# Research on Urban Traffic Active Control in Cooperative Vehicle Infrastructure

Authors: Li-li Zhang; Li Wang; Qi Zhao; Fang Wang; Yadongyang Zhu; Ling-yu Zhang
Journal: Journal of Advanced Transportation
 (2021)

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## Abstract

Urban intersection control mainly undertakes two tasks: traffic safety and traffic efficiency. Traditional intersection control models and methods have been insufficient in improving traffic efficiency, which is composed of the increase in traffic demand and the complexity of demand at present. In this paper, we propose a novel model and method called ATCM, which is based on the advanced technology of cooperative vehicle infrastructure. In this paper, a novel active traffic control model (ATCM) is proposed, which is based on the advanced technology of cooperative vehicle infrastructure. ATCM increases the intersection control model variables from the traditional two dimensions to five dimensions. It reshapes intersection control from the perspective of road designers and managers, so it can achieve more flexible and efficient traffic control. To this end, a multivariable active traffic control model is constructed, which includes road speed, lane control, sequence, phase, and green light time; a D-double layer optimization method is designed for this model. The first part of this optimization method combines speed control and dynamic phase sequence control. The second part is realized by the combination of lane control and dynamic phase sequence control. By conducting comprehensive experiments, the results demonstrate that the proposed approach is more flexible and efficient than traditional methods.


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## Body

## 1. Introduction

The essence of trafﬁc ﬂow change is that the trafﬁc demand matches the space-time resources. The trafﬁc control at the intersection is a way to allocate space-time resources based on ensuring trafﬁc safety. Therefore, the space-time resource variables which can accurately describe the characteristics of intersections directly affect the ﬂexibility and advancement of trafﬁc control.Today, the most widely used trafﬁc signal control systems (such as SCOOT [1, 2] and SCATS [3, 4]) use the expert experience to design static variables (lanes, phases, and phase sequences) at intersections and then use models and algorithms to implement the control strategy with the green light time as the main variable. However, the dynamic characteristics of the trafﬁc ﬂow often do not match well with the capacity of the road, which makes the traditional trafﬁc control based on the allocation of time resources difﬁcult to effectively allocate road space resources. Unfortunately, many road congestions are caused by insufﬁcient space resource allocation.In recent years, with the development of technologies such as cooperative vehicle infrastructure [5, 6] and autonomous driving [7–9], it has become possible to allocate space resources in real time; and what is encouraging is that it can reshape the traffic flow by changing the distribution of traffic demand when spatial resources really cannot meet the traffic demand of overload. This happens to solve a significant problem: “The shape of urban intersections, the number of lanes, and lane flow are designed based on historical traffic data and survey data. The designer of the intersection control strategy carries out signal control on its basis. However, it is worth thinking about that the growth of cars in many cities is very fast, and the design limit capacity of intersections will soon be broken. Some intersections have problems at the beginning of the operation. These problems have caused the design of intersections to fail to meet the needs of increasing traffic flow, and also lead to the failure of traffic control.”Surprisingly, although the new technology has been widely used in the ﬁeld of trafﬁc control [10, 11], it is still mainly based on the allocation of time resources in the traditional theoretical framework of trafﬁc control, and no one has tried to increase the dimension and further research on extended control capabilities. In this paper, a multivariable active control model for intersections is proposed, which is fully considered in the cooperative vehicle infrastructure technology. More specifically, a multivariable control model and optimization method including vehicle speed, lane, phase, phase sequence, and green light time is designed. It can reshape the traffic flow through control. It is called active control to distinguish the passive control of traditional traffic. The definition of active control is as follows: “Active control is the control that can influence the whole process of traffic flow from forming to passing through the intersection in terms of time and space.” Then traditional traffic control models and methods can be called passive control because some control methods can only affect the passage of traffic flow in time or space, while others can only affect the formation of traffic flow.The main contributions of this paper include the following:(i)
The multivariable active control model is a new intersection control model. It can not only adapt to traffic demand but also actively change traffic demand.(ii)
This model can effectively adapt and change different traffic flow requirements through the control of vehicle speed variables and lane variables to reduce the problem of intersection congestion caused by defects in intersection design.(iii)
This model allows designers and implementers of control algorithms to have greater flexibility and can create more optimized algorithms in cooperative vehicle infrastructure.The remainder of this paper is organized as follows: Section2 presents a literature review of related work. Section 3 proposes a multivariable active control model for intersections. Section 4 designs a D-double layer optimization method for the active control model. The first part of this optimization method combines speed control and dynamic phase sequence control. The second part is realized by the combination of lane control and dynamic phase sequence control. Section 5 describes the simulation experiments and presents the experimental results. Section 6 concludes this paper and discusses directions for future research.


## 2. Literature Review

Urban intersections control is an age-old issue that goes back to the 1950s [12]. This is the most important issue in the ﬁeld of urban trafﬁc, even in the future of vehicle-road collaboration and the popularity of autonomous driving. Therefore, it has attracted the attention of many scholars. Existing methods can be divided into two categories.


### 2.1. Passive Traffic Control

Based on the traditional urban road trafﬁc control theory, combining models and algorithms of modern control, intelligent control, and other theories have achieved considerable development and application in the ﬁeld of trafﬁc control. Modern control theory assumes that the mathematical model of the controlled object is known. Trafﬁc control methods based on modern control theory are mostly called model-based trafﬁc control theory and methods [10, 11, 13–16]. At the beginning of this century, the advancement of trafﬁc information and the development of detection technology have greatly improved the types and accuracy of trafﬁc detection data. At the same time, the explosive growth of road trafﬁc travel requirements has made traditional trafﬁc control methods stretched. People began to think about the data-driven trafﬁc control theory and method [17], because when it is difﬁcult to develop a model for a controlled system, the system input and output data can be used to implement control and decision-making.


### 2.2. Active Traffic Control

The abundance of traffic control data benefited from the development of information technology, and the theory of traffic control may therefore be changed. Therefore, some studies have proposed active traffic control. At present, there are two main types of research on active traffic control at intersections: One is the active control based on traffic flow prediction, which is realized by building a traffic flow prediction model combined with traditional traffic control [18–21]. The other is active control based on cooperative vehicle infrastructure, which combines vehicle speed guidance and traffic control to achieve active control through the use of cooperative vehicle infrastructure information [22–25].However, to the best of the authors’ knowledge, it is difficult to obtain satisfactory results in terms of the effectiveness and flexibility of current and future intersection control. There are two main reasons: One is that the limit capacity considered in the design of the intersection will soon be broken, and some intersections have problems at the beginning of the design. The existing research traffic control models and methods hardly consider this problem, so they often cause traffic control failures in practical applications. The other is that both traditional traffic control and active control are based on traditional traffic control theories. They only use phase, sequence, and green light time as control variables and their scalability and flexibility are not high. As a result, the application of traffic control in the development of technologies such as cooperative vehicle infrastructure and autonomous driving is restricted. It can be said that the collision between the flexibility of new theories and new technologies and the limitations of traditional traffic control cannot give full play to its true capabilities in the fettered traffic control system. Therefore, an effective way to solve this problem is to expand the set of control variables and to effectively allocate road time and space resources as the goal to build a multivariable active traffic control model at intersections.


## 2.1. Passive Traffic Control

Based on the traditional urban road trafﬁc control theory, combining models and algorithms of modern control, intelligent control, and other theories have achieved considerable development and application in the ﬁeld of trafﬁc control. Modern control theory assumes that the mathematical model of the controlled object is known. Trafﬁc control methods based on modern control theory are mostly called model-based trafﬁc control theory and methods [10, 11, 13–16]. At the beginning of this century, the advancement of trafﬁc information and the development of detection technology have greatly improved the types and accuracy of trafﬁc detection data. At the same time, the explosive growth of road trafﬁc travel requirements has made traditional trafﬁc control methods stretched. People began to think about the data-driven trafﬁc control theory and method [17], because when it is difﬁcult to develop a model for a controlled system, the system input and output data can be used to implement control and decision-making.


## 2.2. Active Traffic Control

The abundance of traffic control data benefited from the development of information technology, and the theory of traffic control may therefore be changed. Therefore, some studies have proposed active traffic control. At present, there are two main types of research on active traffic control at intersections: One is the active control based on traffic flow prediction, which is realized by building a traffic flow prediction model combined with traditional traffic control [18–21]. The other is active control based on cooperative vehicle infrastructure, which combines vehicle speed guidance and traffic control to achieve active control through the use of cooperative vehicle infrastructure information [22–25].However, to the best of the authors’ knowledge, it is difficult to obtain satisfactory results in terms of the effectiveness and flexibility of current and future intersection control. There are two main reasons: One is that the limit capacity considered in the design of the intersection will soon be broken, and some intersections have problems at the beginning of the design. The existing research traffic control models and methods hardly consider this problem, so they often cause traffic control failures in practical applications. The other is that both traditional traffic control and active control are based on traditional traffic control theories. They only use phase, sequence, and green light time as control variables and their scalability and flexibility are not high. As a result, the application of traffic control in the development of technologies such as cooperative vehicle infrastructure and autonomous driving is restricted. It can be said that the collision between the flexibility of new theories and new technologies and the limitations of traditional traffic control cannot give full play to its true capabilities in the fettered traffic control system. Therefore, an effective way to solve this problem is to expand the set of control variables and to effectively allocate road time and space resources as the goal to build a multivariable active traffic control model at intersections.


## 3. Active Control Model of Intersection

The intersection active traffic control model is composed of a time-space resource scheduling model and speed control model. The model is divided into two parts, the speed control area and the lane control area, as shown in Figure1.Figure 1
Building active traffic control model of intersection.The length of the lane control area isLj,a, and the length of the vehicle speed control area is Lj,b, as shown in Figure 2.Figure 2
Active traffic control model of intersection.


### 3.1. Time-Space Resource Scheduling Model

The intersection consists of an internal conflict area and upstream and downstream connecting sections, as shown in Figure3. Consider the state formula of link j in the set of connected links at the intersection by formula (1).Figure 3
Storage and forwarding model of intersection.(1)nj,ak+1=nj,ak+qj,a,ink−qj,a,outk.In the formula,nj,ak is the number of vehicles in period k on road j,a, qj,a,ink is the number of vehicles in period k entering road j,a, and qj,a,outk is the number of vehicles in period k leaving road j,a.


#### 3.1.1. The Space Variables [26]

To accurately characterize the dynamic characteristics of lane properties, the paper ﬁrst proposes the concept of “lane genes.” Then the turning properties of the lane change into a control variable. As shown in Figure4(a), the turning properties of the lane include left turn, straight turn, and right turn, which are described as L, T, and R.Figure 4
Intersection lane genome.
(a)(b)(2)Γj,ak=ϖj,a,oko=1,2,…,ωj,ak,Further, the smallest unit of traffic scheduling at the intersection is composed of the turning attribute of the entrance lane of the intersection and the downstream link. As shown in Figure4(b), j,a is the upstream road and o is the downstream road. Fj,ak=frj,akr=1,2,…,m is the lane gene expression combination in period k, where frj,ak represents the gene expression of lane r, frj,ak=Guj,a⟶rku=1,2,3, where Guj,a⟶rk is the gene of lane r and Guj,a⟶rk=0,if Gene doesn't be express1,Gene is express. A lane consists of three genes: G1, G2, and G3. G1⟶L means that the first gene map is turned left, G2⟶T means that the second gene map goes straight, and G3⟶R means that the third gene map is turned right.where Γj,ak is the set of spatial variables. ϖj,a,ok is the control variable, which is a function of the number of lanes, as shown in formula (3). ωj,ak=∑u=13GFj,ak∪u, and ωj,ak is the number of connections from road j,a to road o. Fj,ak∪=fr=1j,ak∪fr=2j,ak∪⋯∪fr=mj,ak, GFj,ak∪1 is the first gene in the lane set gene expression, GFj,ak∪2 is the second gene in the lane set gene expression, and GFj,ak∪3 is the third gene in the lane set gene expression.(3)ϖj,a,ok=ωoj,akm,ωoj,ak=∑i=1mGi,uj,a⟶ou=1,2,3,s.t.0<ϖj,a,ok≤1,where ϖoj,ak is the number of identical genes after lane gene expression.


#### 3.1.2. Integrated Model

From formulas (1) and (2), formula (4) can be obtained:(4)nj,ak+1=nj,ak+qj,a,ink−∑o=0minωj,ak,ωj,aXxkϖj,a,ok⋅Sj,a⋅gj,a,ok,where Sj,a is the capacity of the road section, gj,a,ok is the green light time of the phase of the road section j,a in the sampling period k, and gj,a,ok≥gj,a,min⋅gj,a,ok is obtained from the following solution space.


#### 3.1.3. Solution Space

The expression set of lane genome in all directions of the entrance section of the intersection is as follows:(5)Φxk=FIxkI=1,2,…,ε.A set of phase combinations of lanes in all directions of the entrance section of an intersection is as follows.When expressed in a fixed genome,(6)PΦxk=OIIΦxkII=1,2,…,σ.The set of the fixed phase combination time sequence of the lane in all directions of the entrance section of the intersection when a fixed gene is expressed is as follows:(7)ℜPΦxk=RIIIPΦxkIII=1,2,…,ς.From formulas (5)–(7), the solution space of lane gene, phase, and phase sequence relationship of intersection is obtained, as shown in Figure 5.Figure 5
Solution space.The solution space shown in Figure5 is described as a feasible solution gj,a,ok found in the solution space of formula (4) of the sampling period k. The feasible solution can be applied to formula (4) to adjust the time and space variables of green light. Formula (4) is used to adjust the time and space variables of green light.(8)Xx=∑I=1ε∑II=1σ∑III=1ςℵI,II,III,s.t.FIxk⟶OIIΦxk⟶RIIIPΦxk,where ωj,aXxk is to find a feasible solution in the constrained solution space of {gene, phase, phase sequence} within period k and the number of phases belonging to road j, a in the phase combination can be obtained, as shown in the following formula:(9)ωj,aXxk=Xx:OIIΦxk⊂j|FIxk,RIIIPΦxk.In the formula,o of the green time gj,a,ok and the spatial variable Γj,ak are related to the number of phases, so they can be represented by ωj,aXxk. minωj,ak,ωj,aXxk represents that the number of upstream and downstream links is not the same as the number of phases. The reason is that ωj,ak≥1ωj,aXxk≥0, and the upstream and downstream links cannot be disconnected, but the phases cannot be subordinate to the phase sequence within the sampling period k.


### 3.2. Speed Control Model

To realize the study of discrete state and speed control of urban road traffic flow, the basic road traffic flow operation condition is described, as shown in Figure6.Figure 6
Speed control model.It is described as follows: the current traffic flow density of roadj is equal to the sum of the traffic flow density of road j and the change in traffic flow density of road j,b in the previous time interval.(10)ρj,bk+1=ρj,bk+TLj,b⋅λj,bqj,b,ink−qj,b,outk,where road j,b is used as an example. qj,b,ink is the input flow of road j,b in period k. qj,b,outk is the output flow of road j,b in period k. vj,bk is the average speed of traffic flow on road j,b in period k. Q is the traffic flow density of road j,b in period k. Lj,b is the length of road j,b.The relationship between dynamic velocity and density parameter and expected velocity of roadj,b is constructed to describe the physical characteristics of traffic flow of road j,b according to formula (10). In the model, the dynamic velocity value in the k+1 sampling interval is equal to the deviation between the average vehicle velocity in the k sampling interval and the expected driver velocity Vρj,bk:(11)vj,bk+1=vj,bk+TτVρj,bk−vj,bk,where τ,υ is the model parameter and the expected velocity is(12)Vρj,bk=vj,b,free⋅exp−1αj,bρj,bkρj,b,critαj,b,where vj,b,free is the free flow velocity of road j,b, αj,b is the model parameter, and ρj,b,crit is the critical density of road j,b.


### 3.3. Active Control Model of Intersection

The active traffic control model of the intersection is composed of the temporal and spatial resource dynamic allocation model and the speed control model.Firstly, the store and forward form of the active traffic control model at intersections is as follows:(13)qj,b,outk=qj,b,ink−Lj,b⋅ρj,bk,nj,ak+1=nj,ak+qj,a,ink−qj,a,outk,where set qj,b,outk=qj,a,ink, and formula (1) is transformed into(14)nj,ak+1=nj,ak+qj,b,ink−Lj,b⋅ρj,bk−qj,a,outk.The complete form of the active traffic control model at the intersection is obtained from formulas (4) and (10):(15)nj,ak+1=nj,ak−Vk−Gk.Make(16)Vk=Lj,b⋅ρj,bk,Gk=qj,a,ink−∑o=0minnj,ak,nj,aΧxkϖj,a,ok⋅Sj,a⋅gj,a,ok.Putvk=vcrit⋅lnρjam/ρk into Vk to get Vk=Lj,b⋅exp−vj,bk/vj,b,crit. Put it into formula (16) to get(17)Vk=Lj,b⋅exp−vj,bkvj,b,crit,Gk=qj,a,ink−∑o=0minnj,ak,nj,aΧxkϖj,a,ok⋅Sj,a⋅gj,a,ok.


## 3.1. Time-Space Resource Scheduling Model

The intersection consists of an internal conflict area and upstream and downstream connecting sections, as shown in Figure3. Consider the state formula of link j in the set of connected links at the intersection by formula (1).Figure 3
Storage and forwarding model of intersection.(1)nj,ak+1=nj,ak+qj,a,ink−qj,a,outk.In the formula,nj,ak is the number of vehicles in period k on road j,a, qj,a,ink is the number of vehicles in period k entering road j,a, and qj,a,outk is the number of vehicles in period k leaving road j,a.


### 3.1.1. The Space Variables [26]

To accurately characterize the dynamic characteristics of lane properties, the paper ﬁrst proposes the concept of “lane genes.” Then the turning properties of the lane change into a control variable. As shown in Figure4(a), the turning properties of the lane include left turn, straight turn, and right turn, which are described as L, T, and R.Figure 4
Intersection lane genome.
(a)(b)(2)Γj,ak=ϖj,a,oko=1,2,…,ωj,ak,Further, the smallest unit of traffic scheduling at the intersection is composed of the turning attribute of the entrance lane of the intersection and the downstream link. As shown in Figure4(b), j,a is the upstream road and o is the downstream road. Fj,ak=frj,akr=1,2,…,m is the lane gene expression combination in period k, where frj,ak represents the gene expression of lane r, frj,ak=Guj,a⟶rku=1,2,3, where Guj,a⟶rk is the gene of lane r and Guj,a⟶rk=0,if Gene doesn't be express1,Gene is express. A lane consists of three genes: G1, G2, and G3. G1⟶L means that the first gene map is turned left, G2⟶T means that the second gene map goes straight, and G3⟶R means that the third gene map is turned right.where Γj,ak is the set of spatial variables. ϖj,a,ok is the control variable, which is a function of the number of lanes, as shown in formula (3). ωj,ak=∑u=13GFj,ak∪u, and ωj,ak is the number of connections from road j,a to road o. Fj,ak∪=fr=1j,ak∪fr=2j,ak∪⋯∪fr=mj,ak, GFj,ak∪1 is the first gene in the lane set gene expression, GFj,ak∪2 is the second gene in the lane set gene expression, and GFj,ak∪3 is the third gene in the lane set gene expression.(3)ϖj,a,ok=ωoj,akm,ωoj,ak=∑i=1mGi,uj,a⟶ou=1,2,3,s.t.0<ϖj,a,ok≤1,where ϖoj,ak is the number of identical genes after lane gene expression.


### 3.1.2. Integrated Model

From formulas (1) and (2), formula (4) can be obtained:(4)nj,ak+1=nj,ak+qj,a,ink−∑o=0minωj,ak,ωj,aXxkϖj,a,ok⋅Sj,a⋅gj,a,ok,where Sj,a is the capacity of the road section, gj,a,ok is the green light time of the phase of the road section j,a in the sampling period k, and gj,a,ok≥gj,a,min⋅gj,a,ok is obtained from the following solution space.


### 3.1.3. Solution Space

The expression set of lane genome in all directions of the entrance section of the intersection is as follows:(5)Φxk=FIxkI=1,2,…,ε.A set of phase combinations of lanes in all directions of the entrance section of an intersection is as follows.When expressed in a fixed genome,(6)PΦxk=OIIΦxkII=1,2,…,σ.The set of the fixed phase combination time sequence of the lane in all directions of the entrance section of the intersection when a fixed gene is expressed is as follows:(7)ℜPΦxk=RIIIPΦxkIII=1,2,…,ς.From formulas (5)–(7), the solution space of lane gene, phase, and phase sequence relationship of intersection is obtained, as shown in Figure 5.Figure 5
Solution space.The solution space shown in Figure5 is described as a feasible solution gj,a,ok found in the solution space of formula (4) of the sampling period k. The feasible solution can be applied to formula (4) to adjust the time and space variables of green light. Formula (4) is used to adjust the time and space variables of green light.(8)Xx=∑I=1ε∑II=1σ∑III=1ςℵI,II,III,s.t.FIxk⟶OIIΦxk⟶RIIIPΦxk,where ωj,aXxk is to find a feasible solution in the constrained solution space of {gene, phase, phase sequence} within period k and the number of phases belonging to road j, a in the phase combination can be obtained, as shown in the following formula:(9)ωj,aXxk=Xx:OIIΦxk⊂j|FIxk,RIIIPΦxk.In the formula,o of the green time gj,a,ok and the spatial variable Γj,ak are related to the number of phases, so they can be represented by ωj,aXxk. minωj,ak,ωj,aXxk represents that the number of upstream and downstream links is not the same as the number of phases. The reason is that ωj,ak≥1ωj,aXxk≥0, and the upstream and downstream links cannot be disconnected, but the phases cannot be subordinate to the phase sequence within the sampling period k.


## 3.1.1. The Space Variables [26]

To accurately characterize the dynamic characteristics of lane properties, the paper ﬁrst proposes the concept of “lane genes.” Then the turning properties of the lane change into a control variable. As shown in Figure4(a), the turning properties of the lane include left turn, straight turn, and right turn, which are described as L, T, and R.Figure 4
Intersection lane genome.
(a)(b)(2)Γj,ak=ϖj,a,oko=1,2,…,ωj,ak,Further, the smallest unit of traffic scheduling at the intersection is composed of the turning attribute of the entrance lane of the intersection and the downstream link. As shown in Figure4(b), j,a is the upstream road and o is the downstream road. Fj,ak=frj,akr=1,2,…,m is the lane gene expression combination in period k, where frj,ak represents the gene expression of lane r, frj,ak=Guj,a⟶rku=1,2,3, where Guj,a⟶rk is the gene of lane r and Guj,a⟶rk=0,if Gene doesn't be express1,Gene is express. A lane consists of three genes: G1, G2, and G3. G1⟶L means that the first gene map is turned left, G2⟶T means that the second gene map goes straight, and G3⟶R means that the third gene map is turned right.where Γj,ak is the set of spatial variables. ϖj,a,ok is the control variable, which is a function of the number of lanes, as shown in formula (3). ωj,ak=∑u=13GFj,ak∪u, and ωj,ak is the number of connections from road j,a to road o. Fj,ak∪=fr=1j,ak∪fr=2j,ak∪⋯∪fr=mj,ak, GFj,ak∪1 is the first gene in the lane set gene expression, GFj,ak∪2 is the second gene in the lane set gene expression, and GFj,ak∪3 is the third gene in the lane set gene expression.(3)ϖj,a,ok=ωoj,akm,ωoj,ak=∑i=1mGi,uj,a⟶ou=1,2,3,s.t.0<ϖj,a,ok≤1,where ϖoj,ak is the number of identical genes after lane gene expression.


## 3.1.2. Integrated Model

From formulas (1) and (2), formula (4) can be obtained:(4)nj,ak+1=nj,ak+qj,a,ink−∑o=0minωj,ak,ωj,aXxkϖj,a,ok⋅Sj,a⋅gj,a,ok,where Sj,a is the capacity of the road section, gj,a,ok is the green light time of the phase of the road section j,a in the sampling period k, and gj,a,ok≥gj,a,min⋅gj,a,ok is obtained from the following solution space.


## 3.1.3. Solution Space

The expression set of lane genome in all directions of the entrance section of the intersection is as follows:(5)Φxk=FIxkI=1,2,…,ε.A set of phase combinations of lanes in all directions of the entrance section of an intersection is as follows.When expressed in a fixed genome,(6)PΦxk=OIIΦxkII=1,2,…,σ.The set of the fixed phase combination time sequence of the lane in all directions of the entrance section of the intersection when a fixed gene is expressed is as follows:(7)ℜPΦxk=RIIIPΦxkIII=1,2,…,ς.From formulas (5)–(7), the solution space of lane gene, phase, and phase sequence relationship of intersection is obtained, as shown in Figure 5.Figure 5
Solution space.The solution space shown in Figure5 is described as a feasible solution gj,a,ok found in the solution space of formula (4) of the sampling period k. The feasible solution can be applied to formula (4) to adjust the time and space variables of green light. Formula (4) is used to adjust the time and space variables of green light.(8)Xx=∑I=1ε∑II=1σ∑III=1ςℵI,II,III,s.t.FIxk⟶OIIΦxk⟶RIIIPΦxk,where ωj,aXxk is to find a feasible solution in the constrained solution space of {gene, phase, phase sequence} within period k and the number of phases belonging to road j, a in the phase combination can be obtained, as shown in the following formula:(9)ωj,aXxk=Xx:OIIΦxk⊂j|FIxk,RIIIPΦxk.In the formula,o of the green time gj,a,ok and the spatial variable Γj,ak are related to the number of phases, so they can be represented by ωj,aXxk. minωj,ak,ωj,aXxk represents that the number of upstream and downstream links is not the same as the number of phases. The reason is that ωj,ak≥1ωj,aXxk≥0, and the upstream and downstream links cannot be disconnected, but the phases cannot be subordinate to the phase sequence within the sampling period k.


## 3.2. Speed Control Model

To realize the study of discrete state and speed control of urban road traffic flow, the basic road traffic flow operation condition is described, as shown in Figure6.Figure 6
Speed control model.It is described as follows: the current traffic flow density of roadj is equal to the sum of the traffic flow density of road j and the change in traffic flow density of road j,b in the previous time interval.(10)ρj,bk+1=ρj,bk+TLj,b⋅λj,bqj,b,ink−qj,b,outk,where road j,b is used as an example. qj,b,ink is the input flow of road j,b in period k. qj,b,outk is the output flow of road j,b in period k. vj,bk is the average speed of traffic flow on road j,b in period k. Q is the traffic flow density of road j,b in period k. Lj,b is the length of road j,b.The relationship between dynamic velocity and density parameter and expected velocity of roadj,b is constructed to describe the physical characteristics of traffic flow of road j,b according to formula (10). In the model, the dynamic velocity value in the k+1 sampling interval is equal to the deviation between the average vehicle velocity in the k sampling interval and the expected driver velocity Vρj,bk:(11)vj,bk+1=vj,bk+TτVρj,bk−vj,bk,where τ,υ is the model parameter and the expected velocity is(12)Vρj,bk=vj,b,free⋅exp−1αj,bρj,bkρj,b,critαj,b,where vj,b,free is the free flow velocity of road j,b, αj,b is the model parameter, and ρj,b,crit is the critical density of road j,b.


## 3.3. Active Control Model of Intersection

The active traffic control model of the intersection is composed of the temporal and spatial resource dynamic allocation model and the speed control model.Firstly, the store and forward form of the active traffic control model at intersections is as follows:(13)qj,b,outk=qj,b,ink−Lj,b⋅ρj,bk,nj,ak+1=nj,ak+qj,a,ink−qj,a,outk,where set qj,b,outk=qj,a,ink, and formula (1) is transformed into(14)nj,ak+1=nj,ak+qj,b,ink−Lj,b⋅ρj,bk−qj,a,outk.The complete form of the active traffic control model at the intersection is obtained from formulas (4) and (10):(15)nj,ak+1=nj,ak−Vk−Gk.Make(16)Vk=Lj,b⋅ρj,bk,Gk=qj,a,ink−∑o=0minnj,ak,nj,aΧxkϖj,a,ok⋅Sj,a⋅gj,a,ok.Putvk=vcrit⋅lnρjam/ρk into Vk to get Vk=Lj,b⋅exp−vj,bk/vj,b,crit. Put it into formula (16) to get(17)Vk=Lj,b⋅exp−vj,bkvj,b,crit,Gk=qj,a,ink−∑o=0minnj,ak,nj,aΧxkϖj,a,ok⋅Sj,a⋅gj,a,ok.


## 4. Optimization Method

The active control method of the intersection is designed to meet the characteristics of the mixed scene and the requirements of the control goal. Firstly, the current scene of the intersection needs to be accurately identified. Secondly, the objective function is determined based on the identified scene, and then the matching control strategy will be selected. Thirdly, it is necessary to judge whether the capacity coefficient exceeds the critical value when performing phase control. If the critical value is exceeded, boundary control will be activated. Finally, it is necessary to judge whether the capacity exceeds the critical value when performing boundary control. If the critical value is exceeded, lane control will be activated. The active control of the intersection is realized by a two-layer optimization algorithm, as shown in Figure7.Figure 7
Structure of active control at the intersection.


### 4.1. Objective Function Set

The mixed scene characteristics of the intersection determine the difference of the control objective function. Considering the unity of objective function design, the lower control objective of the two-layer optimization method is as follows:(18)minαJTTS+βJSTS,s.t.α+β=1,where JTTS represents the travel time of all vehicles at the intersection; JSTS represents the travel time of a special vehicle.The choice of weight coefficient is determined by the scene of the intersection. Here are a few examples:(1)
When the scene at the intersection is a common scene, it is to minimize the total travel time of vehicles passing at the intersection as the objective function.(2)
When the scene at the intersection is a special scene of emergency vehicles, it is to minimize the travel time for emergency vehicles to pass through the intersection as the objective function.(3)
When the scene at the intersection is a special scene of bus priority vehicles, it is to minimize the travel time of bus priority vehicles and all other passing vehicles at the intersection as the objective function.The difference in starting order and conditions between speed control and lane control should be considered. The upper control objectives of the two-layer optimization method are characterized by time continuity and form unity. The upper control objective of the two-layer optimization method is as follows:(19)maxt⟶ΔJst.Make(20)limt⟶τJst−Js¯=ε,limt⟶πJst−Js¯=ε,s.t.t⟶τ⟶π,where Js¯=0 represents the critical value of the capacity coefficient; ε⟶0 is the minimum.


### 4.2. Control of Dynamic Phase and Virtual Phase

Dynamic phase control adopts the phase control algorithm of model predictive control. The particularity of bus priority and emergency control is considered. The dynamic phase control algorithm is extended and a control algorithm combining dynamic phase and virtual phase is adopted. It is an extension of the length of the control chain in the dynamic phase control algorithm, where the last phase of the predictive control chain is defined as a virtual phase to respond to the control requirements in special scenarios. Among them, the virtual phase description does not specify a specific phase type. When a special scene requires its expression, the best phase is selected in the intersection phase set to respond.A control algorithm combining the dynamic phase and virtual phase is shown in Figure8. When a special scene appears, the virtual phase is activated. At this time, its input is the traffic and queuing at the intersection when a certain phase is executed in the sampling period k. Then, the candidate phase to be executed in the next step is to search for n phases that match the currently executed phase in the solution space. Finally, the generation of the control chain is to select m consecutively executed phases in each candidate phase. J=minαJTTS+βJSTS,s.t.α+β=1 is taken as the objective function. According to the adjustment weight value, the form of the objective function is changed. The GA algorithm is used to execute n control chains and rank the resulting J of n control chains. The first phase of the control chain with the minimum J obtained as a result is regarded as the next execution phase of the current phase, and the obtained interval time, phase, and green light time are used as output.Figure 8
The control algorithm of dynamic phase and virtual phase combination.


### 4.3. Two-Layer Optimization 1: Speed Control

As shown in Figure9, the combination of speed control and dynamic phase and its extended control methods form the internal and external control areas of the intersection with boundary characteristics. They are called speed control zones and lane control zones. The boundary control idea is adopted. It determines whether to start speed control by judging the change of JS. It can achieve the purpose of reducing the number of vehicles in the control area by suppressing the input flow.Figure 9
Boundary control.Two-level optimization 1 uses a two-level programming algorithm. The basis of the upper-level planning is the speed control of the speed control area in Figure9. When theJS control area reaches the critical value, it means that the traffic capacity has reached the limit. At this time, formula (21) is used as the objective function of the upper-level planning:(21)Jupt=maxt⟶ΔJst=maxt⟶ΔJMt−JNt.The specific form of upper-level planning constraints and capacity coefficientJS is as follows:(22)JM=∑j=1nSj,a⋅gj,a,ok∑j=1nSj,a⋅gj,a,ok+Δnj,ak/nj,a¯,JN=∑i=1nΔnj,ak/nj,a¯∑j=1nSj,a⋅gj,a,ok+Δnj,ak/nj,a¯,Δnj,ak=nj,ak+1−nj,ak=−Vk−Gklimt⟶τJsk−Js¯=ε.The objective function and constraint conditions of the lower-level planning adopt formula (21). The lower-level planning solution of the two-level optimization 1 uses a combination of dynamic phase and virtual phase control algorithm.


### 4.4. Two-Layer Optimization 2: Lane Control

Two-layer optimization 2 uses a two-level planning algorithm composed of dynamic phase and virtual phase control and lane control. The objective functions of the upper and lower layers need to follow the requirements of the objective function set above, and the time when the lane control is activated is determined bylimt⟶τJst−Js¯=ε,limt⟶πJst−Js¯=ε,s.t.t⟶τ⟶π.


### 4.5. Algorithm for Active Control of Intersection

The algorithm flow is shown in Figure10 and the algorithm steps are shown in Algorithm 1.Figure 10
Algorithm flow of active control of intersection.Algorithm 1: Algorithm steps.
Stage 1: startStep 1.1: data collection and scene recognitionStep 1.2: it judges whether the scene recognized by Step 1.1 is a special scene. If it is, the dynamic phase and virtual phase combination control are activated at the current intersection. First, the virtual phase is activated, and the best phase suitable for the scene is selected for control in the phase set of the intersection. The imaginary phase can be the continuation of the current phase or any phase in the phase set. The optimization of the objective function corresponding to the scene determines whether it is the best phase, and outputs {virtual phase, phase sequence, green light time}. Otherwise, go to Step 1.3.Step 1.3: the dynamic phase control is activated and {phase, phase sequence, green time} is output.Step 1.4: go to stage 2.Stage 2: two-layer optimization 1Step 2.1: ifJS≥0 exists for n consecutive sampling periods, go to Step 1.1. Otherwise, go to Step 2.2.Step 2.2: if there isJS=0 for n consecutive sampling periods, the speed control is activated and the output {phase/virtual phase, phase sequence, green time, speed}. If there is JS≥0 for n consecutive sampling periods, if it is, go to Step 1.1. Otherwise, go to Step 2.3.Step 2.3: go to stage 3;Stage 3: two-layer optimization 2Step 3.1: ifJS=0 exists for n consecutive sampling periods, lane control is activated. The lane attributes, phase set, and control chain of the intersection are updated, and output {phase/virtual phase, phase sequence, green time, speed, lane}, and Go to Stage 1.


## 4.1. Objective Function Set

The mixed scene characteristics of the intersection determine the difference of the control objective function. Considering the unity of objective function design, the lower control objective of the two-layer optimization method is as follows:(18)minαJTTS+βJSTS,s.t.α+β=1,where JTTS represents the travel time of all vehicles at the intersection; JSTS represents the travel time of a special vehicle.The choice of weight coefficient is determined by the scene of the intersection. Here are a few examples:(1)
When the scene at the intersection is a common scene, it is to minimize the total travel time of vehicles passing at the intersection as the objective function.(2)
When the scene at the intersection is a special scene of emergency vehicles, it is to minimize the travel time for emergency vehicles to pass through the intersection as the objective function.(3)
When the scene at the intersection is a special scene of bus priority vehicles, it is to minimize the travel time of bus priority vehicles and all other passing vehicles at the intersection as the objective function.The difference in starting order and conditions between speed control and lane control should be considered. The upper control objectives of the two-layer optimization method are characterized by time continuity and form unity. The upper control objective of the two-layer optimization method is as follows:(19)maxt⟶ΔJst.Make(20)limt⟶τJst−Js¯=ε,limt⟶πJst−Js¯=ε,s.t.t⟶τ⟶π,where Js¯=0 represents the critical value of the capacity coefficient; ε⟶0 is the minimum.


## 4.2. Control of Dynamic Phase and Virtual Phase

Dynamic phase control adopts the phase control algorithm of model predictive control. The particularity of bus priority and emergency control is considered. The dynamic phase control algorithm is extended and a control algorithm combining dynamic phase and virtual phase is adopted. It is an extension of the length of the control chain in the dynamic phase control algorithm, where the last phase of the predictive control chain is defined as a virtual phase to respond to the control requirements in special scenarios. Among them, the virtual phase description does not specify a specific phase type. When a special scene requires its expression, the best phase is selected in the intersection phase set to respond.A control algorithm combining the dynamic phase and virtual phase is shown in Figure8. When a special scene appears, the virtual phase is activated. At this time, its input is the traffic and queuing at the intersection when a certain phase is executed in the sampling period k. Then, the candidate phase to be executed in the next step is to search for n phases that match the currently executed phase in the solution space. Finally, the generation of the control chain is to select m consecutively executed phases in each candidate phase. J=minαJTTS+βJSTS,s.t.α+β=1 is taken as the objective function. According to the adjustment weight value, the form of the objective function is changed. The GA algorithm is used to execute n control chains and rank the resulting J of n control chains. The first phase of the control chain with the minimum J obtained as a result is regarded as the next execution phase of the current phase, and the obtained interval time, phase, and green light time are used as output.Figure 8
The control algorithm of dynamic phase and virtual phase combination.


## 4.3. Two-Layer Optimization 1: Speed Control

As shown in Figure9, the combination of speed control and dynamic phase and its extended control methods form the internal and external control areas of the intersection with boundary characteristics. They are called speed control zones and lane control zones. The boundary control idea is adopted. It determines whether to start speed control by judging the change of JS. It can achieve the purpose of reducing the number of vehicles in the control area by suppressing the input flow.Figure 9
Boundary control.Two-level optimization 1 uses a two-level programming algorithm. The basis of the upper-level planning is the speed control of the speed control area in Figure9. When theJS control area reaches the critical value, it means that the traffic capacity has reached the limit. At this time, formula (21) is used as the objective function of the upper-level planning:(21)Jupt=maxt⟶ΔJst=maxt⟶ΔJMt−JNt.The specific form of upper-level planning constraints and capacity coefficientJS is as follows:(22)JM=∑j=1nSj,a⋅gj,a,ok∑j=1nSj,a⋅gj,a,ok+Δnj,ak/nj,a¯,JN=∑i=1nΔnj,ak/nj,a¯∑j=1nSj,a⋅gj,a,ok+Δnj,ak/nj,a¯,Δnj,ak=nj,ak+1−nj,ak=−Vk−Gklimt⟶τJsk−Js¯=ε.The objective function and constraint conditions of the lower-level planning adopt formula (21). The lower-level planning solution of the two-level optimization 1 uses a combination of dynamic phase and virtual phase control algorithm.


## 4.4. Two-Layer Optimization 2: Lane Control

Two-layer optimization 2 uses a two-level planning algorithm composed of dynamic phase and virtual phase control and lane control. The objective functions of the upper and lower layers need to follow the requirements of the objective function set above, and the time when the lane control is activated is determined bylimt⟶τJst−Js¯=ε,limt⟶πJst−Js¯=ε,s.t.t⟶τ⟶π.


## 4.5. Algorithm for Active Control of Intersection

The algorithm flow is shown in Figure10 and the algorithm steps are shown in Algorithm 1.Figure 10
Algorithm flow of active control of intersection.Algorithm 1: Algorithm steps.
Stage 1: startStep 1.1: data collection and scene recognitionStep 1.2: it judges whether the scene recognized by Step 1.1 is a special scene. If it is, the dynamic phase and virtual phase combination control are activated at the current intersection. First, the virtual phase is activated, and the best phase suitable for the scene is selected for control in the phase set of the intersection. The imaginary phase can be the continuation of the current phase or any phase in the phase set. The optimization of the objective function corresponding to the scene determines whether it is the best phase, and outputs {virtual phase, phase sequence, green light time}. Otherwise, go to Step 1.3.Step 1.3: the dynamic phase control is activated and {phase, phase sequence, green time} is output.Step 1.4: go to stage 2.Stage 2: two-layer optimization 1Step 2.1: ifJS≥0 exists for n consecutive sampling periods, go to Step 1.1. Otherwise, go to Step 2.2.Step 2.2: if there isJS=0 for n consecutive sampling periods, the speed control is activated and the output {phase/virtual phase, phase sequence, green time, speed}. If there is JS≥0 for n consecutive sampling periods, if it is, go to Step 1.1. Otherwise, go to Step 2.3.Step 2.3: go to stage 3;Stage 3: two-layer optimization 2Step 3.1: ifJS=0 exists for n consecutive sampling periods, lane control is activated. The lane attributes, phase set, and control chain of the intersection are updated, and output {phase/virtual phase, phase sequence, green time, speed, lane}, and Go to Stage 1.


## 5. Simulation Experiment

### 5.1. Simulation Environment

The six scenarios in the paper are designed for comparison with traditional methods that include undersaturation, oversaturation, undersaturation and bus priority, oversaturation and bus priority, undersaturation and emergency vehicles, and oversaturation and emergency vehicles, which are divided into three groups for experiments. The self-developed Open Simulation Platform (OSP) is used for experiments. The simulated road network is shown in Figure11, and the specific parameter settings are shown in Table 1.Figure 11
Road simulation of OSP.Table 1
Basic parameters of the simulation.
ParameterContentRoadThe road network is 3∗3 intersections; the length of the intersection connecting section is 470 m−490 m; the section uses two-way 4 lanes, and the channelization is set at 30 meters at the entrance of the intersection. The width is 3.5 mVehicleThe speed distribution is [20 km/h, 60 km/h], the ratio of vehicle types is 1 : 99 (large cars: small cars), and the ratio of buses to emergency vehicles is 99 : 1 in the large carFlowInitial: the flow of stage 1 is 1000 v/h; the flow of stage 2 is 500 v/h; the flow of stage 3 is 1000 v/h; the flow of stage 4 is 500 v/h. Every 3600 s multiply the flow of each stage by the coefficient of changex, 0.5 < x < 2Intersection and signal controlThe intersections are numbered A, B, E, F, H, I, L, N, and O, the number of which that is controlled in this chapter is F; except for intersection F, all other intersections are controlled by 4-stage signal lights. The stages are stage1: north-south straight; stage2: north-south left; stage3: east-west straight; stage4: turn left from east to west; straight-right vehicles and straight-going vehicles are released at the same time; the signal control period is 120 s; the interval time is 3 s for yellow light and 2 s for all red; Tstage1 is 35 s, Tstage2 is 15 s; Tstage3 is 35 s; and Tstage4 is 15 sScenariosUndersaturation, oversaturation, undersaturation and bus priority, oversaturation and bus priority, undersaturation and emergency vehicles, and oversaturation and emergency vehiclesData collectionCollect the road section number, lane number, whole road section density, flow, and vehicle speed. The acquisition interval is 600 sEvaluation parametersThe average number of stops and average delay timeA further explanation for the experiment is as follows:Traditional control methods are generally pertinent; that is, different scenarios will adopt adaptive control methods.(1)
For the reasonableness of comparison, in the first set of {undersaturated and oversaturated} two scenarios, the comparison is with timing control; in the second set of {undersaturated and bus priority, oversaturated and bus priority} two scenarios, the comparison is with traditional bus priority control [27] (using phase green light extension and red light shortening); in the third set of {undersaturated and emergency vehicles, oversaturated and emergency vehicles} two scenarios, the comparison is with traditional emergency vehicle control [28] (using trigger response; that is, when a traffic request is detected, the phase is locked or jumped immediately).(2)
In the simulation, the detection points are used to replace the commonly used RFID detectors in practice, and the detection points are, respectively, arranged at positions about 150 m away from the parking line.(3)
All buses appearing in the simulation are subject to public transportation priority control, and all emergency vehicles appearing are subject to emergency priority control.(4)
In the simulation, select the objective function parametersα and β: in the first set of scenarios {undersaturated, oversaturated}, set α=1,β=0; that is, consider the minimum total travel time of vehicles passing through the intersection as the objective function. In the second set of scenarios {undersaturation and bus priority, oversaturation and bus priority}, set α=0,β=1; that is, consider the minimum travel time of bus priority vehicles passing through the intersection as the objective function. In the third set of scenarios {undersaturated and emergency vehicles, oversaturated and emergency vehicles}, set α=0,β=1; that is, consider the minimum travel time of emergency vehicles through the intersection as the objective function (the purpose of choosing the objective function parameters in this way is to be consistent with the traditional comparison of control methods).


### 5.2. Analysis Results

#### 5.2.1. The First Set of Scenes: {Undersaturated, Oversaturated}

Figure12 shows the change of the capacity coefficient JS when the two scenarios included in the first group are compared. It can be seen from Figure 12 that the time to reach the JS threshold is later when using the method in this paper than when using the traditional control method. Arrow 1 (speed control) shown in the figure indicates that JS<0, and the speed control is started, but it is found that JS of the next data point is further reduced, indicating that the speed control can no longer control the decline of JS at this time, and then start lane control shown in Figure 12, due to the subsequent improvement of the traffic state and the effect of lane control, makes JS return to the control threshold.Figure 12
Change of capacity coefficient.Figures13(a) and 13(b), respectively, show the average number of stops and average delay time of vehicles passing through the intersection in the first set of scenarios. It can be seen from Figure 13 that the control effect of the active control method proposed in this article is better than that of the traditional control method in the two scenarios of undersaturation and oversaturation.Figure 13
The contrast of control effect of the first set of scenarios. (a) Average number of vehicle stops at intersections. (b) Average delay time of vehicle at the intersection.
(a)(b)


#### 5.2.2. The Second Set of Scenarios: {Undersaturation and Bus Priority, Oversaturation and Bus Priority}

Figures14(a) and 14(b), respectively, show the average number of stops and average delay time of buses passing through the intersection in the second set of scenarios. It can be seen from Figure 14 that, in the scenario of undersaturation and bus priority, the control effect of the active control method proposed in this article is similar to that of the traditional control method; however, as the traffic flow changes, the scene changes from undersaturation and bus priority to oversaturation and bus priority scenario, and the control effect of the active control method proposed in this paper is better than that of the traditional control method.Figure 14
The contrast of control effect of the second set of scenarios. (a) Average number of bus stops. (b) Average delay time of the bus.
(a)(b)


#### 5.2.3. The Third Set of Scenes: {Undersaturated and Emergency Vehicles, Oversaturated and Emergency Vehicles}

Figures15(a) and 15(b), respectively, show the average number of stops and average delay time of buses passing through the intersection in the third set of scenarios. It can be seen from Figure 15 that, in the scenario of undersaturated and emergency vehicles, the control effect of the active control method proposed in this article is similar to that of the traditional control method; and in the scenario of oversaturated and emergency vehicle, the control effect of the active control method proposed in this paper is better than that of the traditional control method.Figure 15
The contrast of control effect of the third set of scenarios. (a) Average number emergency vehicle stops. (b) Average delay time of emergency vehicle.
(a)(b)As shown in Table2, compared with the traditional method, in the first set of scenarios, the average parking delay time at intersections is reduced by 35.93%%, and the average number of stops is 31.80%; in the second set of scenarios, the average bus parking delay time is reduced by 22.35%, and the average number of parking times is 26.58%; in the third group of scenarios, the average parking delay time of emergency vehicles is reduced by 14.81%, and the average number of parking times is 47.06%. It can be seen that the method in this paper can give suitable control responses for different scenarios, which is very efficient in traffic.Table 2
Comparison of simulation results of control methods.
Experimental sceneMethodEvaluation parametersResultsImproveThe first set of scenesTraditionalAverage stops92.4—PaperAverage delay time59.235.93%TraditionalAverage stops2.41—PaperAverage delay time1.6431.80%The second set of scenesTraditionalAverage stops50.1—PaperAverage delay time38.422.35%TraditionalAverage stops0.79—PaperAverage delay time0.5826.58%The third set of scenesTraditionalAverage stops16.2—PaperAverage delay time13.814.81%TraditionalAverage stops0.17—PaperAverage delay time0.0947.06%


## 5.1. Simulation Environment

The six scenarios in the paper are designed for comparison with traditional methods that include undersaturation, oversaturation, undersaturation and bus priority, oversaturation and bus priority, undersaturation and emergency vehicles, and oversaturation and emergency vehicles, which are divided into three groups for experiments. The self-developed Open Simulation Platform (OSP) is used for experiments. The simulated road network is shown in Figure11, and the specific parameter settings are shown in Table 1.Figure 11
Road simulation of OSP.Table 1
Basic parameters of the simulation.
ParameterContentRoadThe road network is 3∗3 intersections; the length of the intersection connecting section is 470 m−490 m; the section uses two-way 4 lanes, and the channelization is set at 30 meters at the entrance of the intersection. The width is 3.5 mVehicleThe speed distribution is [20 km/h, 60 km/h], the ratio of vehicle types is 1 : 99 (large cars: small cars), and the ratio of buses to emergency vehicles is 99 : 1 in the large carFlowInitial: the flow of stage 1 is 1000 v/h; the flow of stage 2 is 500 v/h; the flow of stage 3 is 1000 v/h; the flow of stage 4 is 500 v/h. Every 3600 s multiply the flow of each stage by the coefficient of changex, 0.5 < x < 2Intersection and signal controlThe intersections are numbered A, B, E, F, H, I, L, N, and O, the number of which that is controlled in this chapter is F; except for intersection F, all other intersections are controlled by 4-stage signal lights. The stages are stage1: north-south straight; stage2: north-south left; stage3: east-west straight; stage4: turn left from east to west; straight-right vehicles and straight-going vehicles are released at the same time; the signal control period is 120 s; the interval time is 3 s for yellow light and 2 s for all red; Tstage1 is 35 s, Tstage2 is 15 s; Tstage3 is 35 s; and Tstage4 is 15 sScenariosUndersaturation, oversaturation, undersaturation and bus priority, oversaturation and bus priority, undersaturation and emergency vehicles, and oversaturation and emergency vehiclesData collectionCollect the road section number, lane number, whole road section density, flow, and vehicle speed. The acquisition interval is 600 sEvaluation parametersThe average number of stops and average delay timeA further explanation for the experiment is as follows:Traditional control methods are generally pertinent; that is, different scenarios will adopt adaptive control methods.(1)
For the reasonableness of comparison, in the first set of {undersaturated and oversaturated} two scenarios, the comparison is with timing control; in the second set of {undersaturated and bus priority, oversaturated and bus priority} two scenarios, the comparison is with traditional bus priority control [27] (using phase green light extension and red light shortening); in the third set of {undersaturated and emergency vehicles, oversaturated and emergency vehicles} two scenarios, the comparison is with traditional emergency vehicle control [28] (using trigger response; that is, when a traffic request is detected, the phase is locked or jumped immediately).(2)
In the simulation, the detection points are used to replace the commonly used RFID detectors in practice, and the detection points are, respectively, arranged at positions about 150 m away from the parking line.(3)
All buses appearing in the simulation are subject to public transportation priority control, and all emergency vehicles appearing are subject to emergency priority control.(4)
In the simulation, select the objective function parametersα and β: in the first set of scenarios {undersaturated, oversaturated}, set α=1,β=0; that is, consider the minimum total travel time of vehicles passing through the intersection as the objective function. In the second set of scenarios {undersaturation and bus priority, oversaturation and bus priority}, set α=0,β=1; that is, consider the minimum travel time of bus priority vehicles passing through the intersection as the objective function. In the third set of scenarios {undersaturated and emergency vehicles, oversaturated and emergency vehicles}, set α=0,β=1; that is, consider the minimum travel time of emergency vehicles through the intersection as the objective function (the purpose of choosing the objective function parameters in this way is to be consistent with the traditional comparison of control methods).


## 5.2. Analysis Results

### 5.2.1. The First Set of Scenes: {Undersaturated, Oversaturated}

Figure12 shows the change of the capacity coefficient JS when the two scenarios included in the first group are compared. It can be seen from Figure 12 that the time to reach the JS threshold is later when using the method in this paper than when using the traditional control method. Arrow 1 (speed control) shown in the figure indicates that JS<0, and the speed control is started, but it is found that JS of the next data point is further reduced, indicating that the speed control can no longer control the decline of JS at this time, and then start lane control shown in Figure 12, due to the subsequent improvement of the traffic state and the effect of lane control, makes JS return to the control threshold.Figure 12
Change of capacity coefficient.Figures13(a) and 13(b), respectively, show the average number of stops and average delay time of vehicles passing through the intersection in the first set of scenarios. It can be seen from Figure 13 that the control effect of the active control method proposed in this article is better than that of the traditional control method in the two scenarios of undersaturation and oversaturation.Figure 13
The contrast of control effect of the first set of scenarios. (a) Average number of vehicle stops at intersections. (b) Average delay time of vehicle at the intersection.
(a)(b)


### 5.2.2. The Second Set of Scenarios: {Undersaturation and Bus Priority, Oversaturation and Bus Priority}

Figures14(a) and 14(b), respectively, show the average number of stops and average delay time of buses passing through the intersection in the second set of scenarios. It can be seen from Figure 14 that, in the scenario of undersaturation and bus priority, the control effect of the active control method proposed in this article is similar to that of the traditional control method; however, as the traffic flow changes, the scene changes from undersaturation and bus priority to oversaturation and bus priority scenario, and the control effect of the active control method proposed in this paper is better than that of the traditional control method.Figure 14
The contrast of control effect of the second set of scenarios. (a) Average number of bus stops. (b) Average delay time of the bus.
(a)(b)


### 5.2.3. The Third Set of Scenes: {Undersaturated and Emergency Vehicles, Oversaturated and Emergency Vehicles}

Figures15(a) and 15(b), respectively, show the average number of stops and average delay time of buses passing through the intersection in the third set of scenarios. It can be seen from Figure 15 that, in the scenario of undersaturated and emergency vehicles, the control effect of the active control method proposed in this article is similar to that of the traditional control method; and in the scenario of oversaturated and emergency vehicle, the control effect of the active control method proposed in this paper is better than that of the traditional control method.Figure 15
The contrast of control effect of the third set of scenarios. (a) Average number emergency vehicle stops. (b) Average delay time of emergency vehicle.
(a)(b)As shown in Table2, compared with the traditional method, in the first set of scenarios, the average parking delay time at intersections is reduced by 35.93%%, and the average number of stops is 31.80%; in the second set of scenarios, the average bus parking delay time is reduced by 22.35%, and the average number of parking times is 26.58%; in the third group of scenarios, the average parking delay time of emergency vehicles is reduced by 14.81%, and the average number of parking times is 47.06%. It can be seen that the method in this paper can give suitable control responses for different scenarios, which is very efficient in traffic.Table 2
Comparison of simulation results of control methods.
Experimental sceneMethodEvaluation parametersResultsImproveThe first set of scenesTraditionalAverage stops92.4—PaperAverage delay time59.235.93%TraditionalAverage stops2.41—PaperAverage delay time1.6431.80%The second set of scenesTraditionalAverage stops50.1—PaperAverage delay time38.422.35%TraditionalAverage stops0.79—PaperAverage delay time0.5826.58%The third set of scenesTraditionalAverage stops16.2—PaperAverage delay time13.814.81%TraditionalAverage stops0.17—PaperAverage delay time0.0947.06%


## 5.2.1. The First Set of Scenes: {Undersaturated, Oversaturated}

Figure12 shows the change of the capacity coefficient JS when the two scenarios included in the first group are compared. It can be seen from Figure 12 that the time to reach the JS threshold is later when using the method in this paper than when using the traditional control method. Arrow 1 (speed control) shown in the figure indicates that JS<0, and the speed control is started, but it is found that JS of the next data point is further reduced, indicating that the speed control can no longer control the decline of JS at this time, and then start lane control shown in Figure 12, due to the subsequent improvement of the traffic state and the effect of lane control, makes JS return to the control threshold.Figure 12
Change of capacity coefficient.Figures13(a) and 13(b), respectively, show the average number of stops and average delay time of vehicles passing through the intersection in the first set of scenarios. It can be seen from Figure 13 that the control effect of the active control method proposed in this article is better than that of the traditional control method in the two scenarios of undersaturation and oversaturation.Figure 13
The contrast of control effect of the first set of scenarios. (a) Average number of vehicle stops at intersections. (b) Average delay time of vehicle at the intersection.
(a)(b)


## 5.2.2. The Second Set of Scenarios: {Undersaturation and Bus Priority, Oversaturation and Bus Priority}

Figures14(a) and 14(b), respectively, show the average number of stops and average delay time of buses passing through the intersection in the second set of scenarios. It can be seen from Figure 14 that, in the scenario of undersaturation and bus priority, the control effect of the active control method proposed in this article is similar to that of the traditional control method; however, as the traffic flow changes, the scene changes from undersaturation and bus priority to oversaturation and bus priority scenario, and the control effect of the active control method proposed in this paper is better than that of the traditional control method.Figure 14
The contrast of control effect of the second set of scenarios. (a) Average number of bus stops. (b) Average delay time of the bus.
(a)(b)


## 5.2.3. The Third Set of Scenes: {Undersaturated and Emergency Vehicles, Oversaturated and Emergency Vehicles}

Figures15(a) and 15(b), respectively, show the average number of stops and average delay time of buses passing through the intersection in the third set of scenarios. It can be seen from Figure 15 that, in the scenario of undersaturated and emergency vehicles, the control effect of the active control method proposed in this article is similar to that of the traditional control method; and in the scenario of oversaturated and emergency vehicle, the control effect of the active control method proposed in this paper is better than that of the traditional control method.Figure 15
The contrast of control effect of the third set of scenarios. (a) Average number emergency vehicle stops. (b) Average delay time of emergency vehicle.
(a)(b)As shown in Table2, compared with the traditional method, in the first set of scenarios, the average parking delay time at intersections is reduced by 35.93%%, and the average number of stops is 31.80%; in the second set of scenarios, the average bus parking delay time is reduced by 22.35%, and the average number of parking times is 26.58%; in the third group of scenarios, the average parking delay time of emergency vehicles is reduced by 14.81%, and the average number of parking times is 47.06%. It can be seen that the method in this paper can give suitable control responses for different scenarios, which is very efficient in traffic.Table 2
Comparison of simulation results of control methods.
Experimental sceneMethodEvaluation parametersResultsImproveThe first set of scenesTraditionalAverage stops92.4—PaperAverage delay time59.235.93%TraditionalAverage stops2.41—PaperAverage delay time1.6431.80%The second set of scenesTraditionalAverage stops50.1—PaperAverage delay time38.422.35%TraditionalAverage stops0.79—PaperAverage delay time0.5826.58%The third set of scenesTraditionalAverage stops16.2—PaperAverage delay time13.814.81%TraditionalAverage stops0.17—PaperAverage delay time0.0947.06%


## 6. Conclusion Remark and Future Work

This paper proposes a multivariable active traffic control model (ATCM) based on the vehicle infrastructure cooperative technology. The model increases the control variables from two dimensions to five dimensions and almost contains all the time and space variables of the intersection. It can be imagined that the flexibility of intersection control will be greatly improved, and in particular it can reshape the traffic flow organization and traffic control mode of intersection, which is very beneficial for the future fully automatic driving scene. The d-bilevel optimization method is designed for ATCM. In the first part of the method, boundary control is used to combine speed control with dynamic phase sequence control to provide initial control scheme. In the second part, space-time coordinated control is used to combine lane control with dynamic phase sequence control to provide more powerful control scheme. The traditional simulation platform is difficult to meet the experimental requirements of the paper, so the OSP is adopted. Three contrast scenarios are designed in the simulation. The {undersaturated and oversaturated} scenarios are used to verify the congestion mitigation capability of the model, the {undersaturated and bus priority, oversaturated and bus priority} scenarios are used to verify the capability of the model for bus priority, and the {undersaturated and emergency vehicles, oversaturated and emergency vehicles} scenarios are used to simulate the capability of the model to deal with the sudden demand of characteristic vehicles. The experimental results show that the proposed method is superior to the traditional method in reducing the average delay time and the average number of stops. It can be seen that ATCM has great potential to adapt to more complex control requirements of the intersection. In the future work, this method will be extended to hybrid driving traffic control, fully automatic driving traffic control, and other fields.



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*Source: 9965749-2021-04-21.xml*