# The Impact of Three Specific Collaborative Merging Strategies on Traffic Flow

Authors: Xue-Cheng Shang; Feng Liu; Xin-Gang Li; Davy Janssens; Geert Wets
Journal: Journal of Advanced Transportation
 (2023)

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## Abstract

On-ramps are considered to be one of the common traffic bottlenecks. In order to improve the operation efficiency of on-ramps, scholars worldwide have proposed various vehicle merging strategies. In this study, we designed different rules to express three collaborative strategies and studied their impact on on-ramp systems. Cellular automata models were used to simulate the systems under different situations, and the average speed and traffic flow rate of both the main roads and ramps were analyzed. The results show that (1) all the three merging strategies give excessive “priority” to the merging vehicle, leading to a severe reduction in the traffic performance of the main road; (2) nevertheless, these strategies have different effects on the entire system with a one-lane or two-lane main road. Due to the lane-changing behavior, the system with a two-lane main road has more advantages than that featured with a one-lane road, making the former system performing better than the latter under the same strategies; (3) the vehicles on the ramp and main road affect each other, and as the vehicle entering probabilities become large, the traffic flow rate on the main road decreases whereas that on the ramp increases. However, the effect is not unlimited, the flow rate on both roads finally reaches a stable level (forming a “platform”); and (4) large values of the merging safety distance parameter decrease the flow rate of the entire system. All the previous results provide a deep understanding of the impact of the three merging strategies on traffic flow, contributing to the design of on-ramp systems that have better operation efficiency and low levels of congestion.


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## Body

## 1. Introduction

The rapid development of cities is bound to bring serious traffic problems (such as traffic congestion and traffic accidents), which will further lead to an adverse effect on economic development. In order to understand the evolution mechanism of traffic, various models have been proposed. Helbing [1] reviewed the major approaches to modeling vehicle traffic, including microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models. Particularly, regarding microscopic models, Gipps [2] proposed a car-following model and used it to reproduce some characteristics of real traffic flow, while Nagel and Schreckenberg [3] constructed a basic cellular automaton traffic flow model (i.e., the NaSch model). Moreover, Kerner and Rehborn [4, 5] developed the three-phase traffic flow theory based on real traffic 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 specific markets. The vehicles can communicate with each other and cooperate to complete certain driving tasks (such as lane changing and collaborative merging) [8].Traffic congestion often occurs on on-ramps, leading to the sections of roads being considered as one of the common traffic bottlenecks [9, 10]. Moreover, congestion can easily spread to the upstream parts of the main roads and seriously affect the operation efficiency 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 traffic condition of the systems have been put forward [16, 17]. These 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 traffic variables (e.g., flow rate, travel time, fuel consumption, and comfort levels) [18]. In comparison, simulation aims to mimic driving behavior or traffic rules in order to study the impact of the different behavior or rules on on-ramp systems. Particularly, cellular automata (CA) (microscopic) models are widely adopted to simulate traffic flow systems, because of the models’ simple rules and easy implementation. From the classic single-lane NaSch traffic flow model [3] to the improved models [19–22], 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 [30–32] to devise vehicle driving behavior (e.g., vehicle acceleration or deceleration) at ramps, in order to facilitate the vehicle merging process and improve the traffic condition of on-ramp systems. Scarinci and Heydecker [17] summarized the major merging strategies and reviewed existing evaluation methods on the overall effect of the strategies. However, none of the existing studies have conducted comprehensive analysis and detailed comparison among strategies. To fill 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). The 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 first expressed by the corresponding merging rules, and simulation is performed to reproduce the on-ramp system. The average speed and traffic flow rate of the roads in the system are then obtained, and the impact of these strategies is finally examined. The major contributions of this study lie in the following aspects: (1) it conducts a comparative analysis of the impact of different merging strategies on on-ramp systems, (2) it examines the influence of lane-changing behavior on the operation efficiency of the systems, and (3) it further investigates the effect of merging safety distances on the performance of the systems.The remainder of this paper is organized as follows: Section2 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.


## 2. Merging Strategies and Update Rules

In this section, we first introduce the CA model and then give the definition 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.


### 2.1. The Cellular Automata (CA) Model

The CA model is a discrete model method in time and space first 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 traffic flow, 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 reflect the evolution process of the traffic flow system.


### 2.2. Variable Definition

Vehm, the merging vehicle m on the acceleration lane;Vehm,back2 and Vehm,back1, the second and first (nearest) vehicles behind Vehm on the main road, respectively;Vehm,front1 and Vehm,front2, the first and second (nearest) vehicles in front of Vehm on the main road, respectively;xm, xm,back2, xm,back1, xm,front1 and xm,front2, the position of Vehm, Vehm,back2, Vehm,back1, Vehm,front1, and Vehm,front2, respectively;vm, vm,back2, vm,back1, vm,front1 and vm,front2, the velocity of Vehm, Vehm,back2, Vehm,back1, Vehm,front1, and Vehm,front2, respectively;Δt, the time step during which vehicles are updated in the CA model;Sm, the traffic state array of Vehm (defined in equation (1));Tm, the threat array of Vehm (defined in equation (2)).Some notations are shown in Figure1.Figure 1
Schematic diagram of an on-ramp system with an (a) one-lane main road and (b) a two-lane main road.
(a)(b)The state arraySm and threat array Tm of Vehm are defined as follows [8]:(1)Sm=S1m,S2m,S3m,S4m,S5m=xm,back2+vm,back2⋅Δt,xm,back1+vm,back1⋅Δt,xm+vm⋅Δt,xm,front1+vm,front1⋅Δt,xm,front2+vm,front2⋅Δt,(2)Tm=T1m,T2m=S3m−S2m,S4m−S3m−l−dsafe,t=S3m−S2m−l−dsafe,t,S4m−S3m−l−dsafe,t.In equation (1), Sim (i = 1,…,5) is the i th element in Sm, while in equation (2), l is the vehicle length, dsafe,t is the safety distance of merging strategies, and Tjm (j = 1, 2) is the j th element in Tm. The state array Sm represents the position (S3m) of vehicle Vehm as well as the positions (S1m,S2m,S4mandS5m) of the four nearest vehicles around Vehm after a time step (Δt). The threat array Tjm (j = 1, 2) refers to the relative distance (T1m) between Vehm and Vehm,back1 as well as the distance (T2m) between Vehm and Vehm,front1. The elements in Tm reflect whether Vehm has a collision after Δt. When Tjm (j = 1, 2) is greater than or equal to 0, no accident would occur; on the contrary, if Tjm is smaller than 0, a collision is likely to happen.


### 2.3. 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) defines the safety condition when Vehm merges into the main road.(3)T1m≥0,T2m≥0.Combining equations (2) and (3), we obtain(4)S3m−S2m−l−dsafe,t≥0,S4m−S3m−l−dsafe,t≥0.The first part of equation (4) shows that Vehm will not be hit by Vehm,back1 after merging, while the second part indicates that Vehm will not strike Vehm,front1 after merging. If equation (3) (or equation (4)) is satisfied, Vehm 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:Vehm,front1 accelerates to provide safety condition for VehmStrategy 2:Vehm,back1 decelerates to provide safety condition for VehmStrategy 3:Vehm,front1 accelerates and Vehm,back1 decelerates to provide safety condition for Vehm


### 2.4. Update Rules

The 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.


#### 2.4.1. Entry Rules

The same entry rules as those proposed in Reference [12] are considered. The 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). The leftmost cells of the road serve as the entry area, and the number of the cells covered by this area is Δt⋅vmax (the maximum velocity of vehicles). Let xlast be the location of the current leftmost vehicle on the main lane (or ramp) before each time step (Δt) update. If xlast>vmax⋅Δt, a new vehicle will enter the position of minxlast−vmax⋅Δt,vmax⋅Δt on the main road (or ramp) with the probability of a1 (or a2).Figure 2
Schematic diagram of parameters in the update rules: (a) forward situation and (b) lane-changing situation.
(a)(b)


#### 2.4.2. Forward Rules

The 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/Δt2), deceleration (deceleration rate is −1 cell/Δt2), randomization, and position updating after a time step.Step1: acceleration:vn⟶minvmax,vn+1cell/Δt;Step2: deceleration:vn⟶minvn,dn/Δt;Step3: randomization:vn⟶maxvn−1cell/Δt,0 with probability ps;Step4: position updating:xn⟶xn+vn⋅Δt, where xn and vn denote the position and velocity of the subject vehicle (represented as Vehn), respectively, and dn refers to as the distance between Vehn and the nearest vehicle Vehn+1 in front of it (see Figure 2(a)). Step 1 depicts the acceleration behavior of Vehn for which the speed should not reach the maximum velocity vmax of vehicles, while Step 2 reflects the deceleration behavior of Vehn to ensure that this vehicle is not hitting the vehicle in front of it. Step 3 represents the random deceleration behavior of Vehn.


#### 2.4.3. Lane Changing Rules

The lane changing rules on the two-lane main road (see Figure2(b)) consist of two criterions as follows:(1)
Incentive criterion as follows:(5)dn,front<minvn+1⋅Δt,vmax⋅Δtanddn,front<dn,front_t,dn,front=xn+1−xn−l,dn,front_t=xn+1,t−xn−l.(2)
Safety criterion as follows:(6)dn,back_t>dsafe,l,dn,back_t=xn−xn−1,t−l.In equation (5), xn+1 and xn+1,t denote the positions of the preceding vehicles (Vehn+1) on the same (as Vehn) and target lanes, and dn,front and dn,front_t are the distances between Vehn and Vehn+1 on the same lane as well as on the target lane, respectively. In equation (6), dn,back_t refers to as the distance between Vehn and the vehicle behind it (Vehn−1) on the target lane, with xn−1,t being the position of Vehn−1, while dsafe,l represents the safe distance of lane changing. The incentive criterion indicates the condition under which the front vehicle Vehn+1 on the same lane (as Vehn) hinders the acceleration of Vehn (i.e., due to the short distance of dn,front), whereas the front vehicle Vehn+1 on the target lane provides the opportunity for Vehn’s acceleration (i.e., given the relatively long distance of dn,front_t). The safety criterion ensures the safety of Vehn after changing lanes. If both the criterions are met, Vehn will change lanes with the probability plc. It should be noted that lane changing rules only apply to vehicles on two-lane main roads.


#### 2.4.4. Merging Rules

The merging rules are designed in accordance with the three collaborative merging strategies described in Section2.3. Given the merging vehicle Vehm on the acceleration lane, let Lm (1 or 0) be a parameter indicating whether Vehm merges into the main road. If Lm=1, the vehicle will merge; otherwise, if Lm=0, the vehicle will not merge. The value of Lm is determined based on the following procedure (see Algorithm 1):Algorithm 1: The procedure for determining the value of Lm.
(1)
Initialization:Lm=0;(2)
Safety conditionifT1m≥0andT2m≥0 {//No-StrategiesLm=1;}else{merging strategies; //Strategies 1 or 2 or 3}(3)
Merging strategiesStrategy 1:ifT1m≥0andT2m<0 {if (T2m,front1>0){vm,front1=minvmax,vm,front1+S5m−S4m/ΔtifT2m≥0 {Lm=1;}}}Strategy 2:ifT1m<0andT2m≥0 {ifT1m,back1>0 {vm,back1=max0,vm,back1−S2m−S1m/ΔtifT1m≥0 {Lm=1;}}}Strategy 3:ifT1m<0andT2m<0 {ifT2m,front1>0{vm,front1=minvmax,vm,front1+S5m−S4m/Δt;}ifT1m,back1>0 {vm,back1=max0,vm,back1−S2m−S1m/Δt;}ifT2m≥0andT1m≥0 {Lm=1;}}where as defined in Section2.2, Sim (i = 1, 2, 4, 5) and Tjm (j = 1, 2) are the elements of the traffic state array Sm and thread array Tm of Vehm, while vm,front1 and vm,back1 are the speed of the nearest vehicles in front of and behind VehmVehm,front1andVehm,back1, respectively. Moreover, T2m,front1 and T1m,back1 denote the second and first elements of the threat array Tm,front1 and Tm,back1 of Vehm,front1 and Vehm,back1, respectively. Algorithm 1 in strategy 1 indicates that if T2m<0, Vehm,front1 should increase its speed in order to provide safe merging condition for Vehm, with S5m−S4m/Δt being the maximum acceleration of Vehm,front1 in order to ensure its own safety (i.e., it will not collide with Vehm,front2). Likewise, Algorithm 1 in strategy 2 requires that in the case of T1m<0, Vehm,back1 decreases its speed to provide merging condition for Vehm, with S2m−S1m/Δt being the maximum deceleration of Vehm,back1 to guarantee its safety (i.e., it will not be hit by Vehm,back2). Strategy 3 is the combination of the previous two strategies under the situation of T1m<0andT2m<0, which suggests that both Vehm,front1 accelerate and Vehm,back1 decelerate to try to provide merging condition for Vehm.(4)
MergingIfLm=1, Vehm will merge into the main road. Note that the merging operation and corresponding rules are only applicable to merging vehicles on the acceleration lane.


## 2.1. The Cellular Automata (CA) Model

The CA model is a discrete model method in time and space first 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 traffic flow, 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 reflect the evolution process of the traffic flow system.


## 2.2. Variable Definition

Vehm, the merging vehicle m on the acceleration lane;Vehm,back2 and Vehm,back1, the second and first (nearest) vehicles behind Vehm on the main road, respectively;Vehm,front1 and Vehm,front2, the first and second (nearest) vehicles in front of Vehm on the main road, respectively;xm, xm,back2, xm,back1, xm,front1 and xm,front2, the position of Vehm, Vehm,back2, Vehm,back1, Vehm,front1, and Vehm,front2, respectively;vm, vm,back2, vm,back1, vm,front1 and vm,front2, the velocity of Vehm, Vehm,back2, Vehm,back1, Vehm,front1, and Vehm,front2, respectively;Δt, the time step during which vehicles are updated in the CA model;Sm, the traffic state array of Vehm (defined in equation (1));Tm, the threat array of Vehm (defined in equation (2)).Some notations are shown in Figure1.Figure 1
Schematic diagram of an on-ramp system with an (a) one-lane main road and (b) a two-lane main road.
(a)(b)The state arraySm and threat array Tm of Vehm are defined as follows [8]:(1)Sm=S1m,S2m,S3m,S4m,S5m=xm,back2+vm,back2⋅Δt,xm,back1+vm,back1⋅Δt,xm+vm⋅Δt,xm,front1+vm,front1⋅Δt,xm,front2+vm,front2⋅Δt,(2)Tm=T1m,T2m=S3m−S2m,S4m−S3m−l−dsafe,t=S3m−S2m−l−dsafe,t,S4m−S3m−l−dsafe,t.In equation (1), Sim (i = 1,…,5) is the i th element in Sm, while in equation (2), l is the vehicle length, dsafe,t is the safety distance of merging strategies, and Tjm (j = 1, 2) is the j th element in Tm. The state array Sm represents the position (S3m) of vehicle Vehm as well as the positions (S1m,S2m,S4mandS5m) of the four nearest vehicles around Vehm after a time step (Δt). The threat array Tjm (j = 1, 2) refers to the relative distance (T1m) between Vehm and Vehm,back1 as well as the distance (T2m) between Vehm and Vehm,front1. The elements in Tm reflect whether Vehm has a collision after Δt. When Tjm (j = 1, 2) is greater than or equal to 0, no accident would occur; on the contrary, if Tjm is smaller than 0, a collision is likely to happen.


## 2.3. 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) defines the safety condition when Vehm merges into the main road.(3)T1m≥0,T2m≥0.Combining equations (2) and (3), we obtain(4)S3m−S2m−l−dsafe,t≥0,S4m−S3m−l−dsafe,t≥0.The first part of equation (4) shows that Vehm will not be hit by Vehm,back1 after merging, while the second part indicates that Vehm will not strike Vehm,front1 after merging. If equation (3) (or equation (4)) is satisfied, Vehm 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:Vehm,front1 accelerates to provide safety condition for VehmStrategy 2:Vehm,back1 decelerates to provide safety condition for VehmStrategy 3:Vehm,front1 accelerates and Vehm,back1 decelerates to provide safety condition for Vehm


## 2.4. Update Rules

The 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.


### 2.4.1. Entry Rules

The same entry rules as those proposed in Reference [12] are considered. The 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). The leftmost cells of the road serve as the entry area, and the number of the cells covered by this area is Δt⋅vmax (the maximum velocity of vehicles). Let xlast be the location of the current leftmost vehicle on the main lane (or ramp) before each time step (Δt) update. If xlast>vmax⋅Δt, a new vehicle will enter the position of minxlast−vmax⋅Δt,vmax⋅Δt on the main road (or ramp) with the probability of a1 (or a2).Figure 2
Schematic diagram of parameters in the update rules: (a) forward situation and (b) lane-changing situation.
(a)(b)


### 2.4.2. Forward Rules

The 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/Δt2), deceleration (deceleration rate is −1 cell/Δt2), randomization, and position updating after a time step.Step1: acceleration:vn⟶minvmax,vn+1cell/Δt;Step2: deceleration:vn⟶minvn,dn/Δt;Step3: randomization:vn⟶maxvn−1cell/Δt,0 with probability ps;Step4: position updating:xn⟶xn+vn⋅Δt, where xn and vn denote the position and velocity of the subject vehicle (represented as Vehn), respectively, and dn refers to as the distance between Vehn and the nearest vehicle Vehn+1 in front of it (see Figure 2(a)). Step 1 depicts the acceleration behavior of Vehn for which the speed should not reach the maximum velocity vmax of vehicles, while Step 2 reflects the deceleration behavior of Vehn to ensure that this vehicle is not hitting the vehicle in front of it. Step 3 represents the random deceleration behavior of Vehn.


### 2.4.3. Lane Changing Rules

The lane changing rules on the two-lane main road (see Figure2(b)) consist of two criterions as follows:(1)
Incentive criterion as follows:(5)dn,front<minvn+1⋅Δt,vmax⋅Δtanddn,front<dn,front_t,dn,front=xn+1−xn−l,dn,front_t=xn+1,t−xn−l.(2)
Safety criterion as follows:(6)dn,back_t>dsafe,l,dn,back_t=xn−xn−1,t−l.In equation (5), xn+1 and xn+1,t denote the positions of the preceding vehicles (Vehn+1) on the same (as Vehn) and target lanes, and dn,front and dn,front_t are the distances between Vehn and Vehn+1 on the same lane as well as on the target lane, respectively. In equation (6), dn,back_t refers to as the distance between Vehn and the vehicle behind it (Vehn−1) on the target lane, with xn−1,t being the position of Vehn−1, while dsafe,l represents the safe distance of lane changing. The incentive criterion indicates the condition under which the front vehicle Vehn+1 on the same lane (as Vehn) hinders the acceleration of Vehn (i.e., due to the short distance of dn,front), whereas the front vehicle Vehn+1 on the target lane provides the opportunity for Vehn’s acceleration (i.e., given the relatively long distance of dn,front_t). The safety criterion ensures the safety of Vehn after changing lanes. If both the criterions are met, Vehn will change lanes with the probability plc. It should be noted that lane changing rules only apply to vehicles on two-lane main roads.


### 2.4.4. Merging Rules

The merging rules are designed in accordance with the three collaborative merging strategies described in Section2.3. Given the merging vehicle Vehm on the acceleration lane, let Lm (1 or 0) be a parameter indicating whether Vehm merges into the main road. If Lm=1, the vehicle will merge; otherwise, if Lm=0, the vehicle will not merge. The value of Lm is determined based on the following procedure (see Algorithm 1):Algorithm 1: The procedure for determining the value of Lm.
(1)
Initialization:Lm=0;(2)
Safety conditionifT1m≥0andT2m≥0 {//No-StrategiesLm=1;}else{merging strategies; //Strategies 1 or 2 or 3}(3)
Merging strategiesStrategy 1:ifT1m≥0andT2m<0 {if (T2m,front1>0){vm,front1=minvmax,vm,front1+S5m−S4m/ΔtifT2m≥0 {Lm=1;}}}Strategy 2:ifT1m<0andT2m≥0 {ifT1m,back1>0 {vm,back1=max0,vm,back1−S2m−S1m/ΔtifT1m≥0 {Lm=1;}}}Strategy 3:ifT1m<0andT2m<0 {ifT2m,front1>0{vm,front1=minvmax,vm,front1+S5m−S4m/Δt;}ifT1m,back1>0 {vm,back1=max0,vm,back1−S2m−S1m/Δt;}ifT2m≥0andT1m≥0 {Lm=1;}}where as defined in Section2.2, Sim (i = 1, 2, 4, 5) and Tjm (j = 1, 2) are the elements of the traffic state array Sm and thread array Tm of Vehm, while vm,front1 and vm,back1 are the speed of the nearest vehicles in front of and behind VehmVehm,front1andVehm,back1, respectively. Moreover, T2m,front1 and T1m,back1 denote the second and first elements of the threat array Tm,front1 and Tm,back1 of Vehm,front1 and Vehm,back1, respectively. Algorithm 1 in strategy 1 indicates that if T2m<0, Vehm,front1 should increase its speed in order to provide safe merging condition for Vehm, with S5m−S4m/Δt being the maximum acceleration of Vehm,front1 in order to ensure its own safety (i.e., it will not collide with Vehm,front2). Likewise, Algorithm 1 in strategy 2 requires that in the case of T1m<0, Vehm,back1 decreases its speed to provide merging condition for Vehm, with S2m−S1m/Δt being the maximum deceleration of Vehm,back1 to guarantee its safety (i.e., it will not be hit by Vehm,back2). Strategy 3 is the combination of the previous two strategies under the situation of T1m<0andT2m<0, which suggests that both Vehm,front1 accelerate and Vehm,back1 decelerate to try to provide merging condition for Vehm.(4)
MergingIfLm=1, Vehm will merge into the main road. Note that the merging operation and corresponding rules are only applicable to merging vehicles on the acceleration lane.


## 2.4.1. Entry Rules

The same entry rules as those proposed in Reference [12] are considered. The 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). The leftmost cells of the road serve as the entry area, and the number of the cells covered by this area is Δt⋅vmax (the maximum velocity of vehicles). Let xlast be the location of the current leftmost vehicle on the main lane (or ramp) before each time step (Δt) update. If xlast>vmax⋅Δt, a new vehicle will enter the position of minxlast−vmax⋅Δt,vmax⋅Δt on the main road (or ramp) with the probability of a1 (or a2).Figure 2
Schematic diagram of parameters in the update rules: (a) forward situation and (b) lane-changing situation.
(a)(b)


## 2.4.2. Forward Rules

The 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/Δt2), deceleration (deceleration rate is −1 cell/Δt2), randomization, and position updating after a time step.Step1: acceleration:vn⟶minvmax,vn+1cell/Δt;Step2: deceleration:vn⟶minvn,dn/Δt;Step3: randomization:vn⟶maxvn−1cell/Δt,0 with probability ps;Step4: position updating:xn⟶xn+vn⋅Δt, where xn and vn denote the position and velocity of the subject vehicle (represented as Vehn), respectively, and dn refers to as the distance between Vehn and the nearest vehicle Vehn+1 in front of it (see Figure 2(a)). Step 1 depicts the acceleration behavior of Vehn for which the speed should not reach the maximum velocity vmax of vehicles, while Step 2 reflects the deceleration behavior of Vehn to ensure that this vehicle is not hitting the vehicle in front of it. Step 3 represents the random deceleration behavior of Vehn.


## 2.4.3. Lane Changing Rules

The lane changing rules on the two-lane main road (see Figure2(b)) consist of two criterions as follows:(1)
Incentive criterion as follows:(5)dn,front<minvn+1⋅Δt,vmax⋅Δtanddn,front<dn,front_t,dn,front=xn+1−xn−l,dn,front_t=xn+1,t−xn−l.(2)
Safety criterion as follows:(6)dn,back_t>dsafe,l,dn,back_t=xn−xn−1,t−l.In equation (5), xn+1 and xn+1,t denote the positions of the preceding vehicles (Vehn+1) on the same (as Vehn) and target lanes, and dn,front and dn,front_t are the distances between Vehn and Vehn+1 on the same lane as well as on the target lane, respectively. In equation (6), dn,back_t refers to as the distance between Vehn and the vehicle behind it (Vehn−1) on the target lane, with xn−1,t being the position of Vehn−1, while dsafe,l represents the safe distance of lane changing. The incentive criterion indicates the condition under which the front vehicle Vehn+1 on the same lane (as Vehn) hinders the acceleration of Vehn (i.e., due to the short distance of dn,front), whereas the front vehicle Vehn+1 on the target lane provides the opportunity for Vehn’s acceleration (i.e., given the relatively long distance of dn,front_t). The safety criterion ensures the safety of Vehn after changing lanes. If both the criterions are met, Vehn will change lanes with the probability plc. It should be noted that lane changing rules only apply to vehicles on two-lane main roads.


## 2.4.4. Merging Rules

The merging rules are designed in accordance with the three collaborative merging strategies described in Section2.3. Given the merging vehicle Vehm on the acceleration lane, let Lm (1 or 0) be a parameter indicating whether Vehm merges into the main road. If Lm=1, the vehicle will merge; otherwise, if Lm=0, the vehicle will not merge. The value of Lm is determined based on the following procedure (see Algorithm 1):Algorithm 1: The procedure for determining the value of Lm.
(1)
Initialization:Lm=0;(2)
Safety conditionifT1m≥0andT2m≥0 {//No-StrategiesLm=1;}else{merging strategies; //Strategies 1 or 2 or 3}(3)
Merging strategiesStrategy 1:ifT1m≥0andT2m<0 {if (T2m,front1>0){vm,front1=minvmax,vm,front1+S5m−S4m/ΔtifT2m≥0 {Lm=1;}}}Strategy 2:ifT1m<0andT2m≥0 {ifT1m,back1>0 {vm,back1=max0,vm,back1−S2m−S1m/ΔtifT1m≥0 {Lm=1;}}}Strategy 3:ifT1m<0andT2m<0 {ifT2m,front1>0{vm,front1=minvmax,vm,front1+S5m−S4m/Δt;}ifT1m,back1>0 {vm,back1=max0,vm,back1−S2m−S1m/Δt;}ifT2m≥0andT1m≥0 {Lm=1;}}where as defined in Section2.2, Sim (i = 1, 2, 4, 5) and Tjm (j = 1, 2) are the elements of the traffic state array Sm and thread array Tm of Vehm, while vm,front1 and vm,back1 are the speed of the nearest vehicles in front of and behind VehmVehm,front1andVehm,back1, respectively. Moreover, T2m,front1 and T1m,back1 denote the second and first elements of the threat array Tm,front1 and Tm,back1 of Vehm,front1 and Vehm,back1, respectively. Algorithm 1 in strategy 1 indicates that if T2m<0, Vehm,front1 should increase its speed in order to provide safe merging condition for Vehm, with S5m−S4m/Δt being the maximum acceleration of Vehm,front1 in order to ensure its own safety (i.e., it will not collide with Vehm,front2). Likewise, Algorithm 1 in strategy 2 requires that in the case of T1m<0, Vehm,back1 decreases its speed to provide merging condition for Vehm, with S2m−S1m/Δt being the maximum deceleration of Vehm,back1 to guarantee its safety (i.e., it will not be hit by Vehm,back2). Strategy 3 is the combination of the previous two strategies under the situation of T1m<0andT2m<0, which suggests that both Vehm,front1 accelerate and Vehm,back1 decelerate to try to provide merging condition for Vehm.(4)
MergingIfLm=1, Vehm will merge into the main road. Note that the merging operation and corresponding rules are only applicable to merging vehicles on the acceleration lane.


## 3. Simulation and Discussion

In order to study the influence of the different merging strategies on on-ramp systems, we use the CA model to simulate the systems under four different situations (including no-strategies and strategies 1–3). The 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). The other parameters are set based on the commonly adopted values of the existing research, including the maximum velocity vmax=5cells/time step (i.e. 135 km/h) [3]; the road length L=2000cells and starting position xon of the acceleration lane xon=L/2 [9] (i.e., 1000 cells); the length of the acceleration lane La=5 cells, randomization probability ps=0.3, lane-changing probability plc=0.8 and safe distance of lane changing dsafe,l=2cells (i.e., 15 m) [34]. Moreover, the safe distance of merging vehicles and time step are dsafe,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 different values of vehicle entering probabilitiesa1 (to the main road) and a2 (to the ramp). Let vm¯ and vr¯ be the average velocity of vehicles on the main road (upstream) and on the ramp and Figures 3(a)–3(d) and 4(a)–4(d) present the values of vm¯ and vr¯ in relation to the threshold vsvs=4.5cells/time step (121.5 km/h) for case 1 and case 2, respectively. In these figures, the green, blue, red, and black scatters (denoted by I, II, III, and IV) indicate the areas with (1) vm¯>vs and vr¯>vs, (2) vm¯>vs and vr¯<vs, (3) vm¯<vs and vr¯>vs, and (4) vm¯<vs and vr¯<vs, while the x-axis and y-axis represent the vehicle entering probabilities a1 and a2, respectively.Figure 3
Schematic diagram of the relationship between the average velocity and threshold in the case of (a) no-strategies and (b–d) different merging strategies (strategies 1–3), case 1.
(a)(b)(c)(d)Figure 4
Schematic diagram of the relationship between average velocity and threshold in the case of (a) no-strategies and (b)–(d) different merging strategies (strategies 1–3), case 2.
(a)(b)(c)(d)From Figures3(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 affect the velocity of vehicles on both the main road and ramp, when compared to no strategies (Figure 3(a)). Particularly, all the three strategies reduce the size of area II but increase that of area III, reflecting that there are less combined values of a1 and a2 for vm¯>vs and vr¯<vs but more for vm¯<vs and vr¯>vs. This further suggests that in relation to no strategies, strategies 1–3 can decrease the average velocity of vehicles on the main road when a1 and a2 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 traffic efficiency 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 Figures4(a)–4(d)) display different 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. This signifies that there are more combined values of a1 and a2 under which the average speed of vehicles on the main road and ramp is both high (i.e., vm¯>vs and vr¯>vs), but less combinations of these two probabilities for which the speed of vehicles on the roads is low (i.e., vm¯<vs and vr¯>vs). This 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 effect on the traffic condition of the whole system and leads to the speed of vehicles on the roads higher. When the different situations within case 2 were compared, similar trends to those within case 1 were observed. Specifically, 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 a1 and a2 are in the reduced-part-of-area-II while improving that on the ramp if a1 and a2 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 significantly reduces the traffic efficiency of the main road but increases that on the ramp.


### 3.2. Flow Rate

In addition to speed, the impact of the merging strategies on traffic flow rate (i.e., the number of vehicles passing a reference point per hour) was also inspected. Letfs and ft be the average upstream flow rate on the main road in case 1 and case 2, respectively, while fr be the flow rate on the ramp in both cases. Figures 5–10 visualize the evolution of the flow rates fs, ft, fr, fs+fr, and ft+fr, respectively, under different situations with various combinations of a1 and a2.Figure 5
Upstream traffic flow rate of the main road in the case of (a) no-strategy and (b)–(d) different merging strategies (strategies 1–3), case 1.
(a)(b)(c)(d)Figure 6
Upstream traffic flow rate of the main road in the case of (a) no-strategy and (b)–(d) different merging strategies (strategies 1–3), case 2.
(a)(b)(c)(d)Figure 7
Traffic flow rate of ramp in the case of (a) no-strategy and (b)–(d) different merging strategies (strategies 1–3), case 1.
(a)(b)(c)(d)Figure 8
Traffic flow rate of ramp in the case of (a) no-strategy and (b)–(d) different merging strategies (strategies 1–3), case 2.
(a)(b)(c)(d)Figure 9
Traffic flow rate of main road and ramp in the case of (a) no-strategy and (b)–(d) different merging strategies (strategies 1–3), case 1.
(a)(b)(c)(d)Figure 10
Traffic flow rate of main road and ramp in the case of (a) no-strategy and (b)–(d) different merging strategies (strategies 1–3), case 2.
(a)(b)(c)(d)(Note: in Figure7, in order to better display the changing trends of the z-variable, the x-axis and y-axis represent a2 and a1, respectively (instead of a1 and a2 in Figures 3–6). The same coordinate system is adopted in Figures 8 and 11).Figure 11
Traffic flow rate of the ramp with different strategies: ((a) strategy 1, (b) strategy 2, and (c) strategy 3), case 2,dsafe,t=2.
(a)(b)(c)From Figures5(a)–5(d), it was noted that when a2 is small (i.e., α2≤0.28), the flow rate fs of the main road in case 1 shows no large differences between no-strategies and the other three strategies, with fs reaching the largest value at a2=0 in all these situations. This demonstrates that the merging strategies have little impact on fs when the vehicle entering probability to the ramp is small. However, as a2 increases (a2>0.28), fs begins to be affected by the strategies and displays a decreasing trend. However, this effect is not unlimited, manifested by the observation that fs reduces until reaching a stable level (a “platform”). Moreover, the specific levels of the platforms vary among strategies, with strategy 1 having the highest level while strategy 3 displaying the lowest. This signifies that while all the strategies have a negative impact on the flow rate of the main road, strategy 3 causes the worst effect. A similar conclusion can be drawn for case 2 (in Figures 6(a)–6(d)), except that the threshold of a2 which initiates the impact is higher (a2>0.32). Moreover, the flow rate ft and the stable levels for the “platform” in case 2 are significantly higher than those in case 1 due to the adoption of the additional lane on the main road.Figures7(a)–7(d) and 8(a)–8(d) depict the (positive) impact of the merging strategies on the flow rate fr of the ramp in case 1 and case 2, respectively, showing that when a2 increases, fr rises and reaches a stable level (a “platform”). This points out that while the merging strategies decrease the traffic flow on the main road, they increase that on the ramp. Moreover, similar to the decreasing effect on the main road, the increasing impact on the ramp is not boundless, making the flow rate rising until to a stable level.Figures9(a)–9(d) and 10(a)–10(d) visualize the flow rate over the whole on-ramp system (i.e., the main road and ramp), for case 1 (i.e., fs+fr), and case 2 (i.e. ft+fr), respectively. It was observed that ft+fr is higher than fs+fr at most combined values of a1 and a2, especially when a1 and a2 are large. This suggests that it is more advantageous to set up a two-lane main road at merging sections. With respect to specific merging strategies, strategy 1 has almost no impact on fs+fr or ft+fr, while strategy 2 reduces fs+fr and ft+fr. In comparison, strategy 3 decreases fs+fr but does not bring changes to ft+fr.


### 3.3. Effect ofdsafe,t

Alongside the average velocity and flow rate, the effect of the merging safety distance parameterdsafe,t on whole systems was further examined. In this process, we first simulated the system with dsafe,t=2cells (while the other parameters remaining the same as the original simulation) and then, obtained the flow rate ft, fr, and ft+fr for case 2. Figures 11–13 visualize the values of these variables. When these figures were compared with Figures 6(b)–6(d) 8(b)–8(d), and 10(b)–10(d) (with dsafe,t=1cell in the original simulation), it shows that that when a1 and a2 are small, different values of dsafe,t have little effect on the flow of the on-ramp systems. However, when a2 becomes large, the increase of dsafe,t will increase ft, reduce fr, and reduce ft+fr. Therefore, setting the merging safety distance parameter too large may lead to a negative impact on the whole system.Figure 12
Traffic flow rate of the main road with different strategies: ((a) strategy 1, (b) strategy 2, and (c) strategy 3), case 2,dsafe,t=2.
(a)(b)(c)Figure 13
Traffic flow rate of the main road and ramp with different strategies: ((a) strategy 1, (b) strategy 2, and (c) strategy 3), case 2,dsafe,t=2.
(a)(b)(c)


## 3.1. Average Velocity

We obtained the average velocity of vehicles under each of the situations with different values of vehicle entering probabilitiesa1 (to the main road) and a2 (to the ramp). Let vm¯ and vr¯ be the average velocity of vehicles on the main road (upstream) and on the ramp and Figures 3(a)–3(d) and 4(a)–4(d) present the values of vm¯ and vr¯ in relation to the threshold vsvs=4.5cells/time step (121.5 km/h) for case 1 and case 2, respectively. In these figures, the green, blue, red, and black scatters (denoted by I, II, III, and IV) indicate the areas with (1) vm¯>vs and vr¯>vs, (2) vm¯>vs and vr¯<vs, (3) vm¯<vs and vr¯>vs, and (4) vm¯<vs and vr¯<vs, while the x-axis and y-axis represent the vehicle entering probabilities a1 and a2, respectively.Figure 3
Schematic diagram of the relationship between the average velocity and threshold in the case of (a) no-strategies and (b–d) different merging strategies (strategies 1–3), case 1.
(a)(b)(c)(d)Figure 4
Schematic diagram of the relationship between average velocity and threshold in the case of (a) no-strategies and (b)–(d) different merging strategies (strategies 1–3), case 2.
(a)(b)(c)(d)From Figures3(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 affect the velocity of vehicles on both the main road and ramp, when compared to no strategies (Figure 3(a)). Particularly, all the three strategies reduce the size of area II but increase that of area III, reflecting that there are less combined values of a1 and a2 for vm¯>vs and vr¯<vs but more for vm¯<vs and vr¯>vs. This further suggests that in relation to no strategies, strategies 1–3 can decrease the average velocity of vehicles on the main road when a1 and a2 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 traffic efficiency 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 Figures4(a)–4(d)) display different 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. This signifies that there are more combined values of a1 and a2 under which the average speed of vehicles on the main road and ramp is both high (i.e., vm¯>vs and vr¯>vs), but less combinations of these two probabilities for which the speed of vehicles on the roads is low (i.e., vm¯<vs and vr¯>vs). This 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 effect on the traffic condition of the whole system and leads to the speed of vehicles on the roads higher. When the different situations within case 2 were compared, similar trends to those within case 1 were observed. Specifically, 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 a1 and a2 are in the reduced-part-of-area-II while improving that on the ramp if a1 and a2 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 significantly reduces the traffic efficiency of the main road but increases that on the ramp.


## 3.2. Flow Rate

In addition to speed, the impact of the merging strategies on traffic flow rate (i.e., the number of vehicles passing a reference point per hour) was also inspected. Letfs and ft be the average upstream flow rate on the main road in case 1 and case 2, respectively, while fr be the flow rate on the ramp in both cases. Figures 5–10 visualize the evolution of the flow rates fs, ft, fr, fs+fr, and ft+fr, respectively, under different situations with various combinations of a1 and a2.Figure 5
Upstream traffic flow rate of the main road in the case of (a) no-strategy and (b)–(d) different merging strategies (strategies 1–3), case 1.
(a)(b)(c)(d)Figure 6
Upstream traffic flow rate of the main road in the case of (a) no-strategy and (b)–(d) different merging strategies (strategies 1–3), case 2.
(a)(b)(c)(d)Figure 7
Traffic flow rate of ramp in the case of (a) no-strategy and (b)–(d) different merging strategies (strategies 1–3), case 1.
(a)(b)(c)(d)Figure 8
Traffic flow rate of ramp in the case of (a) no-strategy and (b)–(d) different merging strategies (strategies 1–3), case 2.
(a)(b)(c)(d)Figure 9
Traffic flow rate of main road and ramp in the case of (a) no-strategy and (b)–(d) different merging strategies (strategies 1–3), case 1.
(a)(b)(c)(d)Figure 10
Traffic flow rate of main road and ramp in the case of (a) no-strategy and (b)–(d) different merging strategies (strategies 1–3), case 2.
(a)(b)(c)(d)(Note: in Figure7, in order to better display the changing trends of the z-variable, the x-axis and y-axis represent a2 and a1, respectively (instead of a1 and a2 in Figures 3–6). The same coordinate system is adopted in Figures 8 and 11).Figure 11
Traffic flow rate of the ramp with different strategies: ((a) strategy 1, (b) strategy 2, and (c) strategy 3), case 2,dsafe,t=2.
(a)(b)(c)From Figures5(a)–5(d), it was noted that when a2 is small (i.e., α2≤0.28), the flow rate fs of the main road in case 1 shows no large differences between no-strategies and the other three strategies, with fs reaching the largest value at a2=0 in all these situations. This demonstrates that the merging strategies have little impact on fs when the vehicle entering probability to the ramp is small. However, as a2 increases (a2>0.28), fs begins to be affected by the strategies and displays a decreasing trend. However, this effect is not unlimited, manifested by the observation that fs reduces until reaching a stable level (a “platform”). Moreover, the specific levels of the platforms vary among strategies, with strategy 1 having the highest level while strategy 3 displaying the lowest. This signifies that while all the strategies have a negative impact on the flow rate of the main road, strategy 3 causes the worst effect. A similar conclusion can be drawn for case 2 (in Figures 6(a)–6(d)), except that the threshold of a2 which initiates the impact is higher (a2>0.32). Moreover, the flow rate ft and the stable levels for the “platform” in case 2 are significantly higher than those in case 1 due to the adoption of the additional lane on the main road.Figures7(a)–7(d) and 8(a)–8(d) depict the (positive) impact of the merging strategies on the flow rate fr of the ramp in case 1 and case 2, respectively, showing that when a2 increases, fr rises and reaches a stable level (a “platform”). This points out that while the merging strategies decrease the traffic flow on the main road, they increase that on the ramp. Moreover, similar to the decreasing effect on the main road, the increasing impact on the ramp is not boundless, making the flow rate rising until to a stable level.Figures9(a)–9(d) and 10(a)–10(d) visualize the flow rate over the whole on-ramp system (i.e., the main road and ramp), for case 1 (i.e., fs+fr), and case 2 (i.e. ft+fr), respectively. It was observed that ft+fr is higher than fs+fr at most combined values of a1 and a2, especially when a1 and a2 are large. This suggests that it is more advantageous to set up a two-lane main road at merging sections. With respect to specific merging strategies, strategy 1 has almost no impact on fs+fr or ft+fr, while strategy 2 reduces fs+fr and ft+fr. In comparison, strategy 3 decreases fs+fr but does not bring changes to ft+fr.


## 3.3. Effect ofdsafe,t

Alongside the average velocity and flow rate, the effect of the merging safety distance parameterdsafe,t on whole systems was further examined. In this process, we first simulated the system with dsafe,t=2cells (while the other parameters remaining the same as the original simulation) and then, obtained the flow rate ft, fr, and ft+fr for case 2. Figures 11–13 visualize the values of these variables. When these figures were compared with Figures 6(b)–6(d) 8(b)–8(d), and 10(b)–10(d) (with dsafe,t=1cell in the original simulation), it shows that that when a1 and a2 are small, different values of dsafe,t have little effect on the flow of the on-ramp systems. However, when a2 becomes large, the increase of dsafe,t will increase ft, reduce fr, and reduce ft+fr. Therefore, setting the merging safety distance parameter too large may lead to a negative impact on the whole system.Figure 12
Traffic flow rate of the main road with different strategies: ((a) strategy 1, (b) strategy 2, and (c) strategy 3), case 2,dsafe,t=2.
(a)(b)(c)Figure 13
Traffic flow rate of the main road and ramp with different strategies: ((a) strategy 1, (b) strategy 2, and (c) strategy 3), case 2,dsafe,t=2.
(a)(b)(c)


## 4. Conclusion

In this paper, we first defined traffic state arrays (Sm) and thread arrays (Tm) 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 effect of these strategies on the speed and flow rate of on-ramp systems by means of CA simulation models. Finally, we examined the influence of the merging safety distance parameter (dsafe,t) on the operation efficiency 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 flow rate of the main road. (2) Nevertheless, these strategies have a different effect 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 one-lane main road, making the former system having higher operation efficiency than the latter under the same strategies. Thus, it is recommended that in an on-ramp system, a two-lane (even multiple-lane) main road should be considered. (3) The vehicles on the ramp and main road affect each other, and as the vehicle entering probabilities (a1 and a2) become large, the traffic flow rate on the main road decreases whereas that on the ramp increases. However, the effect is not unlimited. The flow rate on both roads finally reaches a stable level (forming a “platform”). (4) On the premise of ensuring safety, a small value of the merging safety distance parameter (dsafe,t) should be adopted, as a large value would cause a considerable decrease in the flow rate of the whole system.There are some limitations in this study, including the followings: (1) this study only considers three specific strategies, which is not complete, (2) the results derived through simulation should be further compared and verified with the experimental outcomes obtained from actual situations, and (3) the impact of more forward and lane changing rules (in addition to the current ones depicted in Sections2.4.2 and 2.4.3) on the results should be investigated. These drawbacks will be further addressed in the future research.



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*Source: 1375867-2023-01-16.xml*