Eco-Speed Harmonization with Partially Connected and Automated Traffic at an Isolated Intersection

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Introduction
Greenhouse gas emissions are a worldwide issue that demands urgent attention.According to the International Energy Agency (IEA), the transport sector is responsible for 25-30% of a country's total carbon emissions [1].Among various modes of transportation, road transportation alone accounts for approximately 80% of emissions.Consequently, there is an urgent need for efective measures to curb emissions in road transportation.
Eco-driving technology is an important way to reduce emissions.Its main idea is to achieve emission reduction by decreasing stops of the vehicle at signalized intersections.Specifcally, it is realized by changing the speed of the vehicle to make it go through the intersection at green lights.In urban roads, there are many practical applications [2][3][4][5][6][7][8][9].Te ecological speed advice is sent to vehicles through the navigation application on the vehicle terminal.However, due to the driving randomness of human-driven vehicles (HVs), speed advice is not always strictly followed.Tis may lead to the stopping of vehicles at the intersection.Te beneft brought by eco-driving strategies would be impaired.
Fortunately, the emerging connected and automated vehicle (CAV) technologies bring possibilities to solve the issue of driving randomness.CAVs can precisely execute the suggested speed.Tis brings great potential to reduce greenhouse gas emissions at intersections.In the beginning, many studies have developed CAVs-based eco-approach strategies in pure connected and automated trafc [10][11][12][13][14][15][16].In these studies, the CAVs' advantage in precise execution is taken of.It achieves good performance on carbon emissions in pure connected and automated trafc.However, achieving a 100% market penetration rate (MPR) for CAVs is not expected until the 2060s [17].Tis implies that a mixed trafc environment consisting of both CAVs and HVs will exist for a long time.Terefore, it is crucial to develop eco-driving technologies that are compatible with partially connected and automated trafc.
Recently, many ecological driving strategies have been proposed for partially connected and automated trafc [18,19].Most of these strategies either focus on controlling one CAV under the infuence of the front HVs [14][15][16][17] or forming a platoon in mixed trafc [13,16,20].Te former desperates to control a CAV to catch the green lights.Te control trajectory integrates lane-changing and speedchanging.Te latter controls the platoon with a leading CAV.Both of them have shown their potential for carbon emissions.
However, the existing methods have limitations.
Firstly, the existing methods are weak in emission reduction assurance in various trafc demands.Day-to-day demand variations are common existence in the urban city.Most eco-driving strategies demonstrate good performance under limited conditions, such as conditions of low trafc saturation or demand level [16].Te performance under high demand levels cannot be assured.Tese ecological strategies primarily rely on the precise control of the trajectories of vehicles to achieve benefts.Te control strategy includes the change of speed and lane changes [21,22].However, ensuring the precise execution of vehicles in congested trafc conditions is challenging.Te imprecise control of vehicles would lead to poor performance of emission reduction.
Secondly, the existing methods overlook the need for mobility improvement while ensuring emission reduction.Te improvement of mobility at intersections is of great importance.Tis is because mobility is a key index for representing the service level of the trafc for the city.Improving mobility is a key goal for trafc management.However, the existing eco-approach methods are unable to balance the improvement of mobility and emission reduction.Tey are mainly focused on enhancing the beneft of some portion of vehicles.Tis may sometimes damage the beneft of the other surrounding vehicles [16,[23][24][25][26].In these studies, emission reduction is achieved by reducing the stops of controlled vehicles.Considering such a situation that the controlled vehicles conduct lane changes to go through the intersection, with the eco-driving control strategy, the controlled vehicle is able to catch the green light and avoid a stop.Tis is helpful for the mobility and emission reduction of the controlled vehicle.However, due to the frequent lane changes and speed changes of the controlled vehicle, other surrounding vehicles may sufer the beneft of loss of mobility and emission reduction.Terefore, the mobility of the entire trafc is hardly able to be ensured.
Tirdly, the existing eco-approach methods show a limitation at the early stage of CAV roll-out (with low MPR).In most of the existing methods, it requires CAVs to cut through trafc to form a platoon.Te requirements for platoon formation are strict.Each platoon is required to be led by a CAV.All CAVs must be positioned ahead of each HV within the platoon [27].However, under low MPR, platoon formation is not always achievable.Especially when CAVs are much less than HVs, it is of great difculty for CAVs to cut through trafc to form a platoon or become a leading vehicle of each platoon [25,28].Tis impedes the method in the practical application.In this situation, the beneft of emission reduction brought by CAVs is also impaired a lot.
Fourthly, the existing method applications are weak in practicality.Te limitation of the application lies in its high demand for computation power.Te solution of the ecodriving strategy requires a large amount of computational power.It includes multi-task solving: state prediction of surrounding vehicles, decision making, trajectory planning, and control [10,16,21,25,[29][30][31]. Due to the requirement for high-frequency updates on control information, each task solving consumes quite a lot of computational power.Although some studies develop a distributed solution to reduce the computational burden of the onboard unit [32], it is still cost-inefective to have an onboard unit providing such high computation resources.
Given the shortcomings of the existing eco-approach applications, this paper proposes an enhanced eco-approach method.It coordinates the optimization of signal and vehicles' speed under partially connected and automated trafc.It bears the following features: (i) Enhancing carbon emission reduction at various demand levels (ii) Improving mobility of entire trafc at intersection (iii) Enhancing carbon emission reduction with the help of a small portion of connected and automated vehicles (iv) Potential implementations in the near feature Tis paper is organized as follows.Section 2 presents the control mechanism.Section 3 presents the problem description.Section 4 presents the control methods, including trafc status prediction module, signal control module, and CAV speed harmonization module.Section 5 evaluates the performance of proposed method.Section 6 provides the conclusions and future works.

Control Mechanism
Te goal of the proposed controller is to reduce emissions for vehicles approaching an isolated signalized intersection.Te control strategy is able to balance the improvement of emission reduction and mobility of entire trafc at intersections.Tere are three highlights of this proposed controller.

Controlling the Entire Connected and Automated Trafc as a Whole.
To address the issue of the computation burden, the control object is transformed from individual CAVs to the entire connected and automated trafc as a whole.Te control variable is reduced to a one-dimension variable (desired speed of CAVs).Te dimension of the control variable is not increasing with the number of CAVs.Tis helps to avoid computing burden issues.

Cooperation of Demand Management and Signal Control.
Te proposed speed harmonization method aims to achieve a balance between demand and supply.Te demand control is to adjust fow through CAV speed harmonization.In the speed harmonization module, the desired speed for CAVs is 2 Journal of Advanced Transportation determined based on the signal status.Tis design aims to achieve an optimal match between the arrival demands and the signal status, ultimately reducing the average frequency of stops.Te supply control is the throughput adjustment by signal control.Te signal control module switches the signal control status based on the trafc fow state.It aims to ensure the maximum throughput at the intersection.

Problem Statements
Te studied scenario is an isolated signalized intersection, as shown in Figure 1.It is a typical 4-leg, 3-lane (in each direction) signalized intersection.Te three lanes serve diferent purposes: a through/left-turning lane, a through lane, and a through/right-turning lane.Te signal timing plan is predetermined and consists of either 2 or 4 signal phases.Te signal phases are not optimized variables.Each phase is divided into an efective green interval and a clearance time (including yellow and all-red time).Te clearance time is predesigned and fxed within the system.Te proposed method only modifes the green duration of each phase during the optimization process, without a fxed cycle duration.Te maximum and minimum green time schemes comply with standard signal design practices.
In this study, the scenario operates in a partially connected and automated trafc environment.Te vehicles in this scenario are CAVs and connected humandriving vehicles (CHVs).All vehicles have the ability to communicate with roadside units through Vehicle-to-Vehicle (V2V) and Vehicle-to-Infrastructure (V2I) technologies in real time.Tis means that the vehicles can obtain real-time signal timing information.Te roadside control center can obtain real-time vehicle status information (position, speed).Te control segment is from the upstream segment to the location before the forbidden Lane Changing Zone, which is usually a few hundred meters.In the control segment, CAVs are scattered among CHVs with no platoon formed.Desired speed commands are provided from a control center to CAVs with an update frequency of Δt.When CAVs travel on a road segment under control, all CAVs receive an identical desired speed command.

Methods
Tis section provides a detailed representation of the proposed method, including the control structure, signal control module, and CAV speed harmonization module.Te signal control module is adjusted according to the phantom density of the trafc.It is predesigned with an optimal signal timing confguration during time interval (m + 1).Details on the signal control method are presented in Section 4.4.
CAV speed harmonization module is adjusted according to the information of signal timing and phantom density.It calculates the desired speed for CAVs and outputs a series of control profles of CAVs.Te output information includes the future speed decision of CAVs.Te implementation of these control profles obeys a rolling-horizon rule.Only the frst step of the profles is executed by CAVs.
Te frst step of the control command is to output it for implementation by CAVs.Furthermore, it predicts the desired speed for CAVs during time interval (m + 2) and outputs it to the trafc status prediction module.Section 4.5 will present more detailed information on this process.Details on the CAV speed harmonization method are presented in Section 4.4.

Trafc Status Prediction Module.
Te trafc status is characterized by the density level.Te density is commonly utilized to describe the congestion level of trafc status.Some studies suggest that preventing the density from reaching the critical zone is crucial for efective control [33,34].Density serves as an important criterion for trafc control.Building upon this idea, the objective of the trafc status prediction module is to predict the density change.Tis forecasting holds signifcant value as it provides a realistic representation of the dynamic changes in road trafc conditions resulting from CAVs' speed change.Tat is, the proposed prediction model is actually to describe the change of density under the infuence of CAVs' speed change.Tis serves as the foundation for the design of the proposed strategy.
Te coordination between CAVs is infuenced by signal timing.During the red interval, CAVs slow down in advance to reduce the number of stops at intersections.During the green interval, CAVs operate at a maximum acceleration to catch the green light.Here the trafc status prediction model is piecewise based on the signal timing.Details are as follows.
(i) Situation 1: when it is during the red interval.
During the red interval, the speed of trafc fow changes due to CAVs' deceleration and Journal of Advanced Transportation   Te number of queued vehicles in the current lane pcu

N m
Te number of vehicles on the controlled road segment during time interval where  k d m+1 is the phantom density when CAVs are decelerating during update time interval +1.c m is the portion of vehicles under the infuence of CAVs' speed change at update time interval m. ξ m is the penetration rate of CAVs at update time interval m.When CAVs are more than HVs (ξ > 1/2), the movements of all HVs are enforced by CAVs' speed reduction, c � 1.Otherwise, only the movements of HVs that are right behind CAVs are infuenced, c � 2ξ.v m is the average speed of all vehicles at update time interval m. u m+1 is the desired speed of CAVs, the control vector at update time interval m + 1. l is the average length of vehicles.m is the index of the update time interval.t LC is average lane-changing duration.∆t is the update time interval.T is the length of time that the average speed approaches CAVs' desired speed.N m is the number of vehicles at update time interval m. t i m is the travel time of vehicle i on the control segment at update time interval m.L is the length of control segment.Note that the density  k m+1 in equation ( 1) is not actual conventional density.Instead, it is a new concept named phantom density.In terms of phantom density, it refers to the collective summation of both real vehicles and phantom vehicles traveling at a unit distance.Phantom vehicles are utilized to quantify not only occupancy caused by physical space taken by actual vehicles but also the additional occupancy caused by motions, such as slowing down and lane-changing.When vehicles are slowing down or lane-changing, the same number of vehicles occupies greater space.Te greater space occupied is as if there were more vehicles.Te derivation and proof of equation ( 1) have been achieved with a combination of multiple empirical observations and theories.Te conservation of vehicles is guaranteed.Te related work has been peer-reviewed and published in IEEE Transactions on Intelligent Transportation Systems [36].
(ii) Situation 2: when it is during the green interval.
During the green interval, the change of trafc fow is divided into two stages.Te frst stage is the early phase of the green signal, where CAVs accelerate to achieve the free-fow speed.Te second stage is when CAVs have completed acceleration, and the entire trafc fow reaches the free-fow speed.Te entire trafc fow is stable.Te general formulation of the phantom density is as follows:  Journal of Advanced Transportation where  k a m+1 is the phantom density when CAVs are accelerating during update time interval +1.Note that during this period, the density of trafc gradually decreases.It is similar to the impact of CAVs' speed reduction on density (as equation ( 1)).However, equation (3) does not take into account the scenario of CAVs' additional lane changes while accelerating.Tis is because during the red interval, vehicles have already formed a tight trafc fow, and there is no space for lane changes at the beginning of the green interval.

Signal Control Module.
Tis section provides a detailed introduction to the signal control mechanisms.It includes the signal control fow, signal control strategy, and signal switching criteria.

Signal Control Flow.
Te signal control module is to calculate the signal timing based on the predicted phantom density.Te phantom density is a criterion that determines whether to perform green light extension or phase switching.Te working principle of the signal control module is shown in Figure 4.
As shown in the fgure, the module frst fnds the green phase.Tis is done because the control strategy output by the signal control module relies on density evaluation during the green phase.If there is no green phase at the current time m (indicating a phase switch occurred at time interval m − 1), strategy C is executed.If the green phase is found, it is then determined whether a phase switching or an extension of the green time is required.Based on this determination, strategy A or strategy B is executed.

Signal Switching Criteria.
In order to ensure the smooth fow of trafc at intersections, signal switching is based on the maximum phase phantom density.Te defnition of maximum phase phantom density is as follows: where  k D m represents the phantom density of each phase.D represents the number of phases. k max represents the maximum phase phantom density.It serves as a critical parameter in determining the signal switching strategy.
Te signal is switched when the maximum phase phantom density is arrived at a threshold.Since the signal switching is mainly about green light extension or phase switching, the switching criteria are focused on the density during the green interval.Te proposed strategy gives priority to releasing phases with high phantom density.However, these phase switching criteria sometimes result in a waste of efective green time.To address this issue, a switching threshold, denoted as k M , has been introduced in the strategy.Te purpose of this threshold is to ensure the efciency of the entire trafc when a phase switch occurs.It is achieved by introducing a bufer density.
where k D m b is the bufer density for phase switching of the D phase at time interval m.T R m indicates the duration of the red interval during update time interval m.G min represents the minimum green time.Te update of bufer density k D m b is triggered when the duration of the red interval T R m equals G min .Tis value represents the density variation of the current phase within the minimum green time since the last switch from green to red.
Note that equation ( 5) ensures that the switching thresholds for each phase are diferent and constantly updated.Terefore, this ensures the adaptation of the switching thresholds to various trafc conditions.
Equation (6) ensures that the increase in density does not exceed the density diference between the green phase and the current red phase.Te conditions for triggering a phase switch will not be met again within the G min time.
In order to avoid phantom congestion in controlled sections, there should be where k C represents the critical density of the control segment.k G m is the density of the green phase at time interval m.
Before deciding on the signal control strategy for the next time window, it is also necessary to ensure that the green interval duration meets where G min represents the minimum green time.G max represents the maximum green time.(i) Signal control strategy A Strategy description: Te green signal phase will remain green in the next time window.Te other signal phases will remain red.Activated conditions: if equation ( 7) is satisfed.
(ii) Signal control strategy B Strategy description: the green signal phase will change to yellow in the next time window, while the other signal phases will remain green.Activated conditions: if equation ( 7) is not satisfed.(iii) Signal control strategy C Strategy description: in the next time window, the signal phase with the maximum density will be changed to green, while the other signal phases will be changed to red.Activated conditions: if there is no green phase at the current time m.
Note that in strategy C, there is currently no green signal phase.Tis means that strategy B was executed in the previous time window.
To facilitate its operations, the module utilizes a timer T G m , which records the duration of the current green interval.Every time the signal control module is activated, the timer is incremented by ∆t after the output is generated.When the phase changes to red, the timer is reset to zero and begins timing again.According to diferent strategies, the changes in the timer can be represented as follows:

Journal of Advanced Transportation
Te Workfow of CAV Speed Harmonization.Te workfow of the CAV speed harmonization module is shown in Figure 5. CAV speed harmonization module takes the signal timing information for update time interval m + 1 as input and generates the desired speed for CAVs at update time intervals (m + 1) and (m + 2) as output.In order to achieve this, it is necessary to predict the desired speed of CAVs at m + 1.However, due to computational constraints, the strategy employed for m + 1 will be extended to m + 2 for predicting the desired speed.In this paper, the speed harmonization strategy for CAVs is determined based on the signal strategy.It enables the coordination between the CAV speed harmonization strategy and signal control strategy.Based on the input of signal timing, the situation for CAV speed harmonization is divided into four scenarios, as shown in Figure 6.
As shown in the fgure, situation division for CAV speed harmonization consists of four scenarios: (1) green to green, (2) red to red, (3) green to yellow and yellow to red, and (4) red to green.Note that scenario 3 covers two cases.Te switching from green to yellow and subsequently to red represents a continuous change.Hence, the corresponding speed harmonization strategy remains consistent.
CAV Speed Harmonization Strategy.CAV speed harmonization strategy is proposed to adapt to the signal control situations.Te detailed strategies for various situations are as follows.

Speed Harmonization Strategy 1. Activated condition:
where the current phase and the next phase are green.
In this situation, the controller is infuenced by the queue state at the intersection.If there are queued vehicles ahead, the premature acceleration of vehicles may result in an increase in the average number of stops.Terefore, the controller will output acceleration commands only after the queued vehicles have dispersed.If there are no queued vehicles ahead, CAVs will begin accelerating until they reach the speed limit on the road.Tis helps to achieve maximum throughput while maintaining efciency.Te strategy is outlined as follows: where v D m represents the desired speed of CAVs in phase D during update time interval m. v rl represents the road limit speed.t s represents the start-up time of the last vehicle in the queue.
If the queue exists, it is necessary to determine the time when the last vehicle started.We assume that the relationship between trafc fow and density follows the triangular fundamental diagram [37].Te triangular fundamental diagram adopted is shown in Figure 7.
When the upstream density is greater than the downstream density, the dissipation speed of the rarefaction wave can be represented as −w.It is calculated as follows: Since vehicles are queued at the intersection during the red interval, the queue fow is with congested density k j .When the green interval begins, the frst vehicle starts accelerating, and the rarefaction wave begins propagating backward at a speed of w [38].When the rarefaction wave reaches the last queued vehicle, all queued vehicles have completed their start-up behavior.Te analysis of the rarefaction wave provides a theoretical basis for estimating the vehicle start-up time.Te estimation of the time t s when the last vehicle in the queue starts can be expressed as follows: where t s represents the start-up time of the last vehicle in the queue, N q represents the number of queued vehicles in the current lane, h s represents the average stopping distance of vehicles when queuing, and l is the average length of vehicles.

Speed Harmonization Strategy 2. Activated condition:
where the current phase and the next phase are red.In this situation, CAVs would slow down and form a tight queue of trafc fow.Te speed is calculated as follows: where ∆v D m max is the maximum speed change that satisfes equation ( 21) (defned on page 18).
To avoid collision risks created by the preceding CAVs decelerating, it is necessary to impose limitations on the behavior of CAVs' deceleration.Te minimum following distance of a vehicle is composed of three parts: the length of the preceding vehicle, the safety bufer zone, and the driver reaction time gap, as shown in Figure 8.
Te calculation of relevant parameters is as follows: where S min is the shortest following distance, τ is the driver's response time, usually taken between 0.3 s and 2 s, v a is the speed of the preceding vehicle, v b is the speed of the following car, ∆ safe is the safety bufer, v D m is the average speed of the vehicles in phase D during update time interval m, and H s is safe time headway.
In the context of this scenario, we assume that the preceding and following vehicles are moving at the same speed before CAVs conduct decelerating.In this case, the average speed change can be expressed as According to equations ( 16)-( 20), we can obtain Te deceleration of CAVs requires the constraint of speed variation and safety.Te constraint is as follows: where ∆v D m represents phase D during update time interval m. a min and a max are the thresholds for changes in speed.Tese thresholds are designed to prevent CAVs from being unable to efectively execute the desired speed.
According to safety constraints and speed change constraints, the maximum value of speed change can be obtained as follows.
Combining equations ( 19) and ( 20), the maximum value of speed change can be obtained as

Speed Harmonization Strategy 3. Activated condition:
where the current phase is green, but the next phase would switch to yellow.In this situation, CAVs start decelerating from the state of driving at the maximum speed limit.Similar to strategy 2, the desired speed for CAVs in the next time window is

Speed Harmonization Strategy 4. Activated condition:
where the current phase is red, but the next phase will switch to green.In this situation, the strategy should consider the time for vehicles' start-up.It needs to predict the start-up time of the trailing vehicle and deliver acceleration commands to the CAVs after its start-up.Te calculation of the start-up time t s for the trailing vehicle is given by equation (12).
Similar to strategy 1, once the last queued vehicle completes its start-up, the CAVs in the trafc fow would receive acceleration instructions.Te desired speed for CAVs is calculated as

Evaluation
Tis section evaluates the proposed strategy through microscopic simulation.Tis section presents the simulation platform, experimental design, and results.Te experimental design includes test scenarios, compared baseline, sensitivity analysis design, measurement of efectiveness (MOE), and result analysis.Trajectories of the simulated CAVs are validated with results of California Partners for Advanced Transportation Technology (PATH) from their feld experiment in terms of speed, acceleration, and time gap.Hence, the simulation platform has been validated with the capability of replicating the trafc with a mixture of advanced driver-assistance system-(ADAS-) equipped vehicles.Te work has been peer-reviewed and published in Transportation Research Part C [39].
Note that to simulate the phenomenon that CAVs cannot change to the speed delivered by the control center instantly, the speed command passed to the simulation platform is the desired speed of CAVs.Te actual speed of CAVs is calculated by the vehicle actuator.Note that the state-of-the-art strategy selected is based on their feasibility for near-future implementation.Te realtime adaptive signal control strategy is currently advanced technology that has been successfully applied in real-world intersections, making them a suitable reference method.Furthermore, the real-time adaptive control only adjusts the right of way, while the proposed strategy in this paper regulates both the right of way and trafc demand.Tis contrast between the two approaches provides an efective comparison.

Simulation Settings.
Te parameter settings in the simulation experiment are shown in Table 2.

Sensitivity Analysis. Sensitivity analysis of control
methods is conducted for diferent demand levels and MPRs of CAVs.Te demand level is quantifed by the V/C ratio (volume to capacity ratio).Te demand level varies from 0.3 to 0.9 by a 0.3 interval.It represents the low, medium, and high demand levels.Te MPR of CAVs is set as 10%, 30%, 50%, and 90%.

Measurement of Efectiveness.
To investigate the effectiveness of the proposed strategy, three measurements of efectiveness (MOEs) are adopted, including CO 2 emission, stop frequency, and throughput.Tey are utilized to quantify the performance of the proposed strategy in terms of ecology and mobility.
CO 2 emission and the vehicle stop frequency are utilized to measure the improvement of ecology environment.CO 2 emission is calculated using the VSP model [41,42].Te vehicle stop frequency is defned as the average number of stops of all vehicles.It is also utilized to prove the rationale behind the control mechanism (refer to Section 2).Te beneft brought by the proposed controller is the reduction of stops.Results confrmed that the proposed strategy can reduce emissions while maintaining throughput.Te advantages of the proposed strategy can be observed in emission reduction, throughput improvement, and reduction in average stop frequency.
Compared to the non-control base, the proposed approach can achieve a reduction in emissions ranging from 60.50% to 74.04%, an increase in throughput of at least 2.96%, and a decrease in the stop frequency up to 85.82%.Compared to the state-of-the-art strategy, the proposed approach can achieve a reduction in emissions ranging from 4% to 61%, an average increase in throughput of around 14.91%, and a decrease in the stop frequency ranging from 26% to 81%.It performs better at high demand levels.When V/C � 0.9, the strategy achieves a reduction in emissions ranging from 56% to 61% and an increase in throughput ranging from 37% to 46%.Additionally, it reduces the number of stops by 78% to 81%.

CO 2 Emissions
(1) Comparison against Non-Control Baseline.Figure 10 shows CO 2 emissions and benefts under various demand levels and MPRs of CAVs.Te proposed strategy demonstrates signifcant benefts at similar demand levels, with minimal fuctuations in benefts across diferent MPRs of CAVs.It can achieve a reduction in emissions ranging from 60.50% to 74.04%.Tis indicates that the method overcomes the existing system's dependence on high penetration rates of CAVs.Under the same MPR, the method achieves maximum benefts at the middle demand level (V/C � 0.6).Tis is because, at lower demand levels, the number of vehicles afected by CAVs' deceleration is limited, resulting in some CHVs waiting at intersections.However, the proposed strategy at higher demand levels aims to prevent trafc congestion during red intervals, leading to a reduction in CAVs' deceleration behavior.Tis sacrifce in optimization performance is made to ensure trafc fow stability.
(2) Compared with State-of-the-Art Strategy.Figure 11 shows the comparison between the proposed strategy and state-ofthe-art strategy in CO 2 emissions.Compared to the state-ofthe-art strategy, the proposed strategy can reduce emissions by 31% to 61% under medium to high demand levels (V/ C � 0.6 and V/C � 0.9), and the performance is superior to the existing studies (10%∼41%) [25,43].At low demand levels (V/C � 0.3), the strategy can reduce CO 2 emissions by 4% to 16%, with fewer benefts compared to high demand levels.Tis is because, in low demand levels, fewer vehicles need to stop and wait, resulting in limited optimization benefts.

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Journal of Advanced Transportation

Mobility
(1) Comparison against the Non-Control Baseline.Figure 12 shows the average throughput benefts under various demand levels and MPRs of CAVs.Te proposed strategy can achieve an improvement in throughput ranging from 2.96% to 96.69%.Te proposed strategy is benefcial across different demand levels.As demand levels increase, the benefts of the strategies also increase gradually.Te strategies proposed at moderate demand levels and high demand levels (V/C � 0.6 and V/C � 0.9) demonstrate consistent performance across various MPRs of CAVs.Additionally, this demonstrates that the method can ensure throughput at intersections while reducing emissions.
(2) Compared with State-of-the-Art Strategy.Figure 13 shows the comparison between the proposed strategy and the stateof-the-art strategy in average throughput.Compared to the state-of-the-art strategy, the proposed strategy can improve average throughput by around 14.91%.In low demand levels, the efectiveness of both methods is nearly the same.As demand levels increase, the advantages of the proposed strategies gradually become more pronounced.At high demand levels, the throughput is increased by 36% to 46%       Journal of Advanced Transportation compared to the state-of-the-art strategy method.Tis makes sense because non-congested roads can easily handle all vehicles, so there is little room for throughput improvement.

Te Vehicle Stop Frequency
(1) Comparison against the Non-Control Baseline.Figure 14 shows the stop frequency benefts under various demand levels and MPRs of CAVs.Te proposed strategy can achieve a reduction in stop frequency ranging from 32.23% to 85.82%.Te proposed strategy demonstrates signifcant advantages in reducing stop frequency across various demand levels.Te average stop frequency ranges between 0.51 and 0.61 in low congestion and moderate demand levels, which validates the efectiveness of the approach.In moderate and high demand levels, the average parking frequency benefts is reduced by at least 81%.Te proposed strategy shows no signifcant fuctuations across diferent MPRs of CAVs, thereby proving the feasibility of controlling the trafc fow through a small number of CAVs.It is worth mentioning that the average stop frequency of the proposed strategy is less than 1, which means most vehicles are able to travel through the intersection without stopping.
(2) Compared with State-of-the-Art Strategy.Figure 15 shows the comparison between the proposed strategy and the stateof-the-art strategy in average stop frequency.Compared to the state-of-the-art strategy, the proposed strategy can reduce stop frequency from 26% to 81%.Te reason for the signifcant optimization results is that the proposed strategy coordinates signal timing with CAVs' speed harmonization.
As the saturation levels increase, the advantages of this method become more pronounced.When V/C � 0.9, the benefts of the strategy reach 78% to 81%.Te strategy's performance remains stable across diferent MPRs of CAVs.
By combining the analysis in Sections 5.3.1 and 5.3.2, it can be observed that the main reason for the improvement in trafc efciency and emission reduction lies in the signifcant reduction in stop frequency.Since the start-stop behavior of vehicles is closely related to intersection efciency and emissions, reducing the number of parking instances improves the efective utilization of green lights at intersections and directly reduces additional greenhouse gas emissions.

Conclusions and Future Research
Tis study proposes an eco-speed harmonization method for partially connected and automated trafc.Te strategy is able to achieve emission reduction and improve mobility under diferent trafc conditions.It also has potential implementations in the near future (at the early stage where CAVs' MPR is low).To evaluate the proposed controller, a VISSIM-based microscopic simulation evaluation was conducted.Sensitivity analysis was performed for CAV MPR and demand level (V/C ratio).Te evaluation shows the following: (i) Te proposed approach can achieve a reduction in emissions ranging from 4% to 61%, an average increase in throughput of around 14.91%, and a decrease in the stop frequency ranging from 26% to 81%.(ii) Under various MPRs of CAVs, the proposed strategy demonstrates stable optimization efects.
No signifcant fuctuations in the optimization effects have been observed with changes in MPR.Tis indicates the advantages of controlling the entire connected and automated trafc as a whole.(iii) Under diferent demand levels, the benefts of the proposed strategy increase as the demand level rises.It means that the proposed strategy performs better at a high demand level.When V/C � 0.9, compared to the state-of-the-art strategy, the proposed strategy achieves a reduction in emissions ranging from

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Journal of Advanced Transportation 56% to 61%, an increase in throughput ranging from 37% to 46%, and a decrease in the stop frequency ranging from 78% to 81%.(iv) Under varying MPRs and demand levels, the proposed strategy consistently demonstrates a superior performance regarding the average number of stops, which is consistently below 1. Tis indicates that the majority of vehicles can pass through the intersection without having to stop.
It is worth noting that the proposed method is a general eco-approach for controlling partially connected and automated trafc at intersections.It can be extended to dynamic green wave scenarios.In future research, the coordination of signals across multiple intersections could be considered, potentially leading to further reductions in trafc emissions.Furthermore, drawing inspiration from existing methods for eco-driving with CAVs, incorporating varying recommended speeds based on vehicle positions within the trafc fow could be explored, potentially aiding in the enhancement of the method.

Figure 3 :
Figure 3: Te sketch map of the phantom vehicles.

4. 4 . 3 .
Signal Control Strategy.Considering the potential situations like green interval extension and phase switch, three strategies are proposed.Strategies A and B are set at the green phase.Strategy C addresses the situation of the yellow signal phase (when none of the phases are green).Tis design simplifes the execution of signal timing for each phase.Details are as follows.

5. 2 . 1 .
Testbed.Te testbed of the simulation experiment is constructed based on a real intersection.Te intersection is located in Yizhang, Beijing.Te structure of the studied intersection is shown in Figure9.Te signal timing of the intersection is shown in Figure9(c).5.2.2.Tested Scenarios.Tree scenarios considering various compositions of vehicles and signal control schemes are tested: (i) Non-control (base): In this scenario, there is no optimization of vehicles' speed and signal control schemes.All vehicles are CHVs.Tere is no speed advice for CHVs.Te signal control scheme operates on fxed predetermined signal timings.It is a base to illustrate the necessity of optimization.(ii) State-of-the-art strategy: In this scenario, general trafc is composed of CAVs and CHVs.Te signal controller and vehicles can transmit information, which allows intersections to optimize signal timing Journal of Advanced Transportation based on the arrival of vehicles.Te signal timing optimization method adopted refers to a real-time adaptive trafc control algorithm by utilizing data from connected vehicles [40].(iii) Te proposed strategy: In this scenario, general trafc is composed of CAVs and CHVs.All CAVs are controlled by the proposed speed harmonization controller.

Figure 9 :
Figure 9: Te studied scenario: (a) bird view of the intersection, (b) intersection built in simulation, and (c) initial signal phase information.
Reduction While Improving Mobility.By introducing a trafc status prediction model, the impact of speed harmonization strategy on the mobility of the entire trafc is considered in advance.Te prediction model is developed based on "phantom density" (defned on page 8).Te phantom density describes how the density changes with CAVs' desired speed over time.It reveals the current infuence of CAVs' desired speed on future trafc states.Te signal lights prioritize the release of phase with a high phantom density as it indicates a high trafc demand and tightly formed trafc fow.Tis design helps to reduce emissions and maximize the mobility of the entire trafc by reducing vehicle stops.

Table 1 :
Notations and parameters.Te average speed change for CAVs in phase D during the update time interval m