Research on the Platoon Speed Guidance Strategy at Signalized Intersections in the Connected Vehicle Environment

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Introduction
As an important node of the urban road network, intersections are the key to causing urban road trafc congestion [1]. At the intersection, the trafc fow from all directions converges here, which can easily cause trafc congestion [2]. At the same time, intersection signals will also block the trafc fow, and the resulting delays will sometimes afect the road or even the running state of the road network in the surrounding area [3]. In order to alleviate the problem of trafc congestion at intersections, conventional measures such as road widening, canalization, and construction have been adopted [4]. However, due to problem of intersection congestion [9,17,18]. CVs can obtain information including the queuing status of intersections and the status of signal control facilities through V2I and can also obtain information such as the position and speed of surrounding vehicles through V2V. Tese technologies provide the possibility for speed guidance. Te vehicle can adjust the speed in advance through the speed guidance and pass the intersection at the optimized speed, which can reduce the unnecessary queue and stop. Speed guidance can be optimized for diferent objectives, such as safety, fuel economy, and trafc efciency [19]. In the CV environment, it is easier for vehicles to form a platoon, and it is more common for vehicles to travel in a platoon [20][21][22][23]. In this context, this paper proposes a platoon speed guidance strategy at signalized intersections, which enables platoons to pass through the intersection with the minimum delay and fuel consumption, considering the impact of queuing vehicles at intersections. Te contributions of this paper are mainly related to the following four aspects: (1) A platoon speed guidance strategy considering the infuence of the queue at signalized intersections in the CV environment is proposed, including constant speed guidance, deceleration guidance, acceleration guidance, and stop guidance. (2) Te optimal speed calculation method is given for the platoon speed guidance strategy, which includes calculation of the platoon's passable period and its maximum number of vehicles that can pass, platoon restructure, and optimization of the trajectory of the leading vehicle and the following vehicles. (3) Te platoon speed guidance strategy and method are simulated, and the results show that the proposed strategy can efectively reduce platoon fuel consumption and delay and smooth the trafc oscillation. (4) Te infuence of the CVs' penetration rate on the proposed strategy is discussed. Te simulation results show that the platoon speed guidance strategy can reduce the delay and fuel consumption under mixed trafc fow, and the higher the penetration rate, the better the efect.
Te rest of this paper is organized as follows. Section 2 briefy introduces the existing related studies. Section 3 proposes the platoon speed guidance strategy. In Section 4, we present a method to obtain the optimal speed. Section 5 presents the simulation analysis. Section 6 analyzes infuences of diferent queue lengths and penetration rates on the strategy, and the conclusion and future prospects are in Section 7.

Literature Review
Vehicle speed guidance at an intersection is an important means to optimize intersection trafc, and many works have been achieved.
In terms of speed guidance at unsignalized intersections, Lee and Park [24] proposed a cooperative vehicle intersection control algorithm to control the movement of a single vehicle so vehicles can safely pass through the intersection. Te results show that the algorithm improves the intersection performance. Chai et al. [25] proposed a slot preassigning method. When vehicles enter the statusadjusting area, the management center begins to calculate the target status and generate suggestions. Simulation results show that the proposed method performs better than signalbased intersections. Zhao and Li [26] proposed a carfollowing model to explore the impact of V2V communication on driving behavior with two cross-fows. Te results show that by extending the guidance space range and increasing the maximum speed limit, the beneft of the guidance strategy can be improved, and it is more suitable for medium-low trafc density and small safe separation conditions. Chen and Liu [27] proposed a gap-based automatic speed control algorithm for eco-driving. Te algorithm considers acceptable clearance as green time and unacceptable clearance and vehicle length as red time. Te results show that the proposed algorithm can efectively prevent conficts while minimizing vehicle fuel consumption, travel time, and emissions. Huang et al. [28] proposed a guidance strategy and built a simplifed iterative behavior model to predict the behavior of potentially conficting vehicles. Te results show that the guidance strategy can efectively improve the safety and efciency of drivers passing through the intersection at diferent compliance rates. Bifulco et al. [29] proposed a novel cooperative fullydistributed control algorithm for connected automated vehicles (CAVs), considering the safe crossing problem of an unsignalized intersection for mixed trafc fows. Te simulation results show that, the proposed algorithm can strongly improve the safety and mobility performances of the intersection.
In terms of speed guidance at signalized intersections, Chen [30] developed an eco-driving optimization model to analyze the optimal eco-driving trajectory of vehicles. Te results show that eco-driving can reduce substantial emissions without signifcantly increasing driving time. Chen et al. [31] proposed a dynamic eco-driving speed guidance strategy, aiming to optimize the fuel consumption emission curve of vehicles approaching signalized intersections. Te results showed that the strategy signifcantly reduced the number of stops, reducing fuel consumption and emissions. Liu et al. [32] proposed a speed guidance model that considers the mixed trafc fow of electric vehicles and diesel vehicles to achieve the goals of reducing travel delays and reducing emissions and energy consumption. Te results show that the proposed model has good performance, and increasing the proportion of electric vehicles can reduce energy consumption and emissions. Wang et al. [33] proposed a speed guidance model under the green light phase. Te results show that there is a signifcant diference in the time interval distribution with and without speed guidance, and speed guidance can improve the coordination of time interval without reducing the travel efciency. Tang et al. [34] proposed a speed guidance model to explore the impact of driver's bounded rationality on vehicle fuel consumption and emissions during the entire process of vehicles passing through signalized intersections. Te results show that the driver's bounded rationality has a signifcant impact on the vehicle's fuel consumption and emissions, but its impact directly depends on the parameters of the driver's bounded rationality. Wang et al. [35] proposed a speed guidance model to provide diferent guidance strategies for diferent signal phases and timings. Simulation results show that the proposed model can reduce delays, total stop time, and number of stops, and improve trafc efciency at intersections. Yao et al. [36] proposed a trajectory smoothing method based on a single variable speed limit and position optimization, which makes the trajectory of each approaching vehicle run smoothly without stopping according to real-time trafc demand and signal timing information. Te results show that this method can improve trafc efciency and reduce fuel consumption. Ci et al. [37] proposed a V2I-based car-following model at signalized intersections, which considered the impact of V2I on intelligent vehicle operation on the basis of the full velocity diference (FVD) model. Simulation results show that the model can better refect the impact of V2I on vehicle operation at intersections. Ding et al. [38] proposed a comprehensive platoon formation and trajectory optimization method for low-visibility environments. Te simulation results show that the proposed method can avoid overlapping vehicle trajectories and reduce delays. Sun et al. [39] proposed a speed guidance model for buses to improve the level of bus service and maintain a stable headway. Te simulation results show that the variance coefcient of headway and the average waiting time are signifcantly reduced. Wu et al. [40] proposed an integrated control strategy for transit signal priority and speed guidance in the CV environment. Te simulation results show that the strategy reduces the delay of the bus and improves the punctuality of the bus. Liang and Wei [41] proposed a single-intersection bus speed guidance and signal priority control method, and the simulation results show that this method can reduce the average passenger delay. Namazi and Taghavipour [42] proposed a speed guidance method under the CV environment. Combined with real data, the simulation results show that the proposed method can reduce waiting time, fuel consumption, and emissions. Mintsis et al. [43] proposed an enhanced velocity planning algorithm. Simulation results show that the algorithm can reduce CO 2 emissions and improve the comfort and safety of speed recommendations. Wu et al. [44] proposed a cooperative hierarchical eco-driving strategy for CAV platoons that combine the advantages of hierarchical driving techniques and platoon control through an efcient hierarchical framework. Simulation results show that the strategy has good adaptability under random trafc signals and vehicle states, reduces delays through intersections, and improves energy economy.
Furthermore, since the driving behavior of the preceding vehicle afects the following vehicle, the efect of speed guidance for a single vehicle at an intersection is limited, and some scholars began to research on the multiple vehicle speed guidance. Wu et al. [45] proposed a multivehicle speed guidance strategy at signalized intersections. Compared with the single-vehicle speed guidance strategy, multivehicle guidance can signifcantly reduce delay and stop times and improve trafc control efciency. Liu et al. [46] proposed a multivehicle speed guidance strategy in the CV environment with the optimization objective of minimizing travel time. And the research results show that a multivehicle speed guidance strategy can signifcantly improve the trafc efciency of intersections and is more efective than a single one.
On the basis of multivehicle guidance at intersections, some scholars have begun to study platoon speed guidance. Chen et al. [47] proposed an eco-driving speed control algorithm suitable for platoons at signalized intersections. Te results show that when the platoon needs to accelerate through the intersection, a smaller headway leads to less fuel consumption, and if it needs to slow down, a smaller headway results in more fuel consumption. Wu et al. [48] proposed an improved cooperative eco-driving model for platoons passing two consecutive trafc signals at green time. Simulation results show that the proposed model saves fuel signifcantly. Yu et al. [49] proposed a consistent optimal speed advisory model for platoons with unconnected vehicles mixed in signal intersections. Numerical results show that the proposed model can improve the safety and fuel economy of mixed trafc fows. Wang et al. [50] proposed a joint control model that simultaneously optimizes the speed of CVs and coordinates signals along the arterial line. Experiments show that the model can reduce delays and eliminate platoon queues. Ye et al. [51] proposed a signalized intersection optimization model based on the vehicle platoon guidance strategy. Te results show that it has signifcant fuel-saving potential without increasing travel time. Wang et al. [52] proposed a multi-priority control method for CV platoon trajectories, which assigns diferent priorities to throughput, efciency, and fuel consumption emissions. Te results show that the method can signifcantly improve trafc and energy efciency while ensuring the safety of connected and autonomous vehicles at urban signalized intersections. Chen et al. [53] proposed the concept of a "1 + n" mixed platoon, consisting of a leading CAV and n following human-driven vehicles, and formulated a platoonbased optimal control framework for CAV control at signalized intersections. Te results show that mixed platoon control has greater advantages compared to the traditional trajectory optimization approach for a single CAV. Chen et al. [54] proposed a hierarchical eco-driving control strategy for a hybrid platoon of CAVs and human-driven vehicles (HDVs), which minimizes fuel consumption in trajectory optimization and considers the time-varying powertrain efciency of hybrid vehicles to improve the energy economy at signalized intersections. Simulation results show that the strategy can improve fuel economy. Liu et al. [55] proposed a joint control method to simultaneously optimize intersection trafc signals and CAV platoon trajectories by optimizing signal phase length and acceleration to maximize comfort and minimize delays during the signal cycle. Simulation results show that the method has advantages in terms of delay, fuel consumption, and throughput compared to the control of a two-level structure. Ma et al. [56] proposed the ecological cooperative adaptive cruise Journal of Advanced Transportation control (Eco-CACC) to minimize the energy consumption of the CAV platoon. Te results show that the proposed strategy enhances the energy economy.
In summary, scholars have conducted extensive research on the speed guidance at intersections, including speed guidance at diferent types of intersections, single vehicle speed guidance, multiple vehicle speed guidance, and platoon speed guidance, and have achieved a series of results. However, most of them do not consider the impact of queuing vehicles at intersections, and the platoons use a fxed headway. In the CV environment, the headway in the platoon can be changed, and reducing the headway can improve the trafc efciency [57]. Based on this, the paper proposes a platoon speed guidance strategy at signalized intersections in the CV environment to reduce the delay and fuel consumption. Te strategy considers the infuence of queuing vehicles at intersections and sets diferent headways to improve the passing efciency.

Platoon Speed Guidance Strategy
In order to realize the speed guidance for platoons entering the intersection, the guidance area is set based on the V2I communication distance. Te roadside unit (RSU) that realizes real-time information exchange with CVs has been widely used in urban intersections [58]. RSU can obtain realtime platoon information, such as speed, acceleration, position, etc., as well as queuing platoon information and signal phase and timing (SPaT) information. Te RSU can transmit the acquired information to the cloud control center. Te cloud control center calculates the optimal platoon speed guidance strategy by analyzing the acquired information and transmiting it to the platoon. Te platoon changes its driving speed according to the strategy and passes the intersection. Taking a straight lane at an intersection as an example, the schematic diagram of the platoon speed guidance is shown in Figure 1.
In the process of platoon speed guidance, the efects of longitudinal trafc on the strategy are focused on, and some assumptions are made: (a) the driver is completely obedient to the guidance; (b) conficting trafc at intersections is ignored [59]; (c) message transfer delays and strategy calculation times are ignored.
We frstly calculate the passable period [t in , t out ] for platoons according to the phase information of signal lights, the passing time of the queuing platoon, and the entering speed of the incoming platoon. Te guided platoon can pass the intersection within the passable period. Ten, calculate n max , the maximum number of vehicles that can pass through the intersection in the period. If the length of the platoon is not greater than n max , the whole platoon will be guided through the intersection; otherwise, the platoon cannot pass through the intersection and must be guided to restructure. Vehicles that can pass are organized into one platoon, the others which cannot pass are organized into another platoon, called the frst incoming platoon and the second incoming platoon, respectively.
Since the entry speed v r , the length of the platoon n, and the phase of the signal lights are all random when the platoon reaches the guidance area, in order to make the platoon pass the intersection more efciently, four diferent platoon guidance strategies are designed.
(1) Constant speed guidance strategy If the whole platoon can pass the intersection in the passable period at the speed v r , then guide the platoon to drive at v r . (2) Deceleration guidance strategy If the platoon travels at speed v r will lead the platoon though before t in , then calculate the optimal deceleration and guide the platoon to decelerate according to the optimal deceleration. (3) Accelerate the guidance strategy If the platoon drives at speed v r will lead the last vehicle of the platoon cannot pass before t out , then calculate the optimal acceleration, and guide the platoon to accelerate according to the optimal acceleration. (4) Stop guidance strategy.
When the platoon neither through the intersection after t in by deceleration nor through the intersection before t out by acceleration, then calculate the optimal deceleration and guide the platoon to stop according to the optimal deceleration.
After the platoon speed guidance strategy is determined, the driving trajectory of the platoon is calculated. Finally, according to the trajectory optimization model, the optimal trajectory can be obtained, and thus the optimal guidance speed is obtained. Te process of the platoon speed guidance is shown in Figure 2

Calculation of the Passable Period [t in , t out ].
Te passable period can be calculated by the entry speed, the SPaT, and the time of the queuing platoon to pass through the intersection. According to these parameters, a schematic diagram of the passable period can be obtained, as shown in Figure 3.
In Figure 3, t cg is the length of time from the platoon entry time to the start time of the nearest green light time, which can be a negative number. t arr is the shortest time for the leading vehicle of the platoon to pass through the intersection, which accelerates to the maximum speed with the maximum acceleration. t wp is the length of time for the last vehicle of the queuing platoon to through the intersection. t safe is the safe headway between the incoming platoon and the queuing platoon.
According to Figure 3, the passable period start time t in can be obtained, and its calculation formula is as follows: where T is the signal period and t green is the green time.

Journal of Advanced Transportation
Te calculation formula of t arr is as follows: where S lead is the distance from the stop line to the guidance boundary, v max is the maximum speed of the vehicle, and a max is the maximum acceleration of the vehicle. Te calculation of the end time t out is as follows:

Journal of Advanced Transportation
where t red is the red time.

4.2.
Calculation of n max . n max refers to the maximum number of vehicles that can pass through the intersection within [t in , t out ], which is determined by the length of the passable period and the headway of the platoon. Te headway may not be consistent due to the driver's factors, but CV provides support for the consistency of the headway. In the CV environment, the following vehicle can respond faster to the behavior of the front one, so the headway can be reduced.
Reducing the headway can increase the number of passable vehicles in the platoon. Assuming that the minimum headway of the platoon is h t min , so n max can be obtained as follows:

Platoon Restructure Method.
If n > n max , the platoon cannot completely pass through the intersection, and it needs to be reformed. Te frst n max vehicles are organized into a new platoon, which is the frst incoming platoon, and its headway is adjusted to h t min . Te n max + 1 th vehicle and vehicles behind are organized into another platoon, which is the second incoming platoon. Else, the platoon adjusts the headway according to n, which is assumed as h t . If t out − t in /h t < n < n max , the platoon travels at h t min to ensure that all vehicles can pass through the intersection, else the platoon travels at h t to reduce the fuel consumption.

Analysis of the Leading Vehicle Trajectory.
Since the behavior of the leading vehicle in the platoon will afect the following ones, the driving trajectory of the leading vehicle is calculated frst. Diferent trajectories can be formed for the leading vehicle with diferent guided speeds, so we need to get the trajectories of the leading vehicle that can pass the intersection with the guidance. Te calculation methods for the leading vehicle trajectory under diferent platoon guidance strategies are as follows: (1) Constant speed strategy Set S last be the distance from the tail of the platoon to the stop line. When v r × t in ≤ S lead and v r × t out ≥ S last , the platoon driving at v r can make the whole platoon pass the intersection within the passable period. In this case, the leading vehicle is guided to drive at a constant speed v r by using the constant speed guidance strategy. Te leading vehicle trajectory constraint is as follows: (2) Deceleration guidance strategy ) > S lead , the leading vehicle can pass through the intersection before t in by entry speed v r , and also can drive with a speed not less than v min to through the intersection after t in . In this case, the leading vehicle needs to use the deceleration guidance strategy. If there is no queuing vehicle ahead, frst, we guide the leading vehicle to decelerate to the guidance speed v G with the guidance deceleration a G1 and then travel through the intersection with v G . At this situation, the leading vehicle trajectory needs to meet the following constraints: where a min is the minimum acceleration. If there is a queued vehicle ahead, frst, we guide the leading vehicle to slow down to ensure that it can cross the intersection within the passable period, and then travel at a constant speed. After that, an acceleration process is added before the leading vehicle passes through the intersection in order to reduce the trafc oscillation of the platoon merging into the queuing platoon. Te speed of the last queue vehicle in queue through the intersection is used as the target speed for the acceleration process, which is set as v wp .
In the above process, set the guidance deceleration as a G1 , the guidance acceleration as a G2 , and the guidance constant speed as v G . At this situation, the leading vehicle trajectory needs to meet the following constraints: (3) Acceleration guidance strategy ) < S last , the leading vehicle can pass through the intersection but the last one cannot. In this case, the leading vehicle needs to use the acceleration guidance strategy. If there is no queuing vehicle ahead, frst guide the leading vehicle to accelerate to the guidance speed v G with the guidance acceleration a G1 , then travel through the intersection with v G . At this situation, the leading vehicle trajectory needs to meet the following constraints: If there are vehicles queuing up ahead, frst guide the leading vehicle to accelerate to ensure that the leading vehicle can cross the intersection within the passable period, then travel at a constant speed. After that, as the deceleration guidance strategy, a deceleration process is added before the leading vehicle passes through the intersection. Te speed of the last queue vehicle in queue through the intersection is used as the target speed for the acceleration process, which is set as v wp . In the above process, set the guidance acceleration as a G1 , the guidance deceleration as a G2 , and the guidance constant speed as v G . At this situation, the leading vehicle trajectory needs to meet the following constraints: Journal of Advanced Transportation ) > S lead , the leading vehicle of the platoon cannot decelerate through the intersection at a speed greater than v min . In order to reduce the idling time of the platoon, guide the vehicle to stop with a constant guidance deceleration a G . At this situation, the leading vehicle trajectory needs to meet the following constraint: where S stop is the distance from leading vehicle to the stop position. If there is no queued vehicle, it is the distance to the stop line, else is the distance to the position h 0 behind the last queued vehicle.

Analysis of the Trajectory of the following Vehicle.
After the trajectory of the leading vehicle is obtained, the trajectory of the following vehicle can be calculated using the car-following model. Since the speed of the preceding vehicle can be obtained in real time in CV environment, we chose the FVD model [60] to analyze the trajectory of the following vehicles, and its formula is as follows: where ∆x i (t) is the headway between the i th vehicle and the preceding vehicle at time t, i � 2, 3, . . . N; v n (t) is the speed of the n th vehicle at time t; α is the sensitivity; and β is the speed diference coefcient. Te values of α and β are as follows: V(∆x n (t)) is the optimal speed of the n th vehicle, and its formula is as follows: where h c is the headway of the platoon. Te set of trajectories of the leading vehicle obtained needs to meet the requirement that the following vehicles pass through the intersection before t out , and its formula is as follows: where v i t is the speed of the i th vehicle at time t and S i is the distance from the i th vehicle to the stop line.
According to formula (14), the trajectories of the whole platoon are obtained, which is set as M.
4.6. Calculation of the Optimal Trajectory. Te delay and fuel consumption are used as indicators to optimize the platoon trajectory. Te calculation of fuel consumption and delay for each vehicle trajectory is as follows.
(1) Delay Te delay of a vehicle is the diference between the time it takes to pass the intersection after guidance and the time it takes to pass at v max . Te total delay of the platoon is calculated as follows: where t m d is the total delay of the m th trajectory, m ∈ M; t m,i pass is the time for the i th vehicle to pass the intersection under the m th trajectory, and t m,i free is the time for the i th vehicle to pass through the intersection at v max under the m th trajectory.
(2) Fuel consumption Te VT-micro model [61] is used to calculate the fuel consumption, and the formula is as follows: where MOE e is the instantaneous fuel consumption of the vehicle, L/s; L e i,j is the coefcient during acceleration when the powers of speed and acceleration are i and j, and M e i,j is the coefcient during deceleration when the powers of speed and acceleration are i and j. Te fuel consumption of the whole platoon is the sum of the fuel consumption of each vehicle from the moment of guidance to the moment of passing intersection. Te formula is as follows: where f m pass is the total fuel consumption of the m th trajectory.
(3) Optimization model considering fuel consumption and delay According to formula (15) and (17), a trajectory optimization model with the goal of minimizing the sum of the fuel consumption and delay of the platoon is established, and the formula is as follows: where f i free is the fuel consumption of the i th vehicle driving with v max .

Simulation Analysis
MATLAB is used to build the simulation scenes, and the proposed strategy is simulated, in which the genetic algorithm is used to solve the optimization model. Since the speed under constant speed strategy is not changed, we only simulate the scenarios under a deceleration guidance strategy, acceleration guidance strategy, and stop guidance strategy. Te simulation scene is set to a straight lane at a signalized intersection, the boundary of the guidance area is set to be 300 m away from the stop line, the signal light cycle is 60 s, the yellow light time is ignored, and the red time t red and green time t green are both set to 30 s. Te relevant parameters are shown in Table 1.

Simulation of Deceleration Guidance Strategy.
According to whether there are queued vehicles at the intersection when the platoon enters the guidance area, the simulation of the deceleration guidance strategy is divided into two scenarios, namely, scenario A1 and scenario A2. In scenario A1, there are no queued vehicles at the intersection, while in scenario A2 there are queued vehicles. Furthermore, in order to analyze the infuence of the headway adjustment on the incoming platoon, the simulation is also carried out for the scene where the length of the incoming platoon is n max , for which when there are queued vehicles the scenario is set as scenario A3. In these three scenarios, the deceleration guidance strategy is simulated. Trajectories and velocities of the platoon are obtained, as shown in Figures 4-6. At the same time, the fuel consumption, travel time, and delay of the platoon are obtained, as shown in Figures 7-9. In addition, in order to verify the efectiveness of the deceleration guidance strategy, the simulation results of three scenarios without guidance are added in Figures 4-9. Improvements in fuel consumption, driving time, and delays in the deceleration guidance strategy are shown in Table 2.
It can be seen from Figures 4(a) and 4(c) that the guided platoon does not stop at the intersection, while the unguided platoon stops at the intersection. It can be seen from fgure 4(b) and 4(d) that the guided platoon remains stable after decelerating to the optimal speed, while the unguided platoon has trafc oscillations due to stop behavior. Tese show that in this scenario, the guided platoon can pass through the intersection with no stopping and smaller trafc oscillations.
Furthermore, it can be seen from Figure 7 and Table 2 that, compared with the unguided platoon, the total fuel consumption, travel time, and delay of the guided platoon are all reduced, and the reduction in fuel consumption is the most signifcant. Tis is the reason that the strategy allows the platoon to avoid stops and start-up delays.
It can be seen from Figures 5(a) and 5(c) that under the guidance of the strategy, the platoon passes through the intersection without stopping and then merges into the previous queuing platoon. Without guidance, the platoon stops before the intersection and merges into the queuing platoon. In Figures 5(b) and 5(d), it can be found that the guided platoon decelerates to the optimal speed, then drives at a constant speed, and then starts to accelerate when near the queuing platoon. Te speed changes smoothly during the merge process under guidance, while the unguided platoon has a signifcant slowdown when it merges into the queue. Tis shows that in this scenario, the incoming platoon can pass through the intersection without stopping after being guided by the deceleration strategy and merge into the previous queuing platoon with small trafc oscillations.
In addition, it can be seen from Figure 8 and Table 2 that, compared with the unguided platoon, the total fuel consumption of the guided platoon is signifcantly reduced, but the drive time and delay are slightly increased. Tis is because the strategy guidance makes the platoon avoid stopping, but in order to ensure safety when merging into the queue, the safety distance between the leading vehicle and the last one in the queue is slightly increased.
It can be seen from Figures 6(a) and 6(c) that the guided platoon adjusts the headway to h t min , passes through the intersection without stopping, and merges into the previous queuing platoon. Tere are 4 vehicles that cannot pass the intersection during the green time in the unguided platoon. In Figures 6(b) and 6(d), it can be seen that the guided platoon drives at a constant speed after decelerating to the optimal speed, then accelerates through the intersection and smoothly merges into the queuing platoon. Without guidance, the part that can pass through the intersection stops, merges into the queued platoon, and then passes through the intersection. Te part that cannot pass frst slows down with the preceding vehicles, then speeds up with them. Since this part cannot pass, it stops at the stop line and then accelerates when the green light turns on. Tis part had multiple acceleration and deceleration with the speed fuctuating greatly. Tis shows that the strategy can guide the incoming platoon through the intersection without stopping, increasing the number of vehicles passing through and merging into the previously queued platoon with a small trafc oscillation. Furthermore, it can be seen from Figure 9 and Table 2 that under the guidance of the deceleration strategy and adjustment of headway, the total fuel consumption, travel time, and delay of the platoon are all reduced, and the reduction in fuel consumption is the most signifcant. Te signifcant reduction in travel time and delay is due to the fact that reducing the headway increases the number of vehicles passing through the intersection.
In summary, under the deceleration guidance strategy, the platoon avoids stopping at intersections and reduces the total fuel consumption signifcantly. In terms of travel time and delay, it increases slightly in the scene with queuing vehicles but decreases without queuing vehicles. Especially when the length of the platoon is n max , the delay of the platoon can be signifcantly reduced by adjusting the headway.

Simulation of Acceleration Guidance
Strategy. Similar to the deceleration guidance strategy, the simulation of the acceleration guidance strategy is divided into two scenarios, namely, scenario B1 and scenario B2. In scenario B1, there are no queued vehicles at the intersection, while in scenario B2 there are queued vehicles. In order to analyze the infuence of headway adjustment on the incoming platoon, the simulation is also carried out for the scene where the length of the platoon is n max and there are queued vehicles at the intersection, which is named as scenario B3. In these three scenarios, the acceleration guidance strategy is simulated, and the trajectories and speeds of the platoon are obtained, as shown in Figures 10-12, respectively. At the same time, the fuel consumption, travel time, and delay of the platoon are obtained, as shown in Figures 13-15. Similarly, in order to verify the efectiveness of the acceleration guidance strategy, the simulation results of three scenarios without guidance strategy are added to Figures 11-15. Improvements of fuel consumption, driving time, and delays in the acceleration guidance strategy are shown in Table 3.
It can be seen from Figures 10(a) and 10(c) that under the guidance strategy, the whole platoon passed through the intersection, while 2 vehicles could pass in the unguided platoon. In Figures 10(b) and 10(d), it can be seen that the guided platoon accelerates to the optimal speed and then drives at a constant speed, while the part of the unguided platoon that passes through drives at a constant speed, and the two vehicles that cannot pass cause trafc oscillations. Tese show that the incoming platoon increases the number of vehicles passing through the intersection in this scenario, which benefts from the acceleration guidance. Furthermore, it can be seen from Figure 13 and Table 3 that under the acceleration guidance, the total fuel consumption slightly increases but the driving time and delay of the platoon are greatly reduced. Te delay is greatly reduced because, under the acceleration guidance strategy, the platoon not only improves its average speed but also enables it to pass within the passable period without stopping.
While without guidance, the platoon passed without a merge behavior, and 3 vehicles could not pass the intersection. In Figures 11(b) and 11(d), it can be seen that under the strategy guidance, the platoon accelerates to the optimal speed and then slows down to merge into the previous queued platoon. While without guidance, the platoon drives at a constant speed, but 3 vehicles need to stop. Tese show that the incoming platoon can pass through an intersection with a small trafc oscillation and merge into the previous queuing platoon after being guided by the acceleration strategy. Furthermore, it can be seen from Figure 14 and Table 3 that, compared with no strategy guidance, the acceleration strategy guidance makes the platoon's fuel   consumption slightly increase, but the travel time and delay are greatly reduced.
It can be seen from Figures 12(a) and 12(c) that under the guidance of the strategy, the whole platoon passed the intersection and merged into the queuing platoon, while without the strategy guidance, 6 vehicles did not pass. It can be seen from Figures 12(b) and 12(d) that under the guidance of the strategy, the platoon has the same small trafc oscillation as scene B2, while under the guidance of no strategy, the 6 vehicles that did not pass and had an obvious trafc oscillation due to the stopping behavior. Tese show that in this scenario, the incoming platoon can be guided by the acceleration strategy and adjust the headway guidance to increase the number of vehicles passing through the intersection and merging into the queuing platoon with a small oscillation. Furthermore, it can be seen from Figure 15 and Table 3 that, under the acceleration strategy guidance, the platoon fuel consumption increases slightly, but the travel time and delay decrease.
In summary, under the acceleration guidance strategy, the number of vehicles passing through the intersection increases, the platoon fuel consumption increases slightly, but the travel time and delay decrease signifcantly. When the length of the platoon is n max , adjusting the headway can further reduce the platoon delay.

Simulation of the Stop Guidance Strategy.
When the platoon can neither pass through the intersection after t in by decelerating nor pass through the intersection before t out by accelerating, the stop guidance strategy should be used. Since the red phases of the signalized intersection set in the simulation scenarios are short, the strategy can only be applied when there are secondary queued vehicles at the intersection. Terefore, it is assumed that there are 3 secondary queued vehicles at the intersection, which is set as scenario C. In this scenario, the stop guidance strategy is simulated, and the trajectory and velocity of the platoon passing through the intersection are obtained, as shown in Figure 16, and the fuel consumption, travel time, and delay of the platoon are shown in Figure 17. In addition, in order to verify the efectiveness of the stop guidance strategy, the simulation results without strategy are added to Figure 16 and Figure 17, respectively.
It can be seen from Figures 16(a) and 16(c) that the guided platoon merged into the queuing platoon more smoothly than the one without guidance. In Figures 16(b) and 16(d), it can be seen that the guided platoon decelerates with a constant deceleration, and the curve is smoother than that of the unguided one, avoiding a large deceleration. Tis   shows that in this scenario, the incoming platoon can be more safely merged into the queuing platoon through the stop strategy guidance. It can be seen from Figure 17 that the total fuel consumption of the guided platoon is reduced by 3.5%. Tis is because the stop-guidance strategy avoids large decelerations.

Simulation of Platoon Restructure.
In order to explore the impact of the platoon restructure on the platoon, the strategy under the platoon restructure is simulated, set as scenario D, and the trajectory and velocity of the platoon under the strategy guidance are obtained through simulation, as shown in Figure 18. Fuel consumption, travel time, and delays are shown in Figure 19. In addition, the simulation results without strategy are added to Figures 18  and 19, respectively.

Influence of Queue Length and CV Penetration Rate on the Platoon Speed Guidance Strategy
6.1. Infuence of Diferent Queue Lengths. Since the queue length at intersections has an infuence on platoon speed guidance strategies, it is analyzed through scenario A2 and scenario B2, which are typical deceleration scenario and acceleration scenario, respectively. Referring to the analysis method in reference [62], diferent queue lengths in two scenarios are set and simulated. Te results are obtained and shown in Table 4 and Table 5. In addition, the improvements to the strategy under diferent lengths are calculated and shown in Tables 6 and 7.
It can be seen from Table 4 that, as the queue length increases, the fuel consumption, driving time, and delay of the incoming platoon all increase. Table 6 shows that fuel consumption improvement roughly tends to decrease as queue length increases, and drive time and delay both increase slightly.
It can be seen from Tables 5 and 7 that, at queue lengths of 0, 3, 5, fuel consumption, drive time, and delay are the same. Te reason is that the queue length has no infuence on the platoon speed guidance strategy when the queue dissipates before t in . However, at the queue length of 7, the fuel consumption is increased, and the improvement in drive time and delay is reduced. Tis is because when the queue length increases and the n max decreases accordingly, diferent strategies will be used as a result, such as guiding the platoon with a small headway.
In summary, when the queue length afects the passable period, the improvement of the fuel consumption, drive time, and delay will decrease as the queue length increases, and even diferent strategies will used.

Infuence of Diferent CV Penetration Rates.
With the rapid development of the CV technology, CVs have gradually appeared on the actual roads, and the number of them is increasing. However, for a long time in the future, the vehicles on the road will still be mix of CVs and unconnected vehicles [63,64]. Terefore, it is necessary to explore the infuence of the penetration rate of CVs on the platoon speed guidance strategy.
Four typical scenarios are selected for analysis, which are scenarios A2, A3, B1, and D. According to diferent penetration rates, the scenarios of CVs in each position in the platoon are simulated. Te average fuel consumption and delay in diferent positions under the same penetration rate are obtained, which are shown in Figure 20. It should be noted that in the simulation of scenario D, the headway is reduced only when two connected vehicles are adjacent to each other.
It can be seen from Figure 20(a) that in scenario A2, as the penetration rate increases, the average delay of the platoon keeps on slightly increasing; however, the average fuel consumption of the platoon gradually decreases, especially when the penetration rate is 20%. Te average fuel consumption dropped the fastest and then declined more slowly as the penetration rate increased.
It can be seen from Figure 20(b) that in scenario A3, with the increase in the penetration rate, the average fuel consumption decreases gradually, especially when the penetration rate is at 16.67%. But it has a slight increase at 83.34%. Te average delay decreases gradually with the increase of the penetration rate, and the decrease becomes increasingly larger. It reaches a maximum value in the range of 83.34% to 100%, the decrease of which can reach 51.22% of the total decrease. tAs can be seen from Figure 20(c), as the penetration rate increases, the average fuel consumption frst decreases slightly and then increases slightly in scenario B1. Tis is because when the lead vehicle is not a CV, the platoon can only pass 3 vehicles. At this time, if the next vehicle is a CV, it will be separated from the preceding vehicle. Ten, the deceleration guidance strategy is used, which reduces fuel consumption. With the increase in the penetration rate, the number of vehicles with the acceleration guidance strategy increases, and the fuel consumption increases. Te average delay decreases rapidly with the increase of the penetration rate. Tis is because when the lead vehicle is a CV, the entire platoon can pass, and the delay is the lowest. As the penetration rate increases, the probability of the lead vehicle being a CV gradually increases.      It can be seen from Figure 20(d) that under scenario D, the average delay decreases with the increase in the penetration rate, and the magnitude of the decrease becomes increasingly larger. Te average fuel consumption decreases frst, then slightly increases, and then decreases with increasing penetration. Because after the penetration rate reaches a certain level, the penetration rate will allow more vehicles in the platoon to reduce the headway, but not enough to increase the number of passing vehicles, so the fuel consumption will increase slightly at this stage.
However, as the penetration rate continues to increase, the number of passing vehicles increases, reducing the number of vehicles queuing or slowing down, so the fuel consumption begins to decline.
In summary, the average delay and average fuel consumption of the platoon decrease gradually as the penetration rate increases. Although the average delay or average fuel consumption has increased slightly in some scenarios, the corresponding average fuel consumption or average delay has decreased signifcantly in the same scenario. Tis           indicates that the guidance strategy is increasingly efective in reducing delays and fuel consumption in general with the penetration rate increasing.

Conclusion
Tis paper proposes a platoon speed guidance strategy at signalized intersections in the CV environment to optimize the fuel consumption and delay of the platoon. Te strategy includes constant speed guidance, deceleration guidance, acceleration guidance, and stop guidance. At the same time, the calculation method for the optimal speed of the platoon is given, which includes determining the passable period and the maximum number of passing vehicles according to the intersection information, calculating the driving trajectory of the leading vehicle and the following vehicle, respectively, based on diferent guidance strategies of the platoon, and determining the optimal trajectory of the platoon based on an optimization model of fuel consumption and delay.
Eight scenarios of intersections are designed, and the speed guidance strategy of the platoon is simulated. Te results show that the deceleration guidance strategy signifcantly reduces the total fuel consumption of the platoon, the acceleration guidance strategy signifcantly reduces the total delay of the platoon, and reducing the headway of the platoon can increase the number of vehicles passing through the intersection and further reduce the platoon delay. Furthermore, the incoming platoon guided by the stop guidance strategy merges into the queued platoon more safely and reduces fuel consumption. Te platoon restructure method increased the number of vehicles passing through the intersection in the platoon, signifcantly reducing delays and avoiding vehicle stops.
In addition, two typical scenarios are selected to simulate the impact of diferent queue lengths on the platoon speed guidance strategy. Te results show that when the queue length afects the passable period, the improvement in fuel consumption, drive time, and delay will decrease as the queue length increases, and even diferent strategies will be used. Four typical scenarios are selected to simulate the impact of the penetration rate of CVs on the platoon speed guidance strategy. Te results show that as the penetration rate increases, the average delay and average fuel consumption of the platoon gradually decrease, and the guiding strategy is generally increasingly efective in reducing the delay and fuel consumption.
Tis paper studies the speed guidance strategy of platoons at signalized intersections in the CV environment and verifes the efectiveness of the strategy. However, the proposed strategy is only for a single signalized intersection and does not consider multiple intersections, so that the guidance of the vehicle speed of the platoon may be locally optimal. In addition, this paper only considers the speed guidance of the vehicle and does not combine the signal control. If the two are combined, the efect of the guidance can be further improved.

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

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