued as follows:

(iii) MPR of CAVs in a lane and in a segment
It could be imagined that CAVs will be introduced into the market gradually. In this light, this study set the MPR of CAVs as 1%, 5%, 10%, and then, increasing with 10% step to 100%. There are two kinds of MPRs in this study. One is defined as the MPR of CAVs in a lane ( p C ), and the other is named as the MPR of CAVs in a segment ( P CAV ). A freeway segment is made up of several lanes. If the traffic is uniformly distributed across the lanes in a segment, then P CAV equals to p C . Otherwise, P CAV is valued as before, while p C has to be recalculated according to the DL access control policy and the traffic distribution across different lanes as the following Eq. (11).

(iv) PI of CAVs in a lane
To investigate the influence of platoon intensity ( p CC ), this ratio was valued from 0 to 100% with 10% step. However, it should be noted that the lower limit of p CC will be changed when the number of CAVs exceeds the number of HVs. Under this condition, even though every HV is followed by a CAV, there are still ( N C − N H ) CAVs following other CAV. Accordingly, the threshold of p CC will be:

(e) DL access control policy
Under the 'optional use' policy, the willingness of CAV choosing to use DL (selection rate O DL ) is not sure in the future application. Therefore, this study proposes three willingness states (i.e., weak, moderate, and strong) and assigns 0.2, 0.5, and 0.8 to O DL correspondingly. And then, the distribution of CAVs across different types of lanes could be inferred. For instance, if the MPR of CAVs in a segment is P CAV , then the proportion of CAVs traveling on MLs and DLs will be P CAV · (1 − O DL ) and P CAV · O DL respectively. Although the discussion of lane overflow is essential, it is not in the scope of this study and planned in a future study. On this basis, the penetration rate of CAVs on different type of lanes under the optional use policy could be inferred. For example, if the traffic demand of a two-lane mainline segment is D, and one lane is reserved as a CAV DL, then the traffic on the DL is D · P CAV · O DL , and p C on ML is: Besides, it is assumed that if the adjacent lanes belong to the same type, then the traffic will be evenly distributed across these lanes. (11)

Results and evaluations 4.2.1 Capacity
Based on Eq. (5) Figure 3 illustrates the capacity of an ML under the different CAV driving modes and different compositions of p C and p CC , and a darker color represents a larger p C . p C reflects the proportion of CAVs to the traffic in a lane, while p CC indicates the platoon intensity of CAVs. Obviously, the aggressive mode of CAVs significantly increases the ML capacity. From the Fig. 3a-c, it can be seen that both p C and p CC have a positive impact on the capacity, but this impact is insignificant when MPR of CAVs is small especially below 10%. Figure 3d indicates that if CAVs use a safe driving mode, then the increase of CAVs would decrease the ML capacity. This negative impact could be mitigated with the increase of PI ( p CC ). Besides, when p CC grows over 50%, the increase of CAVs will always be beneficial to the capacity in all driving modes. Under an ideal condition, the capacity of a freeway segment would be a sum of all lanes' capacity. According to the applied DL policy, a freeway segment would consist of different types of lanes. The above analysis indicates that only the capacity of ML will be impacted by the traffic conditions (MPR and PI of CAVs). Therefore, when a segment contains ML, its range of capacity variation and ideal traffic condition to achieve the largest capacity are concluded in Table 4. First, Table 4 shows that under the ideal condition, the maximum capacity under no-DL or 'optional use' DL policy is larger than that under the 'mandatory use' DL policy. The ideal condition under no-DL or 'optional use' DL policy is when CAVs fully conquer the vehicle market. On the other hand, the ideal MPR under the 'mandatory use' DL policy to reach the maximum capacity is obviously lower than 100%. Since the 'mandatory use' policy strictly distinguishes the right of way by vehicle type, the ideal condition happens when there is a match between the traffic distribution and the lane composition. Otherwise, the mismatch would lead to a waste of lane resource or a lane congestion. Moreover, under the same traffic condition and DL access control policy, the increase of DL number will benefit the capacity, but this benefit is trivial when P CAV is small. Besides, the 'mandatory use' performs better than the 'optional use' when CAVs use the safe driving mode and P CAV is small.

Throughput
As a start, a freeway segment with two lanes in a direction is taken as an example, and the O DL in the 'optional use' policy is set as 0.5. The traffic throughputs under four traffic demands are inferred based on Eqs. (7)-(9) as shown in Fig. 4.
Some findings could be inferred from the subfigures of Fig. 4. First, when the demand is lower than the capacity, implementing a DL almost has no effect on the throughput. Second, converting a lane into a DL will have a negative impact on the traffic throughput, when the MPR of CAVs ( P CAV ) is low. And this negative impact lasts until P CAV reaches 50%. Third, the DL with 'mandatory use' appears to have the most significant and positive impact when P CAV is within the range of 50% to 60%. The increase of traffic demand would enhance this benefit, which will gradually vanish when the driving mode of CAVs gets more aggressive. Fourth, it indicates that the 'mandatory use' policy overperforms the 'optional use' policy when CAVs in the safe and conservative driving modes and P CAV is lower than 80%, while the 'optional use' policy will be more advantageous when P CAV is over 80%. Under the neutral driving mode, this critical point of P CAV is 90%. Under the aggressive driving mode, the 'mandatory use' policy always has a better performance.
A further discussion is to explore the different willingness states of using the CAV DL which are represented by three different values of O DL 0.2, 0.5, and 0.8. The results of throughput under different demands with CAVs in the same driving mode (safe driving mode) are shown in Fig. 5. And Fig. 6 exhibits the throughput under different driving modes with the same demand (3500 veh/h). It can be concluded from these two figures that encouraging more CAVs to use the DL is beneficial to the traffic throughput. And this encouragement should be enhanced especially under the following conditions: a higher traffic demand, or a safer driving mode. Furthermore, the impact of DL number on the throughput is explored on the three-lane freeway segment. According to the previous findings on O DL , its value is set to 0.8 in this experiment. The results indicate that if DL is going be implemented, then distributing one lane as a DL is sufficient.
Finally, compared with the findings of the existing studies in Table 1, this study has obtained some consistent results, for instance, when MPR of CAV is low, implementing a CAV DL might reduce the throughput. Besides, this study yields some different results which embody in four points. First, for the number of CAV DL, this study would suggest that if DL is going be implemented, one DL is sufficient at the introduction stage of CAVs with a low MPR. Second, with a gradual increase of CAV MPR, the 'mandatory use' access control policy is suggested especially when CAVs adopt a more conservative or safer car-following behavior. Although this policy might negatively impact the freeway capacity and throughput compared with the scenario without the DL, it is better than 'optional use' policy from the view of throughput. Third, when the CAV MPR increases over some specific condition as concluded in Table 4, it is suggested to use the 'optional use' DL or not to implement DL. Fourth, when the 'optional use' policy is adopted, efforts should be made to encourage the CAVs to use the DL and thus benefit the throughput.

Conclusions and future works
This study presents a review of the "state-of-the-art" studies on CAV DL policy under the mixed traffic condition as well as the headway distributions of the mixed traffic. And then, the detailed CAV DL policies and the headway-based theoretical methods evaluating the traffic efficiency are proposed. The discussions based on several numerical experiments give some insights into the relationship between traffic efficiency measures and various conditions (traffic conditions and DL policies). As a final observation, it seems when the MPR of CAVs on a freeway segment is low (e.g., below 50%), the implementation of CAV DL does not have a significant positive impact on traffic efficiency. At this condition, if a DL policy is required, the 'mandatory use' is recommended compared with the 'optional use' , especially when CAVs use the safe driving mode. When MPR of CAVs grows to a high value (e.g., larger than 80%), the 'optional use' policy performs better instead. All in all, distributing one lane as a DL is enough as a beginning stage of DL implementation. In fact, this study has partially finished the discussion, and more extensive explorations are essential. Here is a summation of works that could be conducted in the future. First, different eligibility arrangement of different automation-level vehicles could be explored. Second, to discuss the heterogeneity in headways by using different headway distributions might be interesting. Third, the weaving segment should also be explored to form a complete road network so that the impact of lane overflow could be analyzed. Fourth, except the traffic efficiency, the other safety and equity measures are also needed to validate a DL policy fully.