A Cooperative Lane-Changing Strategy for Weaving Sections of Urban Expressway under the Connected Autonomous Vehicle Environment

. To alleviate the lane-changing conficts between weaving vehicles and enhance the trafc efciency in the weaving section of urban expressway under the connected autonomous vehicle (CAV) environment, a cooperative lane-changing strategy for CAVs is proposed. Te strategy consists of an upper layer of decision making, which determines the lane-changing sequences of weaving vehicles based on their lane-changing advantages quantifed by a set of utility functions, and a lower layer of control, which generates detailed instructions of speed adjustments and lane-changing manoeuvres for weaving vehicles. To verify the efec-tiveness of the proposed strategy under diferent trafc demand settings, a numerical simulation, including a base case and a control case, is conducted. Ten, to further verify the efectiveness of the proposed strategy for the mixed trafc state and compare its performance with the existing CAV lane-changing method, benchmark and comparison tests with six diferent market penetration rates (MPRs) of CAVs are carried out under the congested demand setting. In addition, the delay improvement ratio, inverse time-to-collision, and ratio of large deceleration time are selected as performance indicators to investigate the efect of the proposed strategy on enhancing the operational efciency, trafc safety, and passenger’s comfort within the weaving section. According to the simulation results, the overall efciency, safety and comfort in the weaving section under the CAV environment, are all improved, when the proposed strategy is applied to weaving vehicles. Te proposed strategy is also superior to the existing CAV lane-changing method on maintaining trafc efciency and safety. Terefore, the proposed co-operative lane-changing strategy, based on CAV technologies, shows good potential in solving the problem of lane-changing conficts within the weaving section and facilitating the trafc management and trafc control of urban expressway.


Introduction
Urban expressway, which has the characteristics of large capacity, high speed, and high safety, can facilitate longdistance travel for residents among diferent urban areas. However, with the fast progress of urbanization, the amount of private car travels has signifcantly increased, resulting in frequent trafc congestion in urban expressway during rush hours. In particular, due to the restriction of urban land use and the high density of trafc demand, an expressway oframp often closely follows an on-ramp, and sometimes, the on-ramp and the of-ramp are directly connected by a short auxiliary lane. Such kind of layout forms a typical weaving section. A research study [1] shows that within the short range of weaving section, there are a large number of accelerating, decelerating, and mandatory lane-changing behaviours, which make the trafc conditions in the weaving section relatively complicated and highly indeterminate. Terefore, during the rush hours with the high fow rate, the weaving section can easily become a major congestion spot in the expressway.
In a typical weaving section of urban expressway, there are two major types of mandatory lane-changing vehicles, namely, the diverging vehicles and the merging vehicles, where the former come from the mainline of expressway and change to the auxiliary lane in the weaving section in order to exit the expressway and the latter enter the auxiliary lane and change lane in order to merge into the mainline of expressway. Te opposite origins and destinations of these two types of lane-changing manoeuvres can cause a considerable amount of trafc conficts. Specifcally, in a weaving lane-changing scenario, a diverging vehicle and a merging vehicle, which are close to each other, might intend to change to each other's lane at the same time. Such confict in lane-changing intention will make these two vehicles to "compete" against each other in order to change lane frst and move into the acceptable gap in front of the "opponent" vehicles. Usually, the vehicle with advantages in relative position or relative speed will force the other vehicle to yield in speed or even give up the lane-changing intention temporarily to give way. Such outcome of the "competition" between two weaving vehicles seems rather intuitive, but sometimes, it is highly sensitive to driver's subjective judgment. In the worst-case scenario, the disadvantageous vehicle refuses to give way to the advantageous vehicle, causing a dead lock between two weaving vehicles. Te accumulation of such kind of dead locks will eventually lead to the delay in journey time, reducing the operational effciency of weaving section.
Terefore, it is necessary to thoroughly understand the lane-changing behaviour in the weaving section and design a comprehensive lane-changing strategy for the weaving section [2], as to facilitate trafc management and trafc control of the urban expressway, thus improving the trafc efciency.
In retrospect, there have been numerous literature studies on the study of characteristics of lane-changing behaviour in the weaving section. Hidas [3] developed a lane-changing model for the weaving section by adopting the concept of intelligent agent and classifed the lanechanging behaviour into three types, namely, free, forced, and cooperative. Jin [4] established a LWR lane-changing model for the weaving section, based on whether the vehicles were weaving or nonweaving vehicles. Marczak et al. [5] systematically analysed the lane-changing behaviour in the weaving section at a microscopic level. Chen et al. [6] developed a probability model of car-following and lanechanging binary choice for vehicles in the weaving section. Wan et al. [7] analysed a variety of merging strategies using the NGSIM data set and constructed a combined sequential decision-making model for the weaving section that can dynamically simulate vehicles' choice of target gap and lane-changing strategy. Kusuma et al. [8] found out the group lane-changing behaviour in the weaving section and proposed a random utility formula to characterize diferent lane-changing mechanisms. Peng et al. [9] proposed a multistage lane-changing decision-making model based on the refned cellular automata for the weaving section.
Other researchers focused on alleviating the trafc conficts caused by weaving lane-changing behaviour and improving the efciency of the weaving section. Sun et al. [10] used multiagents modelling technology and established a cooperative lane-changing model to solve the problem of lane-changing conficts in the weaving section. Bham [11] proposed a simple and efcient weaving model using microscopic simulation, so as to guide lane-changing behaviour in the weaving section. Mai et al. [12] adopted the concept of the cooperative intelligent transport system and proposed a lane-changing advisory for the weaving section. Sulejic et al. [13] developed an algorithm based on particle swarm optimization to optimize the lane-changing distribution and alleviate the problem of lane-changing concentration in the weaving section. Tilg et al. [14] applied the automated vehicle technology and proposed a multiclass hybrid model to optimize the lane-changing distribution and increase the capacity of the weaving section.
With the development of CAV technologies, the share of information among vehicles and infrastructures can be realized through V2V and V2I communications [15]. In addition, the optimized instruction generated by roadside control units can be sent to vehicles in real time, efectively improving the travel efciency and safety of vehicles. Tus, inspired by the previous research studies on the optimization of lane-changing behaviour in the weaving section and the concept of CAVs, this paper proposes a novel cooperative lane-changing strategy for CAVs in weaving sections of urban expressway at a microscopic level. In this strategy, an upper layer of decision making is built to give advice on the lane-changing sequences for weaving vehicles and a lower layer of control is built to provide guidelines for vehicles' speed adjustments and lane-changing manoeuvres. Also, a numerical simulation is set to verify the efectiveness of the proposed strategy.
Te main contributions of this study are as follows: (1) Solving the problem of lane-changing conficts in the weaving lane-changing scenario by applying CAV technologies to provide weaving vehicles with the decision of lane-changing sequences and detailed control instructions of speed adjustments and lanechanging manoeuvres. (2) Efectively improving the operational efciency, trafc safety, and passenger's comfort within the weaving section of urban expressway under the CAV environment.
Te rest of the paper is organized as follows. Te design of the cooperative lane-changing strategy is introduced in the next section. After that, the setups and performance indicators of the numerical simulation are thoroughly described, followed by the analysis and discussion of simulation results. At last, some concluding remarks are mentioned to end this paper.

Cooperative Lane-Changing Strategy
In the general case of the lane-changing scenario (see Figure 1), the lane-changing vehicle (SV) takes into consideration its relative position and speed with respect to the leading vehicle (LV) and following the vehicle (FV) in the target lane, as well as the space of acceptable gap (d) between LV and FV.
For example, in the classical Gipps lane-changing model [16] (see equation (1)), the lane-changing manoeuvre is considered safe and can be carried out if d is longer than the length of SV and the condition in equation (2) is fulflled. Specifcally, the required decelerating rates for SV and FV to maintain safe car-following speeds with respect to LV and SV and avoid collision after the lane change cannot exceed the maximum decelerating rate.
where x SV (t) and v SV (t) are the position and speed of SV at time t; x LV (t) and v LV (t) are the position and speed of LV at time t; x FV (t) and v FV (t) are the position and speed of FV at time t; v SV (t + ∆t) and v FV (t + ∆t) are speeds of SV and FV at time (t + ∆t); b max is the maximum decelerating rate of the vehicle; and l is the length of the vehicle.
However, in the case of weaving lane-changing scenario (see Figure 2), both the weaving vehicles (SV1 and SV2) have to simultaneously consider (I) the relative position and speed with respect to the leading vehicles (LV2 and LV1) and following vehicles (FV2 and FV1) in their target lanes, (II) the relative position and speed with respect to each other, and (III) the space of acceptable gaps in front of (d 2.front and d 1.front ) and behind (d 2.rear and d 1.rear ) each other. Terefore, it is improper to simply apply the general microscopic lane-changing model to the weaving lanechanging scenario because it might cause confusion in the decision making of vehicles' lane-changing sequences.
Alternatively, it is more practical to consider the weaving vehicles as a group, namely, the weaving group, and transform the problem of two weaving vehicles' conficting lanechanging manoeuvres into the problem of rearrangement of lane-changing sequences within the weaving group. Due to the vast deployments of the emerging CAV technologies in the near future, it is expected that the information of vehicle states (position and speed) can be easily shared within the weaving group if both the weaving vehicles are CAVs, and optimized instructions regarding driving decision and vehicle control generated by roadside control units can be transferred to the weaving group in real time. In this case, a cooperative lane-change strategy at the microscopic level is proposed for CAVs in the weaving section, which consists of an upper layer of decision making for lane-changing sequences of two weaving vehicles and a lower layer of control for vehicles' speed adjustments and lane-changing manoeuvres.

Decision-Making Layer for Lane-Changing Sequences.
Te main purpose of the decision-making layer is to determine the lane-changing sequences of the two weaving vehicles, that is, whether SV1 or SV2 should change lane frst and move into the acceptable gap in front of the other vehicle (d 2.front or d 1.front ). Te prerequisite for the decision-making layer is shown in equation (3), which ensures that the relative position of two weaving vehicles in the longitudinal direction is less than one vehicle length. In addition, all vehicles in this study are assumed to be small passenger cars with identical attributes.
where x SV1 and x SV2 are positions of SV1 and SV2 and l is the length of vehicle. Figure 1: Schematic diagram of a general lane-changing scenario.
Te most important part of the decision-making process is to quantify how much advantage each weaving vehicle has over the other to change lane frst. Hence, a set of lanechanging utility functions are designed to quantify the lanechanging advantage in the following aspects.

Space of Acceptable Gaps.
Te frst aspect of the lanechanging advantage is related to the space of acceptable gap in front of and behind each weaving vehicle (see equation (4)).
where U 1 1 and U 2 1 are utility values of SV1 and SV2, respectively, regarding the frst aspect of advantage; ω front and ω rear are importance factors regarding the space of acceptable gaps in front of and behind the weaving vehicles (ω front + ω rear � 1); d 1.front and d 2.front are the space of acceptable gaps in front of SV1 and SV2; and d 1.rear and d 2.rear are the acceptable gaps behind SV1 and SV2.
For example, if d 2.front is larger than d 1.front , it will be more favorable for SV1 to move into the acceptable gap in front of SV2. And, if d 1.rear is larger than d 2.rear , it will be more favorable for SV2 to move into the acceptable gap behind SV1. So, U 1 1 will receive a greater value than U 2 1 , and SV1 has the advantage over SV2 to change the lane frst and vice versa.

Relative Speeds with respect to Leading and Following
Vehicles in Target Lanes. Te second aspect of the lanechanging advantage is related to weaving vehicles' relative speeds with respect to the leading and following vehicles in their target lanes (see equation (5)).
where U 1 2 and U 2 2 are the utility values of SV1 and SV2, respectively, regarding the second aspect of advantage; ω lead and ω follow are the importance factors regarding weaving vehicles' relative speeds with respect to the leading vehicles and the following vehicles in their target lanes (ω lead + ω follow � 1); v SV1 and v SV2 are the speeds of SV1 and SV2; v LV1 , v LV2 , v FV1 , and v FV2 are speeds of leading vehicles and following vehicles; and ε � 10 − 7 m/s is an extremely small value set to prevent zero denominator. SV2 ), it will be easier for FV1 to match up the speed of SV2 if SV2 moves into the acceptable behind SV1. So, U 1 2 will receive a greater value than U 2 2 , and SV1 has the advantage over SV2 to change the lane frst and vice versa.

Relative Position between Weaving Vehicles.
Te third aspect of the lane-changing advantage is related to weaving vehicles' relative position with respect to each other (see equation (6)).
where U 1 3 and U 2 3 are the utility values of SV1 and SV2, respectively, regarding the third aspect of advantage.
For example, if x SV1 is larger than x SV2 , it will be more favorable for SV1 to change the lane frst, and thus, U 1 3 will receive a greater value than U 2 3 and vice versa.

Relative Speed between Weaving Vehicles.
Te fourth aspect of the lane-changing advantage is related to weaving vehicles' relative speed with respect to each other (see equation (7)).
where U 1 4 and U 2 4 are the utility values of SV1 and SV2, respectively, regarding the fourth aspect of advantage.
For example, if v SV1 is larger than v SV2 , it will be more favorable for SV1 to change lane frst, and thus, U 1 4 will receive a greater value than U 2 4 and vice versa.

Total Lane-Changing Advantage.
Te total lanechanging advantage for each vehicle in the weaving group (see equation (8)) is the summation of four aspects of advantages defned previously, multiplied by a couple of coefcient factors.
where U 1 Total and U 2 Total are the total utility values of SV1 and SV2, respectively, regarding the total advantage; and λ 1 and λ 2 are the coefcient factors describing the driving styles of SV1 and SV2 (an aggressive driver is expected to have more advantage than a cautious driver to change lane frst); λ 1 or λ 2 > 1 for aggressive driving style � 1 for neutral driving style, < 1 for cautious driving style, are the coefcient factors describing the urgency for the mandatory lane change of SV1 and SV2; L is the total length of the weaving section, measured from merging gore to diverging gore; L lc1 and L lc2 are defned as the required longitudinal distances for lanechanging manoeuvres of SV1 and SV2; and L SV1 and L SV2 are relative distances of SV1 and SV2 with respect to merging gore. As the vehicle drives downstream and approaches the end of the weaving section, its degree of urgency for mandatory lane change increases exponentially.
Since the utility values for four aspects of the lanechanging advantage mentioned previously are normalized to the values within the interval [0, 1] (see equations (4)- (7)), it is considered that all four aspects contribute equally to the total lane-changing advantage.
Overall, the total advantage of SV1 and SV2 is compared against each other to determine their lane-changing sequences. For instance, if U 1 Total is greater than U 2 Total , the lane-changing sequences are decided as SV1 changing the lane frst and moving into the acceptable gap in front of SV2 while SV2 changing the lane later and moving into the acceptable gap behind SV1 and vice versa.

Control Layer for Speed Adjustments and Lane-Changing
Manoeuvres. Te upper layer of decision making gives the advice on the lane-changing sequences for weaving vehicles. Next, the lower layer of control can guide weaving vehicles to adjust their speed and execute the lane-changing manoeuvres simultaneously. In addition, the prerequisite that has to be fulflled for the control layer is shown in equation (10), which ensures enough space for the execution of weaving lane-changing behaviour.
Take the weaving group in Figure 2 as an example, if SV1 is decided to change the lane frst, SV1 will be instructed to accelerate with the maximum accelerating rate (a max ) and SV2 will be instructed to decelerate with a comfortable decelerating rate (b comfort ), until the clearance between SV1 and SV2 fulflls the condition in equation (11), which Journal of Advanced Transportation 5 prevents the collision between SV1 and SV2 during the lanechanging manoeuvres (see Figure 3(a)).
In addition, during the acceleration process of SV1, it has to keep its speed under the maximum car-following speed with respect to LV2 so that it can safely follow LV2 after changing the lane. On the other hand, if SV2 is decided to change the lane frst, the speed adjustment processes for SV1 and SV2 are quite opposite.
Once the condition in equation (10) is fulflled, two weaving vehicles can execute lane-changing manoeuvres and move horizontally into their desired acceptable gaps simultaneously (see Figure 3(b)).  Table 1. In specifc, values of ω front and ω lead are taken as 0.6 and values of ω rear and ω follow are taken as 0.4. It is mainly due to the common sense in the real-world driving scenario that when a vehicle manages to change lane, it usually concerns more about the space of the front acceptable gap than that of the rear acceptable gap in the target lane and concerns more about the relative speed to the leading vehicle than that to the following vehicle in the target lane.

Numerical Simulation
In order to simulate operational condition of urban expressway under diferent trafc demands, six demand settings of diferent trafc fow rates are applied to the simulation scenario (see Table 2), where demand setting #1 is corresponded to the free-fow state and demand setting #6 is corresponded to the congested state.
Here, q main and q aux are total fow rates in the mainline and auxiliary lane, respectively; q MD , q MP , q AM , and q AP are fow rates corresponding to diverging vehicle in the mainline, pass-through vehicle in the mainline, merging vehicle in the auxiliary lane, and pass-through vehicle in the auxiliary lane, respectively; and v des is the desired operating speed of expressway.
Two test cases, base case and control case, are conducted to examine the efectiveness of the proposed strategy under diferent demand settings. Meanwhile, the car-following behaviours in both cases are depicted by the classical Gipps car-following model [17].  (1)), which means that the lane-changing vehicle only executes lane-changing manoeuvre when the acceptable gap in the target lane is adequate. In addition, to prevent the situation that the lanechanging vehicle cannot fnd any adequate acceptable gap and fails to perform lane-changing behaviour while reaching the end of the weaving section, a forced lane-changing mechanism is introduced. In specifc, when the distance between a lane-changing vehicle and the end of the weaving section (diverging gore) is less than v des T, the forced lanechanging mechanism is initiated, and the road segment within the distance v des T away from the end of weaving section is defned as the forced lane-changing segment. In order to perform the forced lane change, the lane-changing vehicle will frst reduce its speed with a decelerating rate of −1 m/s 2 until it fnds a gap, which is longer than the vehicle length, in the target lane. Ten, the lane-changing vehicle will directly execute lane-changing manoeuvre regardless of the relative speed with respect to the following vehicle in the target lane while simultaneously adjusting the speed to match up the safe car-following speed with respect to the leading vehicle in the target lane. As a result, the following vehicle in the target lane will be forced to adjust speed in order to give way to the lane-changing vehicle. Te fow chart of the base case is illustrated in Figure 5(a).

Control Case.
For the control case, all vehicles are assumed to be CAVs. In this case, all lane-changing mechanisms are the same as those in the base case, except that the proposed cooperative lane-changing strategy can be applied to the eligible weaving group of CAVs. Before any lane-changing manoeuvre, the lane-changing vehicle always checks its current condition in the frst place and fgures out if there is a weaving vehicle in the adjacent lane, which intends to change lane at the same time. If a weaving vehicle exists and the relative position of two vehicles fulflls the prerequisite for the decision-making layer of the proposed strategy (see equation (3)), the decision regarding the lane-changing sequences of two weaving vehicles will be automatically generated by the roadside control unit. Meanwhile, if the prerequisite for the control layer of the proposed strategy (see equation (10)) is fulflled, the control instructions of speed adjustments and lane-changing manoeuvres will be sent to the vehicles in real time. Ten, the weaving vehicles can perform lane-changing behaviour safely and efciently. If weaving lane-changing behaviour is unable to be carried out, the vehicle will still be able to perform lane-changing behaviour according to the Gipps lane-changing model. Also, the forced lane-changing mechanism is still applicable if necessary. Te fow chart of the control case is illustrated in Figure 5(b).

Tests for the Mixed Trafc State.
Due to the gradual increase of MPR of CAVs from 0% (base case) to 100% (control case) in the real world, it is expected in the near future that the mixed trafc fow, which consists of HDVs and CAVs at the same time, will dominate the roadway trafc for a relatively long period of time before the complete deployment of CAVs. Terefore, in order to further investigate the efectiveness of the proposed strategy under the mixed trafc state and compare its performance with the existing CAV lane-changing method, two sets of tests (benchmark and comparison tests) with six diferent MPRs (see Table 3) are carried out, under demand setting #6 (congested state). In the benchmark test, weaving CAVs perform the lane-changing behaviour in accordance with the lane-changing mechanisms of the control case in Figure 5(b), for which the proposed cooperative lanechanging strategy is applicable. In the comparison test, weaving CAVs perform lane-changing behaviour according to the cooperative lane-changing strategy proposed by Xue et al. [18]. In addition, HDVs in both tests perform the lanechanging behaviour according to the lane-changing mechanisms of the base case in Figure 5(a).
where δ j is the average delay in journey time per vehicle; T j is the average journey time per vehicle; and T j. exp is the expected journey time per vehicle (see equation (13)).
Ten, the delay improvement ratio (see equation (14)) is used to examine the reduction in average delay in journey time per vehicle of the control case relative to that of the base case under diferent demand settings. A larger delay improvement ratio indicates more efectiveness of the proposed strategy in improving the overall efciency of the weaving section.
where δ base j and δ control j are the average delays in journey time per vehicle for the base case and the control case, respectively.

Trafc Safety.
Te trafc safety in the weaving section is evaluated by the inverse time-to-collision [19] (see equation (15)), which indicates the risk of collision between the weaving vehicle and its current leading vehicle. When TTC − 1 is equal to 0, there is no collision risk. When TTC − 1 is greater than 0, the risk of collision increases as TTC − 1 increases. Since TTC − 1 of the individual vehicle may vary as the vehicle drives downstream in the weaving section, the maximum value of TTC − 1 of each vehicle within the time period that it spends driving in the weaving section is selected and used for the safety evaluation.
where TTC − 1 is the inverse time-to-collision; v SV and x SV are the speed and position of the weaving vehicle; and v LV and x LV are the speed and position of the leading vehicle. Table 1, the comfortable decelerating rate is set to be −3 m/s 2 , which means that a large decelerating rate surpassing −3 m/s 2 will make passenger uncomfortable. In this case, passenger's comfort can be evaluated by the ratio of large deceleration time (see equation (16)), which is defned as the total large deceleration time of an individual vehicle divided by its actual journey time. A smaller ratio of large deceleration time indicates a higher degree of passenger's comfort.

Passenger's Comfort. As seen in
where φ LDT is the ratio of large deceleration time of the individual vehicle; T LD is the total large deceleration time of the individual vehicle; and T j is the actual journey time of the individual vehicle.

Analysis and Discussion of Simulation Results
Te simulation results of performance indicators of operational efciency for the base case and the control case are listed in Table 4, and the average delays in journey time per vehicle for the base case and the control case, respectively, as well as the delay improvement ratios, under six diferent demand settings are plotted in Figure 6. It can be seen that compared with those in the base case, the average delays in journey time per vehicle in the control case are reduced under all six demand settings. Meanwhile, the delay improvement ratios increase as overall trafc fow rates in the weaving section increase from the free-fow state (demand setting #1) to the congested state (demand setting #6). Tis means that the application of the proposed cooperative lanechanging strategy can alleviate the delay in journey time and improve the trafc efciency in the weaving section in general. Also, the efectiveness of the proposed strategy in efciency improvement becomes greater as the trafc fow gets more congested.
In addition, as shown in Figure 6, the incremental trend of the delay improvement ratio is nonlinear. At low fow rates near the free fow, the delay improvement ratios stay low (under 5%) and increase slowly, whereas at high fow rates near congestion, the increments of delay improvement ratios are tremendous (24.8% at congestion), which means that the proposed strategy works much better at the high fow rate than the low fow rate. Figure 7 shows percentages of vehicles that make forced lane changes, against all lane-changing vehicles in the weaving section, under diferent demand settings, for the base case and the control case, respectively. It can be seen that compared with those in the base case, percentages of forced lane-changing vehicles in the control case are reduced       Tis also demonstrates why the proposed strategy is more efective near the congested state. Terefore, the proposed cooperative lane-changing strategy can be used as a good tool for the trafc fow optimization of weaving sections under congestion. Next, Tables 5 and 6 exhibit the simulation results of three categories of performance indicators of benchmark tests and comparison tests, respectively, for the mixed trafc state, under demand setting #6. Besides, the simulation results regarding performance indicators of operational efciency, trafc safety, and passenger's comfort for benchmark tests and comparison tests with diferent CAV MPRs are plotted in Figures 8-10, respectively.
First, it can be seen in Figure 8 that for both the benchmark and comparison tests, the average delay in journey time per vehicle gradually decreases as the CAV MPR increases, which leads to the gradual increase of the delay improvement ratio. However, it is noticed that under any CAV MPR, the average delay in journey time per vehicle of the benchmark test is smaller than that of the comparison test and the delay improvement ratio of the benchmark test is higher than that of the comparison test.
Second, it can be seen in Figure 9 that for the benchmark test, the average inverse time-to-collision per vehicle gradually decreases as the CAV MPR increases, which leads to the gradual increase of the average time-to-collision per vehicle. Quite oppositely, for the comparison test, the average inverse time-to-collision per vehicle gradually increases and the average time-to-collision per vehicle gradually decreases, as the CAV MPR increases. So, under any CAV MPR, the average inverse time-to-collision per vehicle of the benchmark test is smaller than that of the comparison test and the average time-to-collision per vehicle of the benchmark test is larger than that of the comparison test.
Tird, it can be seen in Figure 10 that for both the benchmark and comparison tests, the average ratio of large deceleration time per vehicle gradually decreases as the CAV MPR increases. In addition, it is noticed that under most CAV MPRs, the average ratio of large deceleration time per vehicle of the benchmark test is slightly higher than that of the comparison test, but the diference is quite insignifcant.
Te trends of simulation results of three categories of performance indicators illustrate that with the increasing MPR of CAVs, the application of the proposed cooperative lane-changing strategy can better alleviate the delay in journey time of vehicles, better reduce the collision risk of vehicles by increasing their collision time, and better reduce the average percentage of time, during which each vehicle spends undergoing large deceleration of its entire journey time. Terefore, for the mixed trafc state, the proposed cooperative lane-changing strategy shows decent potential in improving the operational efciency, trafc safety, and passenger's comfort in the weaving section. Besides,  compared with Xue's method, the proposed lane-changing strategy shows considerable superiority on maintaining operational efciency and trafc safety. However, the performance of the proposed strategy on facilitating passenger's comfort is a bit inferior to Xue's method.

Conclusion
By adopting the concept of CAV technologies, a cooperative lane-changing strategy at the microscopic level is proposed, which consists of an upper layer of decision making and a lower layer of control, in order to alleviate the lanechanging conficts between weaving vehicles in the weaving section of urban expressway. Te decision-making layer determines the lane-changing sequences of weaving vehicles based on their lane-changing advantages quantifed by a set of utility functions. Te control layer generates detailed instructions of speed adjustments and lane-changing manoeuvres for weaving vehicles.
A numerical simulation, which includes a base case and a control case, is conducted to verify the efectiveness of the proposed strategy under six diferent trafc demand settings, from the free-fow state to the congested state. In addition, benchmark and comparison tests with six diferent CAV MPRs are carried out under the congested demand setting to further verify the efectiveness of the proposed strategy for the mixed trafc state and compare its performance with the existing CAV lane-changing method. Tree categories of indicators, namely, operational efciency (delay improvement ratio), trafc safety (inverse time-to-collision), and passenger's comfort (ratio of large deceleration time), are used to examine the performance of the proposed strategy. Te simulation results show that the proposed strategy can efectively reduce the delay in journey time of vehicle driving through the weaving section, thus improving the operational efciency of the weaving section. Moreover, as the trafc fow gets more congested, the percentage of vehicles preferring the cooperative lane-changing behaviours becomes higher, which makes the efectiveness of the proposed strategy in efciency improvement become greater. Te simulation results of the benchmark and comparison tests further show that as the CAV MPRs increase, the proposed cooperative lane-changing strategy can better improve the operational efciency, trafc safety, and passenger's comfort in the weaving section for mixed trafc states, and its performance on maintaining operational efciency and trafc safety is superior than the existing CAV lane-changing method.
Overall, it is promising that under the CAV environment in the near future, the proposed cooperative lane-changing strategy can serve as a good method to deal with the problem of lane-changing conficts within the weaving section, thus enhancing the trafc management and control of urban expressway. For future works, it is suggested to validate the efectiveness of the proposed strategy in a more realistic environment, for which the discretionary lane-changing behaviour should be considered, and vehicles' information collected from the real world can be used for simulation as well.

Data Availability
Te Python data used to support the fndings of this study are available from the corresponding author upon request.

Conflicts of Interest
Te authors declare that they have no conficts of interest.