The Impact of Three Specific Collaborative Merging Strategies on Traffic Flow

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Introduction
Te rapid development of cities is bound to bring serious trafc problems (such as trafc congestion and trafc accidents), which will further lead to an adverse efect on economic development.In order to understand the evolution mechanism of trafc, various models have been proposed.Helbing [1] reviewed the major approaches to modeling vehicle trafc, including microscopic (particlebased), mesoscopic (gas-kinetic), and macroscopic (fuiddynamic) models.Particularly, regarding microscopic models, Gipps [2] proposed a car-following model and used it to reproduce some characteristics of real trafc fow, while Nagel and Schreckenberg [3] constructed a basic cellular automaton trafc fow model (i.e., the NaSch model).Moreover, Kerner and Rehborn [4,5] developed the threephase trafc fow theory based on real trafc observation data, and a number of similar models were put forward based on this theory [6,7].In addition, the rapid development of technology gave birth to the concept of intelligent vehicles (e.g., connected and autonomous vehicles), and such vehicles have entered specifc markets.Te vehicles can communicate with each other and cooperate to complete certain driving tasks (such as lane changing and collaborative merging) [8].
Trafc congestion often occurs on on-ramps, leading to the sections of roads being considered as one of the common trafc bottlenecks [9,10].Moreover, congestion can easily spread to the upstream parts of the main roads and seriously afect the operation efciency of the entire on-ramp systems (consisting of ramps and their connected acceleration lanes and main roads) [11].Over the past decades, the study on on-ramps has attracted a lot of attention.From the initial phase diagrams [11,12] to the later coordinated merging strategies [13,14], various characteristics of on-ramp systems have been analyzed [12,15], and methods to improve the trafc condition of the systems have been put forward [16,17].Tese studies can be divided into two major categories: optimization and simulation.Optimization is to design trajectories of vehicles with the goal of systematic or individual optimality in terms of certain trafc variables (e.g., fow rate, travel time, fuel consumption, and comfort levels) [18].In comparison, simulation aims to mimic driving behavior or trafc rules in order to study the impact of the diferent behavior or rules on on-ramp systems.Particularly, cellular automata (CA) (microscopic) models are widely adopted to simulate trafc fow systems, because of the models' simple rules and easy implementation.From the classic single-lane NaSch trafc fow model [3] to the improved models [19][20][21][22], and to the two-lane [23,24] or even multilane [25,26] models, CA methods have demonstrated their value in well-depicting the characteristics of both microdriving behavior and macrosystem evolution.Based on the models, Campari and Levi [27], Zeng et al. [10], Jiang et al. [28], and Diedrich et al. [29] simulated on-ramp systems and investigated their evolution characteristics.
Alongside the micro simulation (by CA models), different merging strategies have been proposed [30][31][32] to devise vehicle driving behavior (e.g., vehicle acceleration or deceleration) at ramps, in order to facilitate the vehicle merging process and improve the trafc condition of onramp systems.Scarinci and Heydecker [17] summarized the major merging strategies and reviewed existing evaluation methods on the overall efect of the strategies.However, none of the existing studies have conducted comprehensive analysis and detailed comparison among strategies.To fll in this gap, this paper examines three representative collaborative merging strategies of connected and autonomous vehicles and analyses their impact on on-ramp systems by means of simulation methods (i.e., CA models).Te core of these strategies proposes that vehicles on the main road provide "priority" condition for the merging vehicles on the acceleration lane (of the ramp) by the change of the speed of the former vehicles within capability ranges.In this analytical process, the three strategies are frst expressed by the corresponding merging rules, and simulation is performed to reproduce the on-ramp system.Te average speed and trafc fow rate of the roads in the system are then obtained, and the impact of these strategies is fnally examined.Te major contributions of this study lie in the following aspects: (1) it conducts a comparative analysis of the impact of diferent merging strategies on on-ramp systems, (2) it examines the infuence of lane-changing behavior on the operation efciency of the systems, and (3) it further investigates the efect of merging safety distances on the performance of the systems.Te remainder of this paper is organized as follows: Section 2 introduces the merging strategies and corresponding merging rules, while Section 3 describes the simulation process and analyses the simulation results.Finally, Section 4 ends this paper with a major conclusion and policy recommendation.

Merging Strategies and Update Rules
In this section, we frst introduce the CA model and then give the defnition of certain important variables.We further summarize the three collaborative merging strategies, and describe the update rules (including the merging rules) adopted in the CA model for simulating an on-ramp system.

Te Cellular Automata (CA) Model.
Te CA model is a discrete model method in time and space frst proposed by von Neumann [33] to simulate the self-replication function of living systems.It is a rule-based system evolution model, in which all individual objects in the system update their states (or positions) according to one or multiple rules.In the CA model for trafc fow, the entire road space is discretized into a set of cells, with each cell having two states including "empty" or "occupied (by a vehicle)."Rules (as described in Section 2.4) are formulated according to real driving behavior, and vehicles are updated according to the established rules to refect the evolution process of the trafc fow system.

Variable Defnition
( In equation ( 1), S m i (i � 1,. ..,5) is the i th element in S m , while in equation ( 2), l is the vehicle length, d safe,t is the safety distance of merging strategies, and T m j (j � 1, 2) is the j th element in T m .Te state array S m represents the position (S m 3 ) of vehicle Veh m as well as the positions (S m 1 , S m 2 , S m 4 and S m 5 ) of the four nearest vehicles around Veh m after a time step (Δt).Te threat array T m j (j � 1, 2) refers to the relative distance (T m 1 ) between Veh m and Veh m,back 1 as well as the distance (T m 2 ) between Veh m and Veh m,front 1 .Te elements in T m refect whether Veh m has a collision after Δt.When T m j (j � 1, 2) is greater than or equal to 0, no accident would occur; on the contrary, if T m j is smaller than 0, a collision is likely to happen.

Merging Strategies.
Emulating the collaborative merging behavior of connected and autonomous vehicles, we consider three merging strategies, each of which ensures the safety of the merging vehicle and its surrounding vehicles.Equation (3) defnes the safety condition when Veh m merges into the main road.
Combining equations ( 2) and (3), we obtain Te frst part of equation (4) shows that Veh m will not be hit by Veh m,back 1 after merging, while the second part indicates that Veh m will not strike Veh m,front 1 after merging.If equation (3) (or equation ( 4)) is satisfed, Veh m will merge into the main road without risks of crash.However, when the safety condition is not met, the following strategies could be considered: Strategy 1: Veh m,front 1 accelerates to provide safety condition for Veh m Strategy 2: Veh m,back 1 decelerates to provide safety condition for Veh m Strategy 3: Veh m,front 1 accelerates and Veh m,back 1 decelerates to provide safety condition for Veh m 2.4.Update Rules.Te rules for simulating an on-ramp system in the CA model include four parts: the rules for vehicles entering the main road or ramp, the forward rules for all vehicles, the lane changing rules for vehicles on the two-lane main road, and the merging rules for the merging vehicles.

Entry Rules. Te same entry rules as those proposed in
Reference [12] are considered.Te on-ramp system adopts open boundary conditions, with the entrance on the left side of the main lane (or ramp) and the exit on the right side; see Figure 2(a).Te leftmost cells of the road serve as the entry area, and the number of the cells covered by this area is Δt • v max (the maximum velocity of vehicles).Let x last be the location of the current leftmost vehicle on the main lane (or ramp) before each time step (Δt) update.If on the main road (or ramp) with the probability of a 1 (or a 2 ).

Forward Rules.
Te forward rules are based on the traditional one-lane CA model, i.e., the NaSch model [3], which consists of acceleration (acceleration rate is 1 cell/Δt 2 ), deceleration (deceleration rate is − 1 cell/Δt 2 ), randomization, and position updating after a time step.
Step1: acceleration: (1) Incentive criterion as follows: (5) (2) Safety criterion as follows: In equation ( 5), x n+1 and x n+1,t denote the positions of the preceding vehicles (Veh n+1 ) on the same (as Veh n ) and target lanes, and d n,front and d n,front t are the distances between Veh n and Veh n+1 on the same lane as well as on the target lane, respectively.In equation ( 6), d n,back t refers to as the distance between Veh n and the vehicle behind it (Veh n− 1 ) on the target lane, with x n− 1,t being the position of Veh n− 1 , while d safe,l represents the safe distance of lane changing.Te incentive criterion indicates the condition under which the front vehicle Veh n+1 on the same lane (as Veh n ) hinders the acceleration of Veh n (i.e., due to the short distance of d n,front ), whereas the front vehicle Veh n+1 on the target lane provides the opportunity for Veh n 's acceleration (i.e., given the relatively long distance of d n,front t ).Te safety criterion ensures the safety of Veh n after changing lanes.If both the criterions are met, Veh n will change lanes with the probability p lc .It should be noted that lane changing rules only apply to vehicles on two-lane main roads.

Merging Rules.
Te merging rules are designed in accordance with the three collaborative merging strategies described in Section 2.3.Given the merging vehicle Veh m on the acceleration lane, let L m (1 or 0) be a parameter indicating whether Veh m merges into the main road.If L m � 1, the vehicle will merge; otherwise, if L m � 0, the vehicle will not merge.Te value of L m is determined based on the following procedure (see Algorithm 1): If L m � 1, Veh m will merge into the main road.Note that the merging operation and corresponding rules are only applicable to merging vehicles on the acceleration lane.

Simulation and Discussion
In order to study the infuence of the diferent merging strategies on on-ramp systems, we use the CA model to simulate the systems under four diferent situations (including no-strategies and strategies 1-3).Te investigated on-ramp systems are divided into two cases, with case 1 for on-ramps having a one-lane main road while case 2 for those featured with a two-lane main road.Similar to most CA models, the length of each cell is 7.5 m and each vehicle occupies one cell (i.e., l � 1).Te other parameters are set based on the commonly adopted values of the existing research, including the maximum velocity v max � 5 cells/time step (i.e.135 km/h) [3]; the road length L � 2000cells and starting position x on of the acceleration lane x on � L/2 [9] (i.e., 1000 cells); the length of the acceleration lane L a � 5 cells, randomization probability p s � 0.3, lane-changing probability p lc � 0.8 and safe distance of lane changing d safe,l � 2 cells (i.e., 15 m) [34].Moreover, the safe distance of merging vehicles and time step are d safe,t � 1 cell (it will be discussed in Section 3.3) and Δt � 1s, respectively.3.1.Average Velocity.We obtained the average velocity of vehicles under each of the situations with diferent values of vehicle entering probabilities a 1 (to the main road) and a 2 (to the ramp).Let v m and v r be the average velocity of vehicles on the main road (upstream) and on the ramp and Figures 3(a From Figures 3(a)-3(d), it was observed that for the system with a one-lane main road (case 1), the merging strategies (Figures 3(b)-3(d)) can afect the velocity of vehicles on both the main road and ramp, when compared to no strategies (Figure 3(a)).Particularly, all the three where as defned in Section 2.2, S m i (i � 1, 2, 4, 5) and T m j (j � 1, 2) are the elements of the trafc state array S m and thread array T m of Veh m , while v m,front 1 and v m,back 1 are the speed of the nearest vehicles in front of and behind Veh m (Veh m,front 1 and Veh m,back 1 ), respectively.Moreover, T m,front 1 2 and T m,back 1 1 denote the second and frst elements of the threat array T m,front 1 and T m,back 1 of Veh m,front 1 and Veh m,back 1 , respectively.Algorithm 1 in strategy 1 indicates that if T m 2 < 0, Veh m,front 1 should increase its speed in order to provide safe merging condition for Veh m , with (S m 5 − S m 4 )/Δt being the maximum acceleration of Veh m,front 1 in order to ensure its own safety (i.e., it will not collide with Veh m,front 2 ).Likewise, Algorithm 1 in strategy 2 requires that in the case of T m 1 < 0, Veh m,back 1 decreases its speed to provide merging condition for Veh m , with (S m 2 − S m 1 )/Δt being the maximum deceleration of Veh m,back 1 to guarantee its safety (i.e., it will not be hit by Veh m,back 2 ).Strategy 3 is the combination of the previous two strategies under the situation of T m 1 < 0 and T m 2 < 0, which suggests that both Veh m,front 1 accelerate and Veh m,back 1 decelerate to try to provide merging condition for Veh m .(4) Merging  6 Journal of Advanced Transportation strategies reduce the size of area II but increase that of area III, refecting that there are less combined values of a 1 and a 2 for v m > v s and v r < v s but more for v m < v s and v r > v s .Tis further suggests that in relation to no strategies, strategies 1-3 can decrease the average velocity of vehicles on the main road when a 1 and a 2 fall into the reduced-part-of-area-II, while improving that on the ramp if the two probabilities are in the increased-part-of-area-III.In addition, deviations also exist among individual strategies in terms of the size of the changed parts of the areas II and III.Strategy 3 has much larger sizes of these two changed parts than strategies 1 and 2, signifying that the former strategy can better improve the trafc efciency of the ramp but at a higher cost of reducing that on the main road than the latter two strategies.
With respect to the system with a two-lane main road (case 2), the four areas (in Figures 4(a)-4(d)) display diferent sizes from the corresponding regions in case 1, particularly regarding areas I and IV which are much larger and smaller than those in case 1, respectively.Tis signifes that there are more combined values of a 1 and a 2 under which the average speed of vehicles on the main road and ramp is both high (i.e., v m > v s and v r > v s ), but less combinations of these two probabilities for which the speed of vehicles on the roads is low (i.e., v m < v s and v r > v s ).Tis can be attributed to the fact that vehicles on the main road (with two lanes) can change lanes and that the lane changing behavior has positive efect on the trafc condition of the whole system and leads to the speed of vehicles on the roads higher.When the diferent situations within case 2 were compared, similar trends to those within case 1 were observed.Specifcally, with reference to no strategies, all the three strategies reduce the size of area II but increase that of area III, signaling that these strategies reduce the average speed of vehicles on the main road when a 1 and a 2 are in the reduced-part-of-area-II while improving that on the ramp if a 1 and a 2 belong to the increased-part-of-area-III.Particularly, strategy 3 is featured with a much smaller size of area II but a larger size of area III, implying that this strategy signifcantly reduces the trafc efciency of the main road but increases that on the ramp.

Flow Rate.
In addition to speed, the impact of the merging strategies on trafc fow rate (i.e., the number of vehicles passing a reference point per hour) was also inspected.Let f s and f t be the average upstream fow rate on the main road in case 1 and case 2, respectively, while f r be the fow rate on the ramp in both cases.Figures 5-10 visualize the evolution of the fow rates f s , f t , f r , f s + f r , and f t + f r , respectively, under diferent situations with various combinations of a 1 and a 2 .
(Note: in Figure 7, in order to better display the changing trends of the z-variable, the x-axis and y-axis represent a 2 Journal of Advanced Transportation and a 1 , respectively (instead of a 1 and a 2 in Figures 3-6).Te same coordinate system is adopted in Figures 8 and 11).
From Figures 5(a)-5(d), it was noted that when a 2 is small (i.e., α 2 ≤ 0.28), the fow rate f s of the main road in case 1 shows no large diferences between no-strategies and the other three strategies, with f s reaching the largest value at a 2 � 0 in all these situations.Tis demonstrates that the merging strategies have little impact on f s when the vehicle entering probability to the ramp is small.However, as a 2 increases (a 2 > 0.28), f s begins to be afected by the strategies and displays a decreasing trend.However, this efect is not unlimited, manifested by the observation that f s reduces until reaching a stable level (a "platform").Moreover, the specifc levels of the platforms vary among strategies, with strategy 1 having the highest level while strategy 3 displaying the lowest.Tis signifes that while all the strategies have a negative impact on the fow rate of the main road, strategy 3 causes the worst efect.A similar conclusion can be drawn for case 2 (in Figures 6(a)-6(d)), except that the threshold of a 2 which initiates the impact is higher (a 2 > 0.32).Moreover, the fow rate f t and the stable levels for the "platform" in case 2 are signifcantly higher than those in case 1 due to the adoption of the additional lane on the main road.
Figures 7(a)-7(d) and 8(a)-8(d) depict the (positive) impact of the merging strategies on the fow rate f r of the ramp in case 1 and case 2, respectively, showing that when a 2 increases, f r rises and reaches a stable level (a "platform").Tis points out that while the merging strategies decrease the trafc fow on the main road, they increase that on the ramp.Moreover, similar to the decreasing efect on the main road, the increasing impact on the ramp is not boundless, making the fow rate rising until to a stable level.
Figures 9(a)-9(d) and 10(a)-10(d) visualize the fow rate over the whole on-ramp system (i.e., the main road and ramp), for case 1 (i.e., f s + f r ), and case 2 (i.e.f t + f r ), respectively.It was observed that f t + f r is higher than f s + f r at most combined values of a 1 and a 2 , especially when a 1 and a 2 are large.Tis suggests that it is more advantageous to set up a two-lane main road at merging sections.With respect to specifc merging strategies, strategy 1 has almost no impact on f s + f r or f t + f r , while strategy 2 reduces f s + f r and f t + f r .In comparison, strategy 3 decreases f s + f r but does not bring changes to f t + f r .

Efect of d safe,t .
Alongside the average velocity and fow rate, the efect of the merging safety distance parameter d safe,t on whole systems was further examined.In this process, we frst simulated the system with d safe,t � 2 cells (while the other parameters remaining the same as the original , it shows that that when a 1 and a 2 are small, diferent values of d safe,t have little efect on the fow of the on-ramp systems.However, when a 2 becomes large, the increase of d safe,t will increase f t , reduce f r , and reduce f t + f r .Terefore, setting the merging safety distance parameter too large may lead to a negative impact on the whole system.

Conclusion
In this paper, we frst defned trafc state arrays (S m ) and thread arrays (T m ) to represent the status of merging vehicles.We then summarized three major collaborative merging strategies and designed merging rules to express these strategies.Next, we analyzed the efect of these strategies on the speed and fow rate of on-ramp systems by means of CA simulation models.Finally, we examined the infuence of the merging safety distance parameter (d safe,t ) on the operation efciency of the systems.
Based on this study, the following key results were obtained: (1) All the merging strategies give excessive "priority" to the merging vehicle, leading to the reduction of average speed and fow rate of the main road.(2) Nevertheless, these strategies have a diferent efect on the entire system with a one-lane or two-lane main road.Due to lane-changing behavior, the system with a two-lane main road has more advantages than that featured with a onelane main road, making the former system having higher operation efciency than the latter under the same strategies.Tus, it is recommended that in an on-ramp system, a two-lane (even multiple-lane) main road should be considered.(3) Te vehicles on the ramp and main road afect each other, and as the vehicle entering probabilities (a 1 and a 2 ) become large, the trafc fow rate on the main road decreases whereas that on the ramp increases.However, the efect is not unlimited.Te fow rate on both roads fnally reaches a stable level (forming a "platform").( 4) On the premise of ensuring safety, a small value of the merging safety distance parameter (d safe,t ) should be adopted, as a large value would cause a considerable decrease in the fow rate of the whole system.
Tere are some limitations in this study, including the followings: (1) this study only considers three specifc strategies, which is not complete, (2) the results derived through simulation should be further compared and verifed with the experimental outcomes obtained from actual situations, and (3) the impact of more forward and rules (in addition to the current ones depicted in Sections 2.4.2 and 2.4.3) on the results should be investigated.Tese drawbacks will be further addressed in the future research.

Figure 1 :
Figure 1: Schematic diagram of an on-ramp system with an (a) one-lane main road and (b) a two-lane main road.

Figure 2 :
Figure 2: Schematic diagram of parameters in the update rules: (a) forward situation and (b) lane-changing situation.
)-3(d) and 4(a)-4(d) present the values of v m and v r in relation to the threshold v s (v s � 4.5 cells/time step) (121.5 km/h) for case 1 and case 2, respectively.In these fgures, the green, blue, red, and black scatters (denoted by I, II, III, and IV) indicate the areas with (1) v m > v s and v r > v s , (2) v m > v s and v r < v s , (3) v m < v s and v r > v s , and (4) v m < v s and v r < v s , while the x-axis and y-axis represent the vehicle entering probabilities a 1 and a 2 , respectively.

ALGORITHM 1 :
Te procedure for determining the value of L m .

Figure 3 :Figure 4 :
Figure 3: Schematic diagram of the relationship between the average velocity and threshold in the case of (a) no-strategies and (b-d) diferent merging strategies (strategies 1-3), case 1.

and Veh m,back 1 , the second and frst (near- est) vehicles behind Veh m on the main road, respectively; Veh m,front 1 and Veh m,front 2 , the frst and second (nearest) vehicles in front of Veh m on the main road
Veh m , the merging vehicle m on the acceleration lane; Veh m,back 2