Priority of Emergency Vehicle Dynamic Right-Of-Way Control Method in Networked Environment

Abstract

This paper proposes a dynamic right-of-way priority control approach for emergency vehicles (PDR-EVs) to improve their efficiency on basic road sections in the city based on a cooperative vehicle infrastructure system. Specifically, a movable physical function area was set in front of the EVs to prohibit connected vehicles (CVs) from entering a lane or to request them to change lanes to avoid a collision. Setting up a dynamic monitoring area at the EV’s front end affords real-time monitoring of the CV’s headway distribution in the inner lane. Moreover, a lane change request is sent when the CVs enter the buffer area, and the traversal search method predicts the optimal time and rate of speed to change the lane change and guides the CVs ahead of the EVs to merge into the target gap. Extensive simulations using the SUMO platform revealed that the priority of the dynamic right-of-way (PDR) control method reduced the average delay of the EVs by more than 70%, given that the road saturation did not exceed 0.8 and hardly increased the delay of the CVs (not more than 8%). Moreover, the simulations revealed that the long buffer area was suitable for low-volume conditions, and the short one was suitable for high-volume conditions. The proposed methodology fully employs the road space resources and enhances the EV’s operating efficiency on basic road sections while considering the CV’s operating efficiency.

1. Introduction

Emergency rescue involves the rapid response of emergency vehicles (EVs) to participate in public emergency rescue operations. In such cases, EVs must arrive at the rescue site quickly. However, in the existing urban roads, the traffic environment changes are highly complex, and, therefore, it is challenging to ensure that EVs are not disturbed by other vehicles. Therefore, EVs should obtain the right-of-way on the road to enhance the their operation efficiency while ensuring safety, which has always been a research hotspot in traffic information control.

The existing literature on EV priority control chiefly focuses on intersection signal priority control, intersection entrance priority control, and route decision control. In the early signal priority control of intersections, the main control method arranged vehicle detection equipment on the roadside to sense the arrival of EVs and optimize the signal scheme structure [1,2]. With the popularization of connected vehicle technology and communication technology, CVs and signal lights can perceive each other, thus improving the efficiency of priority control. Hence, scholars conducted in-depth research on the signal priority control of EVs at intersections through technologies such as multi-agent [3], deep learning [4,5], cellular automata [6], and vehicle–infrastructure cooperation [7]. These investigations can all be attributed to the right-of-way time priority. Concerning the priority control of right-of-way spaces, most researchers have focused on the priority control of the intersection entrance. This strategy guides the next vehicles to a specific lane through the variable message sign (VMS) [8] and employs the entrance’s variable guidance function to clear the target lane [9]. Given the vehicle infrastructure cooperation scheme, CVs are perceived and guided to enter the designated empty target lane without stopping and pass through the intersection [10].

Regarding road section priority, most studies focus on public transport vehicles. For instance, Zhao et al. [11] explored the time-division multiplexing of exclusive right-of-way, but this methodology significantly impacts regular traffic and does not improve the overall service level of the transportation system. Wu et al. [12] extended the principle of intermittent bus lanes to road sections, thus reducing the impact of regular traffic on the operation of bus vehicles, but did not specify a specific control approach. Pang et al. [13] and Chen et al. [14] exploited the communication characteristics of autonomous driving by mixing CVs and bus vehicles on the BRT bus lane. They proposed a control strategy for CVs that utilized a virtual dedicated lane. Considering that CV queuing affects the running speed of public transport vehicles, Wu and Guler [15] proposed a moving bottleneck method based on the traffic wave theory to analyze the running conditions of public transport vehicles to reduce system-generated delays. In conclusion, existing investigations have not adequately investigated the right-of-way space of the road segment, and, therefore, the EV’s operating efficiency on the road segment cannot be guaranteed. The different priority control methods are shown in

Table 1. The different priority control methods.

EV Priority Control	Reference	Method
right-of-way time priority	[1,2,3,4,5,6,7]	Right-Of-Way time priority has evolved from the early days of roadside devices collecting information to the current developments in networked vehicle technology and communications technology, which realize real-time information interactions between CV and signal lights.
right-of-way space priority	[8,9,10]	Right-Of-Way space priority is mostly controlled at the intersection entrance road, and involves the use of variable message signs to guide the movement of vehicles, clear lanes with variable guidance, and the use of vehicle–road collaboration technology to guide vehicle operations.
road section priority	[11,12,13,14,15]	Most of the current roadway priority control targets are bus vehicles; special control methods are used to give priority to bus vehicles on road sections, and only a small number of methods consider the operational efficiency of regular traffic.

.

The conventional right-of-way time priority uses traffic information collection devices for EV vehicle information collection. However, the timeliness and accuracy of information collection cannot be guaranteed, and equipment maintenance costs are also higher. The intelligent and connected technologies that have been developed in recent years are also used in signal priority control, thereby enabling the ability to acquire road and vehicle conditions more accurately than traditional technologies, which allow for timely adjustments. The current priority for the roadway is mainly focused on the priority of public transport vehicles, which are mainly divided into exclusive right-of-way and intermittent bus lanes, and most do not consider the impact on regular traffic.

In summary, most analyses focused on priority control within EVs intersections, with equal spatial right-of-way between EVs and CVs within the spatial extent of the road section. However, there is a lack of research regarding an EV’s spatial right-of-way priority control on road sections. Therefore, it is necessary to propose a priority dynamic right-of-way control method for emergency vehicles. Specifically, this paper set a movable, physical, and functional area ahead of the EVs that prohibits CVs from entering or requesting to alter lanes and reduces the impact of CVs on EV operation, thus reflecting its priority right-of-way characteristics on the road section. Unlike traditional right-of-way priority, through our method, EVs do not fully occupy an entire lane of traffic, which minimizes the impact on CVs while giving priority to EVs.

1.1. PDR-EVs Control Strategy

We set a non-intrusive interval of length at the front end of the EV to ensure driving safety and to make the EV prioritize the right-of-way space. The interval value is related to the EV’s speed and the front CV’s speed and should be determined based on the speed of both [16]. In addition, a buffer interval of length was appropriately set before the no-intrusion interval. When the CVs ahead of the EVs enter the buffer, it is necessary to request them ahead to change lanes in time for them to pass quickly. As depicted in Figure 1, since the EV’s speed exceeds the CVs’, the front CVs should complete a lane change before entering the non-intrusion zone. Among them, CV vehicles are equipped with sensors, controllers, actuators and other devices, and incorporate modern communication technologies that are capable of exchanging information between vehicles and X (vehicles, roads, people, etc.) through sensing, decision-making, and collaborative control functions. Subsequently, the physical meaning of the non-intrusive zone is the safe-following distance that CV vehicles are not allowed to enter, which is adjusted according to the vehicle’s speed in front and behind. The physical meaning of the buffer zone is the perceived space of the EV, for a buffered lane change for CV vehicles, thereby reflecting its right-of-way priority privilege, which is adjusted according to the traffic state. The lengths of the non-intrusive and buffer zones could be flexibly and dynamically adjusted to suit various traffic scenarios. Obviously, EVs can obtain the priority right-of-way space in this process.

1.2. Basic Control Ideas

The scenario studied involved a basic urban road area with four lanes per direction for urban main road and expressways. The virtual lanes for the EVs were set in the outer lanes. It should be emphasized that we do not consider the impact of the downstream intersection (signal) on the traffic flow, i.e., the ends of the road section are away from the intersections, as illustrated in the schematic diagram of Figure 2, where only one direction in the road section is plotted. Exploiting the technical characteristics of the vehicle infrastructure cooperation system can obtain the CV’s real-time position, speed, acceleration, and other information. When the CVs receive the lane-changing signal, the system searches for the optimal voids in the inner lane, guides the CVs to the front end of the EVs, inserts the neutral gear to make them drive toward the inner lane, and restores the original vehicle lane distribution after the EVs pass quickly. Hence, the CV is then back in the original lane.

The above control process is represented by the flowchart in Figure 3. When multiple CVs are in front of the EVs, the guidance control is performed sequentially according to the flow to form a loop. Due to the complex coupling between vehicles and traffic flows, vehicles in mixed traffic flows have unique dynamics and uncertainties. To this end, the following assumptions were made: (1) CVs have a random slowing phenomenon and arrive uniformly. (2) EVs do not change lanes and drive at the desired or maximum drivable speed. The speed is within a certain interval that exceeds the CV’s expected speed. (3) The CVs participating in the interaction obey the guidance signal. (4) The traffic flow composed of CVs is relatively stable and does not reach saturation. (5) Each CV selects a lane change to avoid the EV instead of accelerating.

2. PDR-EVs Control Method

2.1. Definition and Description of Parameters

Table 2. Parameter definition.

Parameter	Meaning
$\mathrm{K}$	the CV set of the inner lane into the dynamic monitoring interval
$J$	collection of CVs in the outer lane into the buffer zone
$G$	headway between the adjacent front and rear CVs in the inner lane within the dynamic monitoring interval
$\mathsf{\Psi }$	collection of instantaneous moments when CVs in the outer lane enter the buffer zone
$\mathsf{\Omega }$	collection of moments at the start of the merge before lane change in the outside lane
$\mathsf{\Theta }$	set of times from the receipt of the guidance signal to the start of the merge by the CV in the outside lane
$\mathsf{\Phi }$	outside lane CV avoidance EV lane change time collection
$\mathrm{A}$	solution set of the acceleration of vehicle $j$, ${\mathrm{A}}_{+}$ denotes a positive solution set, and ${\mathrm{A}}_{-}$ signifies a negative solution set such that $\forall j,j\in J,{\mathrm{A}}_{+}\cup {\mathrm{A}}_{-}=\mathrm{A},{\mathrm{A}}_{+}\cap {\mathrm{A}}_{-}=0$
$t$	moment when the CV is currently running
$j$	outer lane CV number, $\forall t,\forall j,j\in J$
$i$	inside lane CV number
$i+k$	the CV number of the inner lane currently in the dynamic monitoring interval, $\forall t,\forall k,i+k\in \mathrm{K}$
$\tau$	maximum communication delay time of vehicle infrastructure cooperation system
$t_{s,j}$	instantaneous moment when vehicle $j$ enters the buffer interval, $\forall j,t_{s,j}\in \mathsf{\Psi }$
$t_{c,j}$	starting moment of the merging before vehicle $j$ changes lanes, $\forall j,t_{c,j}\in \mathsf{\Omega }$
${\theta }_j$	time between the vehicle j receiving the guidance signal and the start of the merge, $\forall j,{\theta }_j\in \mathsf{\Theta }$
${\delta }_j$	time for vehicle $j$ to avoid EV lane change and enter the inner lane, $\forall j,{\delta }_j\in \mathsf{\Phi }$
$v_{min}$	minimum speed for CV operation
$v_{max}$	maximum speed for CV operation
$a_{max}$	maximum operating speed change of CV

explains the following parameters to describe the proposed control method clearly.

2.2. Dynamic Monitoring Intervals

On actual city roads, EVs are generally faster than CVs. When the front buffer interval of the EV touches the CV’s tail, the search procedure is triggered to search the inside lane for gaps where the CV can merge into. This is demonstrated in Figure 4, which assumes that the moment when the rear of the j-th vehicle touches the buffer interval at the front of the EVs is $t_{s,j}$ and defines the dynamic monitoring interval as the dividing line between EV’s non-intrusive interval and the buffer interval as the starting point of the interval. The rear of the j-th vehicle’s front is the the j + 1-th vehicle as the end of the interval. The dynamic monitoring interval at time $t$ is given by:

$$DMS(t)=X_D(t)-X_S(t)$$

(1)

where $X_S(t)$ represents the spatial position of the buffer start at time $t$, and $X_D(t)$ denotes the spatial position of the end of the buffer at time $t$.

At the same time, the vehicle infrastructure cooperation system obtains the CV’s real-time dynamic position and speed. The distance of the i + k-th vehicle from the starting point of the dynamic monitoring interval at time $t$ is represented by $S_{i+k}(t)$, and the headway of the i + k-th vehicle at moment $t$ is presented by Equation (2):

$$H_{i+k}(t)=S_{i+k+1}(t)-S_{i+k}(t),\forall k\in \mathrm{K}$$

(2)

Let function $D_{id}(t)$ represent the speed of the i-th vehicle at moment $t$, and the speed rate of change is:

$$D_{id}(t)=D_{id}(v_{id}(t),a_{id}(t))$$

(3)

where $v_{id}(t)$ denotes the longitudinal velocity of the id-th vehicle at moment $t$, $a_{id}(t)$ is the longitudinal acceleration of the id-th vehicle at moment $t$, and $id$ is the number of CVs.

2.3. Avoidance of EVs Guidance Control Method

2.3.1. Safe Convergence Gap

When the v-th vehicle enters the buffer zone, it must change lanes in time to avoid passing EVs. Regarding safety, it is assumed that the CV to be changed is $V_0$, and the surrounding CVs are $V_1$, $V_2$, $V_3$, and $V_4$, as presented in Figure 5. The minimum safe time headways that should be met when the V₀-th vehicle merges are $S_0(D_{V1},D_{V0})$, $S_0(D_{V2},D_{V0})$ and $S_0(D_{V3},D_{V0})$, where $S_0(D_{V1},D_{V0})$ is the time headway behind the target lane, $S_0(D_{V2},D_{V0})$ is the time distance ahead of the target lane, and $S_0(D_{V3},D_{V0})$ is the time headway in front of the current lane [17].

When the EV’s front buffer touches the front j-th vehicle (as depicted in Figure 4), it is investigated whether $H_{i+k}(t),\forall k\in \mathrm{K}$ in the interval $DMS(t)$ meets the requirements for safe entry. Let the minimum safe merging gap function be $Ga{p}_{min}(t_{s,j},k,j)$. For the j-th vehicle that is about to change lanes, its minimum safe merging gap can be expressed by:

$$Ga{p}_{min}(t,k,j)=S_0(D_{i+k}(t),D_j(t))+S_0(D_{i+k+1}(t),D_j(t))+l_j,\forall k\in \mathrm{K},\forall j\in J$$

(4)

where $Ga{p}_{min}(t,k,j)$ is the minimum convergence gap at $t$ moments that satisfies the driving state of the j-th vehicle, the i + k-th vehicle, and the i + k + 1-th vehicle, and $l_j$ is the body length of the j-th vehicle. Apparently, the moment to trigger the search procedure is not equal to when the j-th vehicle is merging, and function $Ga{p}_{min}(t_{s,j},k,j)$ cannot be utilized as a judgment condition for the j-th vehicle to merge safely. Therefore, it is not advisable to set the speed of the j-th vehicle as $v_j(t),(v_{min}\le v_j(t)\le v_{max})$ and the EV’s speed as $v_E(t),(v_E(t)>v_j(t))$. The buffer is constantly compressed with time, but, at any moment, it satisfies Equation (5):

$${\displaystyle {\int }_{t_{s,j}}^{{\theta }_j}(v_E}(t)-v_j(t))dt=L_2,\forall j\in J,\forall {\theta }_j\in \mathsf{\Theta }$$

(5)

The magnitude of ${\theta }_j$ is determined by the difference between $v_j(t)$ and $v_E(t)$. Although the magnitudes of $v_j(t)$ and $v_E(t)$ vary with time, ${\theta }_j$ must be between the two values, which can be expressed by ${\theta }_{j,max}\ge {\theta }_j\ge {\theta }_{j,min}$. According to the speed correlations of $S_0(D_{i+k}(t),D_j(t))$ and $S_0(D_{i+k+1}(t),D_j(t))$ with the i + k-th vehicle, the i + k + 1-th vehicle, and the j-th vehicle [18], the speed correlation satisfies.

$$S_0(D_{i+k}(t_{c,j}),D_j(t_{c,j}))={\displaystyle {\int }_{t_c}^{t_c+{\delta }_j}{\displaystyle {\int }_{t_c}^{t_c+\tau }\left|a_{i+k}(\tau )-a_j(\tau )\right|}}d{\delta }_{j}d\tau +\left|v_{i+k}(t_{c,j})-v_j(t_{c,j})\right|\ast {\delta }_j,\forall j\in J,t_{c,j}\in \mathsf{\Omega },{\delta }_j\in \mathsf{\Phi }$$

(6)

$$S_0(D_{i+k+1}(t_{c,j}),D_j(t_{c,j}))={\displaystyle {\int }_{t_c}^{t_c+{\delta }_j}{\displaystyle {\int }_{t_c}^{t_c+\tau }\left|a_{i+k+1}(\tau )-a_j(\tau )\right|}}d{\delta }_{j}d\tau +\left|v_{i+k+1}(t_{c,j})-v_j(t_{c,j})\right|\ast {\delta }_j,\forall j\in J,t_{c,j}\in \mathsf{\Omega },{\delta }_j\in \mathsf{\Phi }$$

(7)

It can be deduced that, subject to $v_j(t_{s,j})=v_{max}$, $Ga{p}_{min}(t_{c,j},k,j)$ satisfies Equation (8):

$$Ga{p}_{min}(t_{c,j},k,j)\le Ga{p}_{min}(t_{s,j},k,j)\left|v_j\right.(t_{s,j})=v_{max},\forall k\in \mathrm{K},\forall j\in J$$

(8)

If the inequality given by Equation (9) is established, the inequality in Equation (10) must be established. That is, the j-th vehicle can safely merge into the inner lane gap. Therefore, the inequality in Equation (10) can be exploited to judge whether the gap meets the safety requirements:

$$H_{i+k}(t_{s,j})\ge Ga{p}_{min}(t_{s,j},k,j)\left|v_j(t_{s,j})=\right.v_{max},\forall j\in J,t_{s,j}\in \mathsf{\Psi }$$

(9)

$$H_{i+k}(t_{c,j})\ge Ga{p}_{min}(t_{c,j},k,j),\forall j\in J,t_{s,j}\in \mathsf{\Psi }$$

(10)

Let the gap set $H_{i+k}(t)\in G$ satisfy the above inequality, denoted by $C$, which is stated by:

$$C=\left\{k\left|\{H_{i+k}(t_{s,j})\ge Ga{p}_{min}(t_{s,j},k,j)\left|v_j(t_{s,j})=\right.v_{max},\forall j\in J,t_{s,j}\in \mathsf{\Psi }\}\right.\right\}$$

(11)

If there are multiple sinkable target gaps in the set $C$, the optimal target gap should be selected, and the function $J(t,k,j)$ is the optimal target gap selection function,

$$J(t,k,j)=min\left\{\left|S_j(t)-S_i(t)\right|,\left|S_j(t)-S_{i+1}(t)\right|,\dots ,\left|S_j(t)-S_{i+k}(t)\right|,\dots \right\},\forall k\in \mathrm{K},\forall j\in J$$

(12)

In summary, the objective function correction for the j-th vehicle to select the best sink gap is provided by the following relation:

$$min\{J(t_{s,j},k,j),\forall j\in J,\forall k\in \mathrm{K}\cap C\}$$

(13)

2.3.2. Guided Control Methods

As illustrated in Figure 4, the j-th vehicle is an obstacle vehicle for the EVs and should be guided into the inner lane. The following three scenarios may exist for its guidance control process:

Case 1: In the interval of $DMS(t_{s,j})$$\forall t_{s,j}\in \mathsf{\Psi },\forall k\in \mathrm{K}$, $\exists H_{i+k}(t_{s,j})$ satisfies the inequality of Equation (9), and the spatial position of the j-th vehicle satisfies:

$$S_{i+k}(t_{s,j})+S_0(D_{i+k}(t_{s,j}),D_j(t_{s,j}))\ge S_j(t_{s,j}),\forall j\in J$$

(14)

The j-th vehicle must accelerate to a position that can converge into the gap, thus assuming that all CV shifting phases are uniformly variable. Then,

$$x_j({\theta }_j+\tau )=\left\{\begin{array}{c}{v}_j(t_{s,j})\ast (t_{c,j}-t_{s,j})+\frac{1}{2}{a}_j\ast {(t_{c,j}-t_{s,j})}^2\\ v_{max}\ast (t_{c,j}-\frac{v_{max}-v_j(t_{s,j})}{a_j}-t_{s,j})+\frac{v_{max}^2-v_j^2(t_{s,j})}{2a_j}\end{array},\right.\forall t_{s,j}\in \mathsf{\Psi },t_{c,j}\in \mathsf{\Omega },{\theta }_j\in \mathsf{\Theta }$$

(15)

If the following inequality is satisfied, the j-th vehicle can safely and smoothly merge into the gap $H_{i+k}(t_{s,j})$, and subtracting $X_S(t_{s,j})$ from both sides of the inequality can be obtained:

$$\left\{\begin{array}{c}{S}_j(t_{s,j})+x_j({\theta }_j+\tau )\ge S_{i+k}(t_{s,j})+S_0(D_{i+k}(t_{s,j}),D_j(t_{s,j}))+{\displaystyle {\int }_{t_{s,j}}^{t_{c,j}}{v}_{i+k}(t)dt}\\ S_j(t_{s,j})+x_j({\theta }_j+\tau )\le S_{i+k+1}(t_{s,j})-S_0(D_{i+k+1}(t_{s,j}),D_j(t_{s,j}))+{\displaystyle {\int }_{t_{s,j}}^{t_{c,j}}{v}_{i+k+1}(t)dt}\\ S_j(t_{s,j})+x_j({\theta }_j+\tau )\le S_{j+1}(t_{s,j})-S_0(D_{j+1}(t_{s,j}),D_j(t_{s,j}))+{\displaystyle {\int }_{t_{s,j}}^{t_{c,j}}{v}_{j+1}(t)dt}\end{array}\right.$$

(16)

In the given formula, $t_{s,j}$ and $\tau$ represent the known system parameters, and the range of $t_{c,j}$ could be easily available from ${\theta }_j$.

$$t_{s,j}+{\theta }_{j,max}+\tau \ge t_{c,j}\ge t_{s,j}+{\theta }_{j,min}+\tau ,\forall j\in J$$

(17)

By combining the above equations and inequalities to form a linear programming model, it can be seen that there exist only two unknown model parameters, i.e., $t_{c,j}$ and $a_j$.

The traversal search approach can be exploited to solve the model [19]. Since the range of $t_{c,j}$ has been determined, the value of $t_{c,j}$ can be substituted into the model from small to large to solve the corresponding $a_j$ until a solution set of $a_j$ is obtained for the model. Notably, the optimal solution method is to give priority to minimize $t_{c,j}$ and then minimize $a_j$, while considering $a_j^{\ast }=min(a_j),\forall j,a_j\in {\mathrm{A}}_{+}$. In the actual system operation, the CVs of the obstacle in front of the EVs merge into the inner lane as soon as possible, thus ensuring the comfort of the shifting process.

Case 2: In an interval of $DMS(t_{s,j})$$\forall t_{s,j}\in \mathsf{\Psi },\forall k\in \mathrm{K}$, $\exists H_{i+k}(t_{s,j})$ satisfies the inequality given in Equation (9), and the spatial position of the j-th vehicle satisfies:

$$S_{i+k}(t_{s,j})+S_0(D_{i+k}(t_{s,j}),D_j(t_{s,j}))<S_j(t_{s,j}),\forall j\in J$$

(18)

The j-th vehicle must decelerate to reach the position where it can merge into the gap. Before reaching the merging position, its displacement can be evaluated by:

$$x_j({\theta }_j+\tau )=\left\{\begin{array}{c}{v}_j(t_{s,j})\ast (t_{c,j}-t_{s,j})-\frac{1}{2}{a}_j\ast {(t_{c,j}-t_{s,j})}^2\\ v_{min}\ast (t_{c,j}-\frac{v_j(t_{s,j})-v_{min}}{a_j}-t_{s,j})+\frac{v_j^2(t_{s,j})-v_{min}^2}{2a_j}\end{array},\right.\forall t_{s,j}\in \mathsf{\Psi },\forall t_{c,j}\in \mathsf{\Omega },\forall {\theta }_j\mathsf{\in }\mathsf{\Theta }$$

(19)

Similarly, $t_{c,j}$ and $a_j$ are calculated by taking $a_j\ast =\max (a_j),\forall j,a_j\in \mathrm{A}$.

Case 3: In the interval of $DMS(t_{s,j})$, $\forall k\in \mathrm{K},\forall j\in J,\forall t_{s,j}\in \mathsf{\Psi }$$H_{i+k}(t_{s,j})<Ga{p}_{min}(t_{s,j},k,j)\left|v_j(t_{s,j})=\right.v_{max}$. There is no $H_{i+k}(t)$ in $DMS(t_{s,j})$ that satisfies the minimum safe entry distance.

The $H_{i+k}(t)$ with the shortest distance is selected as the target merging gap, and the CV’s travel speed in the inner lane is adjusted to provide a gap to merge safely. The optimal target gap is determined by the function of $J(t,k,j)$, and the target gap is denoted by $H_{i+k}^{\ast }(t)$. After the vehicle infrastructure cooperation system sends the guidance signal, the CVs behind the ($i+k$)-th vehicle decelerate cooperatively (including $j$), the speed change rate does not exceed $a_{max}$, and the speed of the CVs in their front remains unchanged, as depicted in the avoidance process of Figure 3. At time $t_{c,j}$, the target gap  $H_{i+k}^{\ast }(t)$ must satisfy:

$$H_{i+k}^{\ast }(t_{c,j})={\displaystyle {\int }_{t_{s,j}}^{t_{s,j}+\tau +{\theta }_j}\{v_{i+k+1}(t)-v_{i+k}(t)}\}dt+H_{i+k}^{\ast }(t_{s,j})\ge Ga{p}_{min}(t_{s,j},k,j)\left|(v_j(t_{s,j})=\right.v_{max})$$

(20)

In the same way, $t_{c,j}$, $a_j$ can be solved. Considering $a_j^{\ast }=max\left|a_j\right|,\forall j,a_j\in \mathrm{A}$, we denote the solution of $t_{c,j}$ as $t_{c,j}^{\ast }$. Then the CVs’ coordinated decelerations behind the vehicle are:

$$a_{i+k}^{\ast }=\frac{v_{i+k}(t_{s,j})-max\left\{v_{i+k}(t_{c,j}^{\ast }),v_{min}\right\}}{t_{c,j}^{\ast }-\tau -t_{s,j}}$$

(21)

At this point, the system sends $t_{c,j}^{\ast }$, $a_j^{\ast }$, and $a_{i+k}^{\ast }$ to the CVs involved in the interaction.

2.3.3. Planning Model Solving Process

The solution method of the above linear programming model is the same, and its specific process can be summarized as demonstrated in Figure 6. Among them, the search step size of the traversal search methodology is set equal to $\mathsf{\Delta }\vartheta$ until the combined linear programming model has a non-empty solution set. At that point, the search is stopped, and the predicted results are provided as outputs.

3. Experimental Verification

3.1. Experiment Overview

To evaluate the performance of the proposed control model in the actual traffic environment, this paper selected Qinghua Road in Wuhan City, Hubei Province, as an actual case for discussion and research. Qinghua Road starts from Qingwang Road in the west and ends at Huashan Avenue in the east, with a total length of about 12 km. It is an essential urban road between the East Third Ring Road and the East Fourth Ring Road in Wuhan. As demonstrated in Figure 7, Qinghua Road is a two-way four-lane road. It is a major traffic road connecting the main urban area and the suburbs, thereby providing great convenience for the passing traffic in the east and west directions. At the same time, this road provides surrounding units and residents with fast travel and good traffic conditions, which are suitable for validating this study’s models and methods. Figure 8 depicts the vehicle infrastructure cooperation network architecture, and Figure 9 presents the microwave radar equipment installed on road sections to collect real-time road traffic data. The real-time traffic data collected by the radar is stored in a database so that SUMO can access the traffic data sources.

The speed limit of Qing Hua Road is 60 km/h, and the road capacity is 1200 pcu/h per lane. In order to analyze the operation effect of different CV flows on EVs and CVs and obtain different CV flows, the adopted flow considered the high road saturation state according to the actual traffic capacity of the road, which can better verify our method’s effectiveness. To verify the influence of the length of the buffer space in the front of EVs on the running time, we set the length of different buffer spaces under a certain flow rate based on the actual conditions of the road and vehicle operation.

3.2. Simulation Experiments and Data Analysis

3.2.1. Experimental Scenario Description

The basic urban road section with a 1000 m two-way four-lane between two adjacent intersections was utilized as the experimental scene (without considering the impact of intersection signal lights on traffic flow). Using SUMO as the experimental platform, the road speed limit was set to 60 km/h, the road capacity was set to 1200 pcu/h per lane, the expected speed of the CVs was 40 km/h, and the expected speed of the EVs was 60 km/h. The flow input obeyed uniformity, the flow distributions of the inner and outer lanes were uniform, and the speed distribution was divided according to the vehicle type. The ACC car-following model was adopted, the vehicle communication protocol adopted the LTE-V2X protocol, and the maximum communication delay was less than 1 s [18]. To avoid a local optimum in the simulation, the search step $\mathsf{\Delta }\vartheta$ for the traversal search method should be less than 1 s, and the simulation accuracy should be as high as possible. The parameter values in the control approach are reported in

Table 3. Simulation parameter input value.

$v_{min}$	$v_{max}$	$a_{max}$	$\tau$	$\mathsf{\Delta }\vartheta$
30 km/h	50 km/h	1.5 m/s2	1000 ms	200 ms

.

3.2.2. Analysis of Experimental Results

The experiment adopted a comparative analysis of control variables and conducted statistical analysis on the running time of vehicles under various traffic scenarios and input conditions.

The traffic organization methodologies are as follows: (1) Equal right-of-way (ER)—CVs and EVs could drive in any lane and change lanes freely without intervention; (2) Priority for special road right-of-way (PSR)—the outer lane is a dedicated lane for EVs, so CVs are not allowed to enter that lane; (3) Dynamic right-of-way (PDR)—the outer lanes are virtual dedicated lanes for EVs so that CVs can enter intermittently. The experimental simulation inputs and output data are presented in

Table 4. Effect of CV flow on running time.

CV’s Input Flow (pcu/h)	ER		PSR		PDR
	EV Average Running Time (s)	CV Average Running Time (s)	EV Average Running Time (s)	CV Average Running Time (s)	EV Average Running Time (s)	CV Average Running Time (s)
600	70.9	84.9	57.5	85.6	59.5	85.215
700	72.5	85	57.5	85.8	59.8	85.36
800	74.3	85.1	57.5	86.1	60.3	85.55
900	75.3	85.3	57.5	86.4	60.5	85.795
1000	76.3	85.4	57.5	86.7	61.1	85.985
1100	77.2	85.6	57.5	87	61.5	86.23
1200	78.7	85.7	57.5	87.4	61.7	86.465
1300	79.2	85.8	57.5	87.6	62.1	86.61
1400	80.2	86	57.5	88.1	62.3	86.945
1500	80.7	86.1	57.5	88.4	62.6	87.135
1600	81.4	86.2	57.5	89	62.9	87.46
1700	82.1	86.4	57.5	90.1	64.4	88.065
1800	82.6	86.5	57.5	91.3	68.6	88.66
1900	82.9	86.6	57.5	92.8	75.9	91.1465
2000	83.1	86.7	57.5	96.5	85.3	103.989

,

Table 5. Impact of the EV buffer length on the running time.

Length between EV Buffers (m)	ER		PSR		PDR
	EV Average Running Time (s)	CV Average Running Time (s)	EV Average Running Time (s)	CV Average Running Time (s)	EV Average Running Time (s)	CV Average Running Time (s)
30	79.2	85.8	57.5	87.6	73.9	86.8061
40	79.2	85.8	57.5	87.6	70.1	87.1452
50	79.2	85.8	57.5	87.6	67.8	87.3094
60	79.2	85.8	57.5	87.6	66	87.4913
70	79.2	85.8	57.5	87.6	64.6	87.8665
80	79.2	85.8	57.5	87.6	63.2	87.9002
90	79.2	85.8	57.5	87.6	62.1	88.2079
100	79.2	85.8	57.5	87.6	61.2	88.2416
110	79.2	85.8	57.5	87.6	60.4	88.2722
120	79.2	85.8	57.5	87.6	59.8	88.1915
130	79.2	85.8	57.5	87.6	59.5	88.2925
140	79.2	85.8	57.5	87.6	59.2	88.292
150	79.2	85.8	57.5	87.6	59.1	88.3

,

Table 6. Impact of CV and EV operation on road congestion.

(a)
Input Saturation	Running Time of CV (s)
	ER	PSR	PDR
0.25	84.9	84.8	85.22
0.29	85	84.9	85.36
0.33	85.1	85	85.55
0.38	85.3	85.15	85.80
0.42	85.4	85.2	85.99
0.46	85.6	85.35	86.23
0.50	85.7	85.45	86.47
0.54	85.8	85.5	86.61
0.58	86	85.6	86.95
0.63	86.1	85.73	87.14
0.67	86.2	85.8	87.46
0.71	86.4	85.95	88.07
0.75	86.5	86	88.66
0.79	86.6	86.12	91.15
(b)
The Desired Speed of the CV and EV	EV Actual Running Speed (s)
	ER	PSR	PDR
0	39.77	40.28	40.09
5	41.91	45.06	44.71
10	42.64	49.85	48.72
15	43.07	54.63	52.05
20	43.18	59.38	55.07
25	43.24	64.17	57.38
30	43.29	69.09	59.38

and

Table 7. Impact of CV and EV operation on the net income of the system.

(a)
CV Flow (puc/h)	System Operation Efficiency Net Benefit (s)
	$w$ = 1	$w$ = 0.8	$w$ = 0.6	$w$ = 0.4	$w$ = 0.2	$w$ = 0
600	10.99854	11.07883	11.15912	11.23942	11.31971	11.4
700	12.4113	12.46904	12.52678	12.58452	12.64226	12.7
800	12.74314	12.99451	13.24588	13.49725	13.74863	14
900	13.9554	14.12432	14.29324	14.46216	14.63108	14.8
1000	14.22697	14.42158	14.61618	14.81079	15.00539	15.2
1100	14.54119	14.77295	15.00471	15.23648	15.46824	15.7
1200	15.37011	15.69609	16.02206	16.34804	16.67402	17
1300	14.88432	15.32746	15.77059	16.21373	16.65686	17.1
1400	15.74119	16.17295	16.60471	17.03648	17.46824	17.9
1500	15.67011	16.15609	16.64206	17.12804	17.61402	18.1
1600	16.01714	16.51371	17.01028	17.50685	18.00343	18.5
1700	12.95346	13.90277	14.85207	15.80138	16.75069	17.7
1800	−3.48919	0.008647	3.506485	7.004323	10.50216	14
1900	−17.9167	−12.9333	−7.94999	−2.96666	2.01667	7
2000	−33.7431	−27.4345	−21.1259	−14.8173	−8.50863	−2.2
(b)
Length between EV Buffers (m)	System Operation Efficiency Net Income Change Rate
	$w$= 1	$w$= 0.8	$w$= 0.6	$w$= 0.4	$w$= 0.2	$w$= 0
30	−99.99%	−79.99%	−60.00%	−40.00%	−20.00%	0.00%
40	−55.42%	−39.20%	−22.98%	−6.76%	9.46%	25.68%
50	−30.72%	−16.34%	−1.95%	12.44%	26.83%	41.22%
60	−8.42%	3.94%	16.30%	28.66%	41.02%	53.38%
70	21.95%	30.13%	38.31%	46.48%	54.66%	62.84%
80	33.29%	41.09%	48.89%	56.69%	64.50%	72.30%
90	57.88%	62.25%	66.62%	70.99%	75.36%	79.73%
100	65.83%	69.83%	73.82%	77.82%	81.81%	85.81%
110	72.95%	76.60%	80.25%	83.91%	87.56%	91.22%
120	72.50%	77.06%	81.61%	86.16%	90.72%	95.27%
130	80.16%	83.59%	87.01%	90.44%	93.87%	97.30%
140	82.16%	85.59%	89.02%	92.46%	95.89%	99.32%
150	83.28%	86.62%	89.97%	93.31%	96.66%	100.00%
30	−99.99%	−79.99%	−60.00%	−40.00%	−20.00%	0.00%
40	−55.42%	−39.20%	−22.98%	−6.76%	9.46%	25.68%

.

Figure 10 depicts the experimental results under various CV flow conditions. Since the three test methods travel the same length of road, the shorter running time indicates that the vehicle is moving faster and more efficiently, where the length of the non-intrusion interval is $L_1=15\mathrm{m}$, and the length of the buffer zone is $L_2=90\mathrm{m}$. In all the presented curves, except for the PSR curve in Figure 10a, which remained unchanged, the other curves revealed an upward trend, but the degree was different. Under PSR conditions, since EVs and CVs drive in separate lanes, the operation of the EVs was not affected by the CVs, so the corresponding curve illustrates a flat trend. Obviously, the EV operation effect was remarkable under the PDR condition (Figure 10a), and it was almost close to the PSR operation effect when the flow rate was less than 1700 pcu/h. In Figure 10b, at flow rates less than 1800 pcu/h, the PDR had less impact on the CVs than the PSR, therein increasing the delay by less than 8% compared to ER. Both the PDR and ER methods were implemented without setting a dedicated lane, while the PSR method required a dedicated lane to be implemented. Combined with the analysis shown in Figure 10a,b, the proposed PDR method could significantly reduce the delay of the EV’s operation. Given that the CVs’ delays were almost unaffected (less than 8%), the maximum delay could be reduced by more than 80% (when the flow rate was 1600 pcu/h), and the conclusion was based on the relative performance of the PDR and ER methods. Figure 10a,b show that the PDR control effect under a high flow rate was more sensitive: the change with the flow rate was large, and the delay was too large. Figure 10a infers that, when the flow rate exceeded 1950 pcu/h, the EV’s delay was greater than that of the ER method, thus indicating that the advantages of the PDR could no longer be reflected. Figure 10b highlights that, when the flow rate exceeded 1900 pcu/h, the CVs’ delay under the PDR method increased sharply, again revealing that the PDR method was unsuitable for high flow conditions. In other words, the PDR approach cannot achieve satisfactory operating results on road sections with a saturation greater than 0.8. The above phenomenon was mainly due to the frequent lane change of the CVs owing to the PDR control method. Given that the CVs must avoid the EVs and change lanes in time, this lane change may destroy the original stable group of following vehicles in the inner lane, thus causing some vehicles to decelerate and even generate deceleration waves. As a result, the phenomenon illustrated in Figure 10a,b occurs in high-traffic situations.

Figure 11 depicts the change curve vs. running time due to various buffer zone lengths in front of the EVs, which reflect the operating efficiency by the change in running time. The shorter the running time, the higher the efficiency when the length of the running section is the same. In addition, the mutual influence is reflected by comparing the trend of EV and CV running times under the same control method. It is worth mentioning that $L_1$ is not discussed in this study, because it is closely related to the vehicle’s driving state ahead, and the variation law is complex. To simplify the test process and obtain a relatively objective trend of the influence of the buffer interval length on the running time, $L_1$ was fixed at 15 m during the simulation, and the flow rate was fixed at 1300 pcu/h. In addition, $L_2$ varied from 30 m to 150 m to derive the variation rule [20]. Figure 11a,b reveal that the ER and PSR had a flat trend. Under PDR conditions, the EV’s running time curve presented a downward trend, and the CV’s running time showed an upward trend. The two aligned with the mutual influence mechanism on operating efficiency. Since EVs do not have physical functional areas under the ER and PSR conditions, which are unaffected by the inter-buffer length, the corresponding curves did not change with the inter-buffer length. In Figure 11a, when the length between the buffer zones exceeded 120 m, the PDR curve gradually tended to be flat and approached the PSR curve. When CVs cannot be imported, the operation effect is similar to PSR. The change in the PDR curve in Figure 11b was exactly opposite to that in Figure 11a, which reveals the result of CVs and EVs preempting limited road space resources. Therefore, when the CV’s flow rate is high, the buffer length should be reduced, and the efficiency of the CV’s operation can be enhanced.

Since the ER and PDR methods compress the running space of CVs to different degrees, the saturation will increase. Figure 12a shows the relationship between the running time and the saturation of different organization methods, where the length of the non-invasive interval was $L_1=15\mathrm{m}$, and the length of the buffer zone was $L_2=90\mathrm{m}$. The flow input changed from 600 pcu/h to 2000 pcu/h. The saturation degree is the flow-to-traffic capacity ratio, with capacity set at 1200 pcu/h per lane. According to the traffic flow theory, the higher the saturation and speed, the greater the corresponding traffic capacity. Visibly, when the saturation is less than 0.8, the traffic capacity of the PSR method is the largest, followed by the PDR method, and the ER method is the smallest, but the traffic capacity corresponding to the PSR method is close to the PDR method. Although the PSR method has excellent advantages concerning traffic capacity, it requires many space resources. The plotted results in Figure 10b reveal that the space resources of the EVs compressed the CVs, declined the CVs’ operation efficiencies, and the PSR method had the most substantial impact on the other vehicles. Therefore, from the system point of view, the PSR method is not a method with better comprehensive performance. Since there is no lane change in the PSR method, the PDR method is a semi-free lane change (CV entry into the buffer requires a forced lane change), and the ER method is a completely free lane change, which also displays that the lane change has an adverse effect on the system, thus reducing the operating efficiency of the system. The results in Figure 12b indicate the effect of the speed difference between EVs and CVs compared to the actual EV operating speed, where the length of the two physical functional areas is depicted in Figure 12a, and the flow input was constant at 1300 pcu/h. The difference between the desired and actual EV speed under the ER method was the largest, thus indicating that EVs have the greatest resistance to travel under the ER condition and the greatest degree of impact on the EV’s operating efficiency. Then, without dedicated lanes (PDR method compared to ER method), the PDR method could significantly reduce EV driving resistance, and the operating effect was almost the same as the PSR when the speed difference was not large. It is not difficult to understand that the EV’s speed was reduced. Combining the above two sets of experiments, it is evident that, under the PDR method, when the EV’s speed is low, the length of the corresponding buffer zone should be reduced, and the corresponding saturation is high. When the EV’s speed is high, the corresponding buffer length should be increased, the saturation is low, and the buffer length and speed present a proportional trend.

By combining the advantages and disadvantages of the three methods mentioned above, it becomes clear that the PSR and ER methods are very extreme. The PSR method reflects a significant advantage for EVs by gaining absolute right-of-way, but this methodology has the greatest impact on other vehicles. In contrast, the ER method guarantees an equal right-of-way for all vehicles and fairness. However, EVs operate the least efficiently under this organization method. The proposed PDR method considers the operational efficiency of both EVs and CVs, and the PDR method has the best overall performance.

The above experiments reveal the interaction mechanism between EVs and CVs from different perspectives. However, the space resources on the road are limited. If the priority of EVs increases, the operating efficiency of the CVs must be reduced, thus showing a trend of trade-offs. In practice, the operating efficiency of EVs should be much higher than that of CVs. Noticeably, the operating efficiency of CVs is directly related to the operating efficiency of EVs. Figure 10a,b demonstrate the mechanism impacting the CVs’ lane change on the operational efficiency of roadway traffic. Therefore, in high-urgency emergency rescue missions, the impact of CVs on EVs can be reduced by adjusting CV lane change rates so that EVs can achieve a higher operational efficiency. In low-urgency emergency missions, the impact on CVs can be minimized while maintaining the efficiency of the EV’s’ operation.

Figure 13 illustrates the net gain of the system operation for the PDR method with different weights of CVs. The value of w reduces the frequency of lane change from the inner CVs to the outer lane to varying degrees. w = 0 represents the curve without attenuated CV influence, while w = 1 denotes the curve under prohibited CV lane changes to the outer lane. In Figure 13a, the length of the non-intrusive interval was $L_1=15\mathrm{m}$, the length of the buffer zone was $L_2=90\mathrm{m}$, and the flow input was changed from 600 pcu/h to 2000 pcu/h. The plotted results indicate that the operating efficiency of EVs was the highest for $w=0$, and the curves achieved the maximum value near the CV flow rate of 1700 pcu/h. In Figure 13b, the length of the non-intrusive interval was $L_1=15\mathrm{m}$, the flow input remained unchanged at 1300 pcu/h, and the buffer length changed from 30 m to 150 m. For $w=0$, the operating efficiency of EVs changed the least, specifically when the buffer interval exceeded 120 m. The change did not exceed 5% of the overall change, and these results can be employed to guide actual emergency rescue missions.

4. Conclusions

An equal right-of-way does not guarantee the efficiency and safety of EVs and has a large impact on CVs. While priority for the special right-of-way largely improves the efficiency of EV operations, it also greatly increases CV delays and does not guarantee the overall operational efficiency of the roadway. The PDR-EVs method proposed in this paper realized the EV’s dynamic priority right-of-way in the vehicle infrastructure cooperation environment. Priority was given to EVs by setting two dynamic variable intervals: the non-intrusive interval and the buffer interval. This approach can also reduce delays for CVs to a certain extent. The main conclusions are summarized as follows:

(1)

The PDR method could reduce EV delay by more than 70% on average without increasing the CVs’ delay (no more than 8%), and its control effect was highly sensitive. The overall EV delay was improved when the CV flow was high, thus revealing that the dynamic right-of-way control method is unsuitable for high saturation (greater than 0.8). In high saturation, the length between the buffers must be reduced to improve the EV’s operating efficiency, but the effect is not great. Therefore, it is extremely difficult to evacuate other vehicles on high-saturated road sections to enhance the operating efficiency of the EVs. Cooperation with management and control through other methods, such as upstream-induced diversion, is necessary.

(2)

In the context of the PDR approach, CVs of the outer lanes frequently change lanes to the inner lanes, which disturbs the stability of the homogeneous traffic flow (both CVs) in the inner lanes. The inappropriate lane-changing behavior directly destroys the original stable vehicle group in the inner lane, thereby resulting in local deceleration of the traffic flow on the road section and reducing the system’s operating efficiency. Therefore, implementing the PDR-EVs control method should be combined with adjusting the lane change rate to ensure the operating efficiency of the EVs and, at the same time, to affect the normal operation of CVs as little as possible.

(3)

EVs can dynamically adjust the length of the non-intrusive zone and the buffer zone in real-time according to the speed of the preceding vehicle and road traffic conditions. When the CV traffic is high, the length of the buffer zone can be reduced. A short buffer zone is suitable for high-traffic conditions, and a long buffer zone is suitable for low-traffic situations. The buffer zone size can be flexibly changed and applied to scenarios with various CV traffic.

(4)

The PDR method can reduce EV driving resistance and is not limited by the speed of the social vehicle. By employing the PDR method, EV running stability is almost close to the PSR and can run at the desired speed. Compared with the ER method, the PDR method can improve the traffic capacity of the road section. The PDR method is a control method that considers the operating efficiency of EVs and CVs and has the best overall performance.

(5)

The model does not quantitatively consider the relationship between the vehicle speed and the vehicle-following distance. Therefore, it is necessary to perform quantitative function analysis on the length of the non-intrusive interval, the length of the buffer zone, and the vehicle speed to optimize the car-following behavior to improve the operating efficiency and calibration. The issue of right-of-way priority under high saturation conditions and research on EV marshaling driving should also be considered. In the experimentation, the length of the non-invasive interval of the EV’s front end remained unchanged and was not discussed. The main purpose was to simplify the model and the experimental process. Using it as a fixed value for experiments can also relatively objectively reflect EV operating rules in various scenarios without affecting the scientific nature of the conclusions.