Moving-Block-Based Lane-Sharing Strategy for Autonomous-Rail Rapid Transit with a Leading Eco-Driving Approach

Abstract

Autonomous-rail Rapid Transit (ART) systems operate on standard roadways while maintaining dedicated right-of-way privileges. Owing to their sustainability, punctual operation, and cost efficiency, ART systems have emerged as a promising solution for medium-capacity urban transit. However, the exclusive lane usage for ART systems frequently leads to inefficient lane utilization, thereby intensifying congestion for non-ART vehicles. This study proposes a moving-block-based lane-sharing strategy for ART with a leading eco-driving approach. First, dynamic lane-access rules are introduced, allowing non-ART vehicles to temporarily use the ART lane without forced clearance or signal coordination. Second, a modified eco-driving trajectory optimization algorithm is constructed on a discrete time–space–state network, allowing the ART trajectory to be obtained through an efficient graph-search procedure while simultaneously guiding following vehicles toward energy-efficient driving patterns. Finally, simulation experiments are conducted to evaluate the impacts of traffic demand, arrival interval, and non-ART vehicles’ compliance rate on system performance. The results demonstrate that the proposed strategy significantly reduces delay and energy consumption for non-ART vehicles by 72.6% and 24.6%, respectively, without compromising ART operations efficiency. This work provides both technical insights and theoretical support for the efficient management of ART systems and the sustainable development of urban transportation.

1. Introduction

The Autonomous-rail Rapid Transit (ART) system is a sustainable and efficient medium-capacity transit solution. Instead of relying on costly steel rail infrastructure, ART operates with rubber-tired vehicles on virtual guidance paths [1]. By embedding specific road markings or sensors, ART vehicles can accurately follow a predefined trajectory, as illustrated by the double dashed lines in Figure 1. The ART system significantly reduces infrastructure investment and offers greater operational flexibility compared with conventional rail transit [2]. Consequently, ART combines the benefits of trams and buses—such as high capacity, punctuality, and cost-effectiveness—making it a promising solution for medium-capacity transit systems. In light of global carbon peaking and neutrality goals, the fully electric and environmentally friendly ART system presents new opportunities for sustainable urban development [3].

Although the flexible virtual track reduces construction costs and provides a dedicated right-of-way, it also occupies the already limited roadway resources, thereby aggravating congestion for non-ART vehicles [4,5]. At present, ART vehicles operate on a dedicated right-of-way, where the innermost lane is exclusively reserved for ART operation. The ART lane is separated from the adjacent regular lane by a solid yellow line marking. Non-ART vehicles are prohibited from using the dedicated lane, except in road sections with extremely limited capacity, such as bridges and tunnels. During peak hours, conventional lanes often reach saturation while the ART lanes remain underutilized, leading to inefficient use of road resources and widespread public criticism [6], as illustrated in Figure 1. However, sharing dedicated lanes with conventional vehicles may compromise the operational efficiency of ART. Therefore, it is urgent to develop an ART lane-sharing strategy that achieves a balance between efficiency and equity, maintaining the advantages of ART operations while minimizing the impact on regular traffic.

While research on lane management for ART systems remains limited, numerous studies have been conducted on bus lane priority strategies, which share similar operational characteristics with ART. The concept of intermittent bus lanes (IBL) was first introduced by Viegas and Lu [7,8], in which the exclusive use of bus lanes is intermittently adjusted based on bus presence. When a bus enters the upstream detection zone, the lane is converted into a bus-only lane, prohibiting new private vehicles from entering while allowing those already in the lane to continue. Once the bus departs, the lane reverts to general traffic use. Inspired by the IBL concept, subsequent control strategies have achieved substantial progress in both research and practice. Field experiments conducted in Portugal, Australia, and France [9,10,11] demonstrated that the average bus speed can be increased by approximately 15%. However, because the IBL strategy does not require vehicles already in the lane to vacate, signal coordination is employed to clear the lane—typically by extending the red phase, shortening the green phase, or inserting an additional phase. Such signal adjustments inevitably increase delays for other movements and disrupt overall intersection performance.

To address these limitations, the concept of bus lanes with intermittent priority (BLIP) was introduced by Eichler and Daganzo [12]. In the BLIP strategy, not only are new vehicles prohibited from entering the bus lane, but those already in the lane are also required to exit [13,14]. Immediate lane clearance is enforced through variable message signs, ensuring that buses receive instantaneous spatial priority. This improvement reduces the strategy’s dependence on signal coordination and more closely adheres to the principles of dedicated bus lane operation. Simulation studies employing models such as cellular automata, VISSIM, and SUMO have evaluated parameters including segment length, traffic demand, and bus frequency, confirming the effectiveness of BLIP [5,13,14]. However, during peak hours or under heavy congestion, non-priority vehicles exiting the dedicated lane may experience difficulties merging back into regular traffic, thereby reducing overall system efficiency.

The development of vehicle connectivity technologies has created new opportunities for the deployment and management of lane-sharing strategies [15]. Vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communications enable fine-grained traffic control, allowing traditional fixed lane segments to evolve into minimal track units analogous to the railway block system, where fixed-block control is replaced by moving-block control [16]. It is reasonable to anticipate that the adoption of moving-block control can achieve more refined block management, thereby enhancing the efficiency of lane-sharing operations for ART systems. Meanwhile, advances in connected technologies have further strengthened ART’s autonomous driving capabilities, allowing for precise motion control [17,18]. By perceiving real-time road conditions, signal timings, and upstream traffic, ART vehicles can autonomously adjust their speed and acceleration to optimize eco-driving trajectories. Under lane-sharing conditions, ART-led mixed platoons can effectively reduce unnecessary stops and speed fluctuations, leading to improved energy efficiency and smoother overall traffic flow [19]. However, existing studies have primarily concentrated on lane resource sharing, while limited attention has been paid to leveraging the leading and guiding capabilities of ART in mixed traffic environments.

To address these gaps, this study proposes a moving-block-based lane-sharing strategy for ART systems incorporating a leading eco-driving approach. The main contributions are summarized as follows:

(1)

A moving block-based lane-sharing strategy is proposed for ART dedicated lanes. The strategy authorizes lane access according to real-time remaining green time, avoiding forced clearance and signal coordination and thus reducing impacts on non-ART vehicles.

(2)

An ART-led eco-driving control framework is developed, which not only provides a stop-free eco-driving trajectory for ART but also improves mixed traffic efficiency through vehicle-following behavior.

(3)

A modified trajectory optimization algorithm is designed that transforms the highly nonlinear programming into a state-space search problem. With a state-space reduction algorithm, the solution achieves a balance between computational efficiency and accuracy.

(4)

The compliance behavior of non-ART vehicles is analyzed. A key challenge in lane-sharing scenarios is the compliance of non-ART vehicles with block control rules. Simulation results show that when the compliance rate of non-ART vehicles exceeds 60%, ART operational efficiency is largely maintained.

The remainder of this study is organized as follows: Section 2 presents the problem statement. Section 3 introduces the moving block-based lane-sharing rules for ART. Section 4 details the eco-driving trajectory optimization model. Section 5 presents the simulation control framework. Section 6 discusses the simulation results. Finally, Section 7 concludes the study and outlines future research directions.

2. Problem Description and Assumptions

2.1. Problem Description

Figure 2 illustrates a typical scenario in which an ART system operates under lane-sharing conditions and performs leading eco-driving. The dedicated ART lane is located on the innermost side of the roadway, whereas the adjacent lanes are designated for non-ART vehicles. Through real-time signal phase and timing (SPaT) information, the ART dynamically optimizes its trajectory by explicitly considering the feasible green window, so as to pass the intersection at the earliest admissible time. A dynamic block zone is maintained ahead of the ART vehicle to ensure smooth passage through the intersection. Non-ART vehicles are temporarily permitted to enter the ART lane when lane-sharing conditions are satisfied, thereby improving lane utilization and mitigating congestion. The block zone applies only to the downstream section in the ART’s travel direction, while the upstream segment remains accessible to non-ART vehicles. Consequently, the purpose of the moving block is to dynamically authorize lane access in front of ART vehicles rather than to regulate the headway between consecutive ART units. The main issues to be addressed are as follows:

(1)

How to update the moving-block zone for non-ART vehicles without compromising the operational efficiency of ART. In addition, signal coordination and forced lane clearance are not preferred options, as they may impose adverse effects on the overall traffic flow.

(2)

How to generate eco-driving trajectories for ART vehicles that achieve a trade-off between computational efficiency and solution accuracy.

2.2. Assumptions

The proposed control system is based on the following assumptions:

(1)

The communication system is ideal, with no delays, packet loss, or failures; all data exchange is real-time and reliable.

(2)

Non-ART vehicles have higher desired speeds than ART but remain below the speed limit, and travel at the maximum allowable speed when unimpeded.

(3)

Non-ART vehicles comply with ART right-of-way signals [20]. The following sections examine the compliance rate of non-ART vehicles.

(4)

All non-ART vehicles are assumed to be homogeneous in physical characteristics (e.g., size and dynamics), as heavy trucks are generally prohibited from operating on urban roads during daytime.

3. Moving Block Control System for ART

This section introduces the moving block control system for ART, including the block control methodology and operating rules for non-ART vehicles.

3.1. Moving Block Control Methodology

Various lane-sharing control strategies have been developed, including time-division, IBL, and BLIP-based schemes. Nevertheless, the time-division approach often overlaps with peak-hour demand, reducing the practical benefit of lane sharing [21]. The IBL strategy avoids forced lane clearance but depends heavily on intersection signal coordination to discharge traffic, which tends to disrupt signal timing and cause inefficiencies [22]. The BLIP scheme, by contrast, enforces lane clearance upon the arrival of buses, which becomes difficult during peak congestion and may increase the risk of traffic accidents [23]. To address these limitations, this study proposes a moving-block-based lane-sharing method that relies neither on signal coordination nor on forced clearance. Once authorized for access, vehicles can travel without the risk of being forced out of the lane.

The moving block control strategy draws inspiration from the three-aspect signaling system in railway operations [24], where red, yellow, and green signals are employed to indicate block-section access authorization, as illustrated in Figure 3.

Red safety block: represents the safety protection area, where non-ART vehicles are strictly prohibited from entering. This ensures that the ART vehicle can stop safely in emergency situations, avoiding conflicts with other road users.

Yellow buffer block: represents a dynamic buffer area. Vehicles already in this zone are allowed to continue moving, but no new vehicles are permitted to enter. This access-only restriction prevents “trapped-in-lane” situations under high saturation.

Green free block: represents a free-access area where lane resources are fully shared, and non-ART vehicles are allowed to freely enter and exit.

Therefore, the key to the moving-block control lies in determining the remaining capacity of the dedicated lane and dynamically updating the length of each block section.

3.1.1. Red Safety Block

To ensure the safety of ART, a red safety block is defined ahead of the vehicle, representing the minimum distance required to avoid rear-end collisions under emergency scenarios. This concept is adapted from railway moving block control [24], and the required safety distance is defined in Equations (1)–(3):

$$D_{\mathrm{r}\mathrm{e}\mathrm{d}}=S_d+S_b+L_s+l_v$$

(1)

$$S_d=v·t_d$$

(2)

$$S_b={\displaystyle \frac{v^2}{2b_{\mathrm{m}\mathrm{a}\mathrm{x}}}}$$

(3)

where $D_{\mathrm{r}\mathrm{e}\mathrm{d}}$ is the red safety block length under worst-case conditions. $S_d$ is the distance due to braking delay, as calculated in Equation (2), where $t_d$ denotes the braking delay time. $S_b$ is the emergency braking distance from speed $v$, as given in Equation (3). $L_s$ is the minimum safe spacing at a standstill. $l_v$ is the length of the leading vehicle.

While the above tracking distance ensures safety under worst-case scenarios, directly applying railway-based values to ART may result in overly conservative spacing. Since ART vehicles typically operate within visual range and rarely require full stops, the emergency braking distance is adjusted accordingly into a modified form, denoted as ${S_b}^{\prime }$, and is defined in Equation (4).

$${S_b}^{\prime }={\displaystyle \frac{v_n^2}{2b_{\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{t}}}}-{\displaystyle \frac{v_{n-1}^2}{2b_{\mathrm{m}\mathrm{a}\mathrm{x}}}}$$

(4)

where ${S_b}^{\prime }$ denotes the modified emergency braking distance. $b_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximum deceleration rate of the preceding vehicle, and $b_{\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{t}}$ is the comfortable deceleration rate of ART. When the preceding vehicle’s speed is available in real time—such as via V2V communication or roadside units (RSUs)—$v_{n-1}$ is set accordingly; otherwise, the ART vehicle’s own speed is used as a conservative estimate.

3.1.2. Yellow Buffer Block

The key to the lane-sharing strategy is to identify and utilize the available green time. To minimize delays for ART, it either maintains the desired speed to pass through the intersection or crosses at the start of the green phase. As a result, the ART’s intersection passing time $t^f$ is predictable, as detailed in Equations (22)–(24). Accordingly, the length of the yellow buffer zone is determined based on the remaining green-light window for the ART lane, as shown in Equation (5).

$$D_{\mathrm{y}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{o}\mathrm{w}}=\left(t^f-T_p\right)·∆L$$

(5)

where $t^f$ is the predicted time for the ART to arrive at the intersection. $T_p$ is the total green time that has already been allocated to preceding vehicles before the ART arrives. $∆L$ is the spatial equivalent per unit green time (i.e., the length associated with one unit of green time remaining). $T_p$ is calculated as shown in Equation (6).

$$T_p=N_p·h$$

(6)

where $N_p$ is the number of non-ART vehicles expected to pass through the intersection within the current green window ahead of the ART, estimated using Equation (7). $h$ is the average headway between non-ART vehicles.

$$N_p=\sum _{i=1}^n{\delta }_i, \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e} {\delta }_i=\left\{\begin{array}{cc}1,& \mathrm{i}\mathrm{f} \mathrm{v}\mathrm{e}\mathrm{h}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e} i \mathrm{i}\mathrm{s} \mathrm{a}\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{d} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{A}\mathrm{R}\mathrm{T} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{a}\mathrm{m}\mathrm{e} \mathrm{g}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{n} \mathrm{p}\mathrm{h}\mathrm{a}\mathrm{s}\mathrm{e}\\ 0,& \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\end{array}\right.$$

(7)

where ${\delta }_i$ is a binary indicator representing whether vehicle $i$ is expected to pass through the intersection during the current green phase ahead of the ART. It equals 1 if the vehicle satisfies this condition, and 0 otherwise.

3.1.3. Green Free Block

Green free block refers to road segments that are neither part of the red safety block nor the yellow buffer block, allowing non-ART vehicles to merge and drive freely. These zones are defined conditionally, as shown in Equation (8).

$$D_{\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{n}}=\sum _{x\in L_{\mathrm{r}\mathrm{o}\mathrm{a}\mathrm{d}}}\beta \left(x\right), \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e} \beta \left(x\right)=\left\{\begin{array}{cc}1,& \mathrm{i}\mathrm{f} x\notin {(D}_{\mathrm{r}\mathrm{e}\mathrm{d}}\cup D_{\mathrm{y}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{o}\mathrm{w}})\\ 0,& \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\end{array}\right.,$$

(8)

where $L_{\mathrm{r}\mathrm{o}\mathrm{a}\mathrm{d}}$ is the total length of the ART lane, and $\beta \left(x\right)$ is an indicator function that identifies segments not occupied by the red or yellow zones. The green zone is thus defined as the union of all such segments.

3.2. Operating Rules for Non-ART Vehicles

Voluntary lane changes and mandatory lane exits are introduced to capture the lane-sharing maneuvers of non-ART vehicles. Although the mandatory lane-change model is established, it is not treated as a primary control measure in this study and is only triggered under conditions of high safety risk. In addition, the longitudinal car-following behavior of non-ART vehicles is modeled using the Intelligent Driver Model (IDM), which is a widely adopted microscopic model for representing human driving behavior and has been extensively validated in the literature [25,26,27].

3.2.1. Voluntary Lane Changing

The lane-changing behavior of non-ART vehicles is primarily motivated by the pursuit of higher speeds and better visibility. Specifically, the lane-changing rules for non-ART vehicles consist of the following components.

• Lane-changing incentive

A vehicle considers changing lanes when it cannot achieve its desired speed in the current lane and the conditions in the target lane are better. Specifically, the incentive condition in the current lane is defined in Equation (9), where the desired speed for the next time step is capped by both the acceleration limit and $V_{\mathrm{m}\mathrm{a}\mathrm{x}}$:

$$\left\{\begin{array}{l}{d}_n<\min \left(v_n\left(t\right)+a·\Delta t,V_{\mathrm{m}\mathrm{a}\mathrm{x}}\right)\\ d_{n,\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}}>d_n\\ t>t_{n,\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}}+t_{\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e},\mathrm{m}\mathrm{i}\mathrm{n}} \end{array}\right.$$

(9)

where $\min \left(v_n\left(t\right)+a·\Delta t,V_{\mathrm{m}\mathrm{a}\mathrm{x}}\right)$ is the capped desired speed of vehicle $n$ for the next time step, limited by both the acceleration capability and the maximum allowable speed. The condition $d_n<\mathrm{m}\mathrm{i}\mathrm{n}\left(v_n\right(t)+a·\Delta t,V_{\mathrm{m}\mathrm{a}\mathrm{x}})$ indicates that the available gap to the preceding vehicle in the current lane is insufficient to support this intended speed, i.e., vehicle $n$ is constrained by its preceding vehicle and thus may consider changing lanes. $d_n$ is the distance between vehicle $n$ and the preceding vehicle $n$ − 1 in the current lane. $v_n\left(t\right)$ is the speed of vehicle $n$ at time $t$. $a$ is the normal acceleration. $\Delta t$ is the time step. $V_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximum allowable speed. $d_{n,\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}}$ is the distance to the preceding vehicle in the target lane. $t_{n,\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}}$ is the time of the last lane change. $t_{\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e},\mathrm{m}\mathrm{i}\mathrm{n}}$ is the minimum lane-changing interval. The vehicle identifiers and their relative positions are illustrated in Figure 4.

• Safety condition

To ensure safety during the lane change, a vehicle must maintain a sufficient gap from the following vehicle in the target lane, as defined by Equation (10).

$$d_{n+1,\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}}>v_{n+1, \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}}$$

(10)

where $d_{n+1,\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}}$ is the distance between vehicle $n$ and the following vehicle $n$ + 1 in the target lane, and $v_{n+1,\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}}$ is the speed of the following vehicle in the target lane.

• Block-aware constraint

Lane changing is prohibited when the vehicle is located within a red or yellow block zone, which is defined in Equation (11). When Equation (11) holds, the lane-change decision is disabled and the vehicle is forced to remain in its current lane.

$$x_n\in {(D}_{\mathrm{r}\mathrm{e}\mathrm{d}}\cup D_{\mathrm{y}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{o}\mathrm{w}})$$

(11)

where $x_n$ denotes the position of vehicle $n$.

• Lane-changing probability

Even when both the incentive and safety conditions are satisfied, non-ART vehicles may not always execute a lane change. Thus, a lane-changing probability $p_{\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e}}$ is introduced. A vehicle will proceed to change lanes if:

$$\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{d}<p_{\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e}}$$

(12)

where $\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{d}$ is a random number uniformly distributed between 0 and 1. When a vehicle satisfies the lane-changing conditions, a random number $\mathrm{rand}$ is generated. The vehicle executes a lane change if $\mathrm{rand}<p_{\mathrm{change}}$; otherwise, it remains in its current lane.

3.2.2. Mandatory Lane Exit

When a non-ART vehicle is located within the red safety block zone, it must execute a mandatory lane exit. Thus, the triggering condition is defined by Equation (13).

$$x_n\in D_{\mathrm{r}\mathrm{e}\mathrm{d}}$$

(13)

where $x_n$ is the current position of the non-ART vehicle.

For mandatory lane exit, a lane change is executed only when the vehicle is required to leave the dedicated lane and a safe condition is satisfied; otherwise, the vehicle keeps searching for an acceptable gap, which is defined in Equation (10).

4. Eco-Driving Modeling for ART Based on Time–Space–State Network

This section presents the models related to ART-led eco-driving, including the ART trajectory optimization model, the ART energy consumption model, and the fuel consumption model for non-ART vehicles.

4.1. Model Formulation

4.1.1. Energy-Efficient Trajectory Optimization Based on Optimal Control

The objective function for platoon-leading optimization should ideally consider the energy consumption of all vehicles in the platoon. However, to reduce computational complexity, this study focuses solely on optimizing the energy consumption of the ART vehicle. Previous research has shown that optimizing only the energy consumption of the leading vehicle can still achieve a significant reduction in the overall energy consumption of the platoon, with a minor difference compared to optimizing all vehicles simultaneously [28].

The original mathematical formulation of the eco-driving trajectory optimization is presented in Equations (14)–(21).

$$\underset{u\left(t\right)}{\min } C={\int }_{t^0}^{t^f}c\left(v\left(t\right),u\left(t\right)\right)dt$$

(14)

Subject to:

$$\dot{x}\left(t\right)=v\left(t\right), \dot{v}\left(t\right)=u\left(t\right),$$

(15)

$$x\left(t^0\right)=x_0, v\left(t^0\right)=v_0,$$

(16)

$$x\left(t^f\right)=x_f, v\left(t^f\right)=v_f,$$

(17)

$$x_{min}\le x\left(t\right)\le x_{max},$$

(18)

$$v_{min}\le v\left(t\right)\le v_{max},$$

(19)

$$x_{n-1}\left(t\right)-x_n\left(t\right)\ge x_{safety},$$

(20)

$$u_{min}\le u\left(t\right)\le u_{max},$$

(21)

where Equation (14) aims to minimize the energy consumption of the ART trajectory. $t^0$ and $t^f$ denote the times when the vehicle enters and exits the control zone, respectively. The function $c\left(v\left(t\right),u\left(t\right)\right)$ represents the instantaneous energy consumption, which depends on the vehicle’s speed $v$ and acceleration $u$. its explicit form will be introduced in Section 4.2. Equation (15) describes the relationship among the position, velocity, and acceleration. Equations (16) and (17) constrain the initial and terminal state conditions. Equations (18) and (19) constrain the range of position and speed, respectively. Equation (20) describes the safety constraint between the ego vehicle and the preceding vehicle. Equation (21) constrains the range of the decision variables.

It should be noted that $t^f$ denotes the earliest feasible passing time of ART at the intersection subject to traffic feasibility, signal feasibility, and timetable constraints. Its value is obtained according to Equations (22)–(24).

$$t_n^f=\max \left(t_n^{f^{\prime }},t_n^g\right),$$

(22)

$$t_n^{f^{\prime }}=\max \left(t_n^{min},t_{n-1}^f+h, t_n^{sch}\right),$$

(23)

$$t_n^g=\left\{\begin{array}{l}{g}_k^s, t_n^{f^{\prime }}\in \left[g_k^s,g_k^s+g_k\right),\\ g_{k+1}^s, t_n^{f^{\prime }}\in \left[g_k^s+g_k,g_{k+1}^s\right].\end{array}\right.$$

(24)

where $t_n^{f^{\prime }}$ is the potential earliest entry time of ART $n$ into the intersection, which is determined by three factors: the earliest arrival time $t_n^{min}$ under free-flow conditions, the saturation headway $h$ considering the preceding vehicle ($n$ − 1), and the schedule-imposed earliest passing time $t_n^{sch}$ at the intersection (obtained from the timetable plan). Moreover, $t_n^g$ is the green signal start time that is close to $t_n^{f^{\prime }}$. Equation (24) determines the green signal start time when $t_n^{f^{\prime }}$ is allowed to enter the intersection, where $g_k^s$ and $g_k$ denote the start time and duration of the green light for the $k$-th cycle, respectively.

4.1.2. Improved Trajectory Optimization Model Based on the Space–Time–State Network

The above model represents a typical optimal control framework. To facilitate online computation, the objective function is often simplified to a quadratic form—for example, by minimizing the square of acceleration. However, for electric ART systems, particularly when considering their regenerative braking characteristics, such simplification may lead to physically inconsistent or even meaningless optimization problems.

To improve the efficiency of trajectory optimization, a time–space–state network model is constructed, allowing vehicles to move over a discretized network. The time-space-velocity dimensions are discretized to construct the time–space–state network, as illustrated in Figure 5. The reason for using discrete modeling is that it enables the transformation of a complex nonlinear programming problem into a state-space search problem. The discretization steps for time, space, and speed are denoted as $(∆t,∆s,∆v)$, where $∆v=∆s/∆t$. Three-dimensional variables $\left(t_i,s_i,v_i\right)$ are used to represent a vehicle’s position $s_i$ and velocity $v_i$ at time $t_i$. Vehicle motion is characterized by the update of position and speed at each time step. Specifically, arcs $\left(t_i^j,s_i^j,v_i^j\right)\in E$ represent transitions from node $i=\left(t_i,s_i,v_i\right)$ to node $j=\left(t_j,s_j,v_j\right)$. The remaining notation is summarized in

Table 1. Notation declaration.

Notation	Definition
$n$	Vehicle Index, $n\in N$
$s_i,s_j$	Space dimension index, $s_i,s_j\in S$
$t_i,t_j$	Time dimension index, $t_i,t_j\in T$
$v_i,v_j$	State (Velocity) dimension index, $v_i,v_j\in V$
$\left(t_i^j,s_i^j,v_i^j\right)$	Space–time–state arc index, $\left(t_i^j,s_i^j,v_i^j\right)\in E$
$c_n\left(t_i^j,s_i^j,v_i^j\right)$	The cost of the vehicle $n$ traveling on the arc $\left(t_i^j,s_i^j,v_i^j\right)$
$o\left(n\right)$	Starting point for vehicle $n$
$d\left(n\right)$	The endpoint of vehicle $n$
$ST\left(n\right)$	Start time of vehicle $n$
$ET\left(n\right)$	End time of vehicle $n$
${\theta }_n\left(t_i,s_i\right)$	Whether vehicle $n$ passes through the space–time node $\left(t_i,s_i\right)$
$\phi \left(\tau ,\kappa \right)$	Conflict region of space–time node $\left(\tau , \kappa \right)$
Sets
$N$	Set of all vehicles
$S$	Space set
$T$	Time set
$V$	State set
$E$	Space–time–state arcs set
Variables
$x_n\left(t_i^j,s_i^j,v_i^j\right)$	$=1$, if vehicle $n$ selects the space–time–state arcs $\left(t_i^j,s_i^j,v_i^j\right)$; $= 0$ otherwise.

.

In this way, the eco-driving trajectory optimization is transformed into a shortest-path problem on time–space–state network, as formulated in Equations (25)–(29).

Objective function:

$$\underset{x_n(t_i^j,s_i^j,v_i^j)}{\min }Z=\sum _{n\in \mathcal{N}}\sum _{\left(t_i^j,s_i^j,v_i^j\right)\in E}{c}_n(t_i^j,s_i^j,v_i^j)·x_n(t_i^j,s_i^j,v_i^j),$$

(25)

Subject to

Flow balance constraint:

$$\sum _{i:\left(t_i^j,s_i^j,v_i^j\right)\in E}{x}_n(t_i^j,s_i^j,v_i^j)-\sum _{i:\left(t_j^i,s_j^i,v_j^i\right)\in E}{x}_n(t_j^i,s_j^i,v_j^i)=\left\{\begin{array}{cc}-1& \forall n\in N,t_j=ST\left(n\right),s_j=o\left(n\right),\\ 1& \forall n\in N,t_j=ET\left(n\right),s_j=d\left(n\right),\\ 0& \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e},\end{array}\right.$$

(26)

Safety Constraints:

$${\theta }_n\left(t_i,s_i\right)=\sum _{j:\left(t_i^j,s_i^j,v_i^j\right)\in E}{x}_n\left(t_i^j,s_i^j,v_i^j\right),\forall \left(t_i,s_i\right),\forall n\in N,$$

(27)

$$\sum _{n\in N}\sum _{\left(t_i,s_i\right)\in \phi \left(\tau ,\kappa \right)}{\theta }_n\left(t_i,s_i\right)\le 1,\forall \tau \in T,\forall \kappa \in S,$$

(28)

Decision Variables:

$$x_n\left(t_i^j,s_i^j,v_i^j\right)=\left\{0,1\right\}, \forall n\in N,\forall \left(t_i^j,s_i^j,v_i^j\right)\in E,$$

(29)

where Equation (25) aims to minimize the total fuel consumption of vehicles by selecting cost-minimal arcs in the time–space–state network. Equation (26) represents the flow balance constraint, which guarantees the continuity of each vehicle’s trajectory by enforcing that a single, continuous path is selected from the origin node to the destination node, while conserving flow at all intermediate nodes. As a result, each vehicle follows exactly one feasible trajectory without branching or discontinuity. To model safety interactions between vehicles, Equation (27) introduces an auxiliary binary variable ${\theta }_n(t_i,s_i)$ to indicate the occupancy of a spatiotemporal node. Specifically, ${\theta }_n(t_i,s_i)=1$ means that vehicle $n$ occupies node $(t_i,s_i)$, whereas ${\theta }_n(t_i,s_i)=0$ indicates that the node is not occupied by vehicle $n$. Based on this node-occupancy representation, Equation (28) formulates the safety constraint between vehicles by restricting each incompatible region in the time–space domain to be occupied by at most one vehicle at any given time, thereby preventing spatiotemporal conflicts, as illustrated in Figure 6. Equation (29) is the binary decision variable that indicates whether an ART chooses the arc $\left(t_i^j,s_i^j,v_i^j\right)$. Other range constraints are converted into the connectivity of the space–time–state network to improve the computational efficiency of the algorithm, as detailed in Section 5.

4.2. Energy Consumption Model for ART

This study adopts an electric vehicle energy consumption model proposed by [29]. The reasons for selecting this model are twofold: (1) it captures the instantaneous energy consumption behavior of the vehicle, accounting for regenerative braking effects with nonlinear recovery parameters, which aligns with the characteristics of electric vehicle braking systems; and (2) the model has been validated against empirical data and has demonstrated high accuracy.

In this study, only the energy consumption due to vehicle motion is considered, while the energy usage from auxiliary systems is neglected. The energy consumption model for ART is given by Equation (30).

$$c_e\left(v\left(t\right),u\left(t\right)\right)=\left\{\begin{array}{c}{\displaystyle \frac{P_W\left(t\right)}{{\eta }_D·{\eta }_{EM}·{\eta }_B}}, \mathrm{if} P_W\left(t\right)\ge 0\\ P_W\left(t\right)·{\eta }_D·{\eta }_{EM}{·\eta }_B{·\eta }_{rb}, \mathrm{if} P_W\left(t\right)<0\end{array}\right.$$

(30)

where $P_W\left(t\right)$ is the power at the wheels, ${\eta }_D$, ${\eta }_{EM}$, and ${\eta }_B$ denote the drivetrain efficiency, electric motor efficiency, and battery-to-motor power transfer efficiency, respectively. The regenerative braking efficiency ${\eta }_{rb}$, which depends on the vehicle acceleration, is defined as Equation (31).

$${\eta }_{rb}\left(t\right)={\left[e^{\left({\displaystyle \frac{\lambda }{\left|u\left(t\right)\right|}}\right)}\right]}^{-1}$$

(31)

The wheel power $P_W\left(t\right)$ is calculated as Equation (32).

$$P_W\left(t\right)=\left(mu\left(t\right)+R\left(t\right)\right)·v\left(t\right)$$

(32)

where $m$ is the vehicle mass and $R\left(t\right)$ represents the total resistance acting on the vehicle, which is the sum of aerodynamic resistance $R_a\left(t\right)$, rolling resistance $R_r\left(t\right)$, and gravitational resistance $R_g\left(t\right)$. These components are given by Equations (33)–(36).

$$R\left(t\right)=R_a\left(t\right)+R_r\left(t\right)+R_g\left(t\right)$$

(33)

$$R_a\left(t\right)={\displaystyle \frac{\rho }{2}}{C}_d{A}_f{v\left(t\right)}^2$$

(34)

$$R_r\left(t\right)=mgcos\left(\theta \right){\displaystyle \frac{c_{r0}}{1000}}\left(c_{r1}v\left(t\right)+c_{r2}\right)$$

(35)

$$R_g\left(t\right)=mgsin\left(\theta \right)$$

(36)

In this study, the vehicle is assumed to operate on a flat road surface, and the gradient is therefore set to zero, i.e., $R_g\left(t\right)$ = 0. The definitions and values of the remaining parameters are provided in

Table 2. Parameter definitions and values for the ART/non-ART vehicles consumption models.

Parameter	Definition	Value
${\eta }_D, {\eta }_{EM},{\eta }_B$	Electric vehicle efficiency	92%, 91%, 90%
$\lambda$	Regenerative efficiency parameter	0.0411
$m$	Vehicle mass	ART: 30,000 $\mathrm{k}\mathrm{g}$; non-ART: 1600 $\mathrm{k}\mathrm{g}$
$\rho$	Air density	1.2256 $\mathrm{k}\mathrm{g}/{\mathrm{m}}^3$
$C_D$	Aerodynamic drag coefficient	ART: 0.75; non-ART: 0.28
$A_f$	Frontal area of the vehicle	ART:8.30 ${\mathrm{m}}^2$; non-ART: 2.34 ${\mathrm{m}}^2$
$c_{r0}$, $c_{r1}$, $c_{r2}$	Rolling resistance coefficients	ART: 2.1, 0.042, 6.2; non-ART: 1.75, 0.0328, 4.575
$\alpha$	Idle fuel consumption rate	0.375 $\mathrm{m}\mathrm{L}/\mathrm{s}$
${\beta }_1$, ${\beta }_2$	Efficiency constants	0.09$\mathrm{m}\mathrm{L}/\mathrm{k}\mathrm{J}$, $0.03 \mathrm{m}\mathrm{L}/(\mathrm{k}\mathrm{J}·\mathrm{m}/{\mathrm{s}}^2$)
$g$	Gravitational acceleration	9.8 $\mathrm{m}/{\mathrm{s}}^2$

.

4.3. Fuel Consumption Model for Non-ART Vehicles

This study adopts a fuel consumption model based on the VT-CPFM-1 framework proposed by [30]. The instantaneous fuel consumption rate $c_e\left(v\left(t\right),u\left(t\right)\right)$ is defined as Equation (37).

$$c_e\left(v\left(t\right),u\left(t\right)\right)=\left\{\begin{array}{c}\alpha u\left(t\right)\le -{\displaystyle \frac{R\left(t\right)}{m_p}}\\ \alpha +{\beta }_1{R}_T\left(t\right)v\left(t\right) u\left(t\right)\in \left(-{\displaystyle \frac{R\left(t\right)}{m_p}},0\right)\\ \alpha +{\beta }_1{R}_T\left(t\right)v\left(t\right)+{\displaystyle \frac{{\beta }_{2}mu{\left(t\right)}^{2}v\left(t\right)}{1000}} u\left(t\right)\ge 0\end{array}\right.$$

(37)

where $R_T\left(t\right)$ denotes the total tractive force, which is defined by Equation (38).

$$R_T\left(t\right)=mu\left(t\right)+R\left(t\right)$$

(38)

The resistance term $R\left(t\right)$ is computed in the same manner as for electric vehicles, using Equations (33)–(36). Definitions and values of the remaining parameters are provided in Table 2, which are derived from relevant literature [31,32] and ART company investigations.

5. Solution Algorithm and Control Framework

5.1. Solution Algorithm

The proposed trajectory optimization model reformulates the nonlinear optimal control problem as a shortest-path problem in a discrete state space. This formulation allows the use of efficient search algorithms such as dynamic programming, Dijkstra’s algorithm, and the A* algorithm. However, the computational efficiency is highly sensitive to the size of the state space. When the dimensionality becomes large, the so-called “curse of dimensionality” arises, making the algorithm difficult to apply in real-time or online computation.

To effectively reduce the state space, this study proposes a state-space reduction algorithm. For clarity of presentation, a two-dimensional schematic is adopted to illustrate the principle. Figure 7a shows the complete search space. Considering the motion of the preceding vehicle and speed constraints, the feasible search region can be reduced, as illustrated in Figure 7b. For a given state $\left(t_i,s_i,v_i\right)$, the vehicle is subject to three categories of constraints: forward-motion, acceleration, and safety constraints. Specifically, the forward-motion constraint restricts the vehicle to move only ahead, the acceleration constraint bounds its speed variation, and the safety constraint maintains a sufficient distance from the preceding vehicle. Consequently, the feasible region is significantly narrowed, as illustrated in Figure 7c [33]. Based on these principles, the trajectory optimization algorithm that integrates dynamic programming with state-space reduction is summarized in Algorithm 1.

Accordingly, Algorithm 1 evaluates only the feasible state transitions after state-space reduction. For each feasible transition, the next state is generated using the discrete vehicle dynamics, and the associated stage cost (e.g., energy/fuel consumption) is calculated. Steps 13–16 update the DP matrix by keeping the minimum cumulative cost among all feasible transitions leading to the same next state, which guarantees that the recovered trajectory is optimal within the reduced feasible region.

Algorithm 1. ART trajectory optimization via dynamic programming with state-space reduction
Input: Initial state $(t_0,i_0,u_0)$; signal timing; model parameters
Output: Optimized trajectory (state and control sequence)
1	Initialization
2	Initialize $DP(t,i,u)\leftarrow \mathrm{\infty }$ for all $t\in T$, $i\in S$, $u\in V$
3	Set $DP(t_0,i_0,u_0)\leftarrow 0$; set predecessor $\mathrm{pred}(t_0,i_0,u_0)\leftarrow \mathrm{\varnothing }$
4	Dynamic programming recursion
5	for each $t\in T$ do
6	${\mathsf{\Omega }}_t\leftarrow$ feasible state set at time $t$ satisfying safety constraints and speed limits
7	for each $(i,u)\in {\mathsf{\Omega }}_t$ do
8	$A_t(i,u)\leftarrow$ admissible acceleration set under vehicle dynamics
9	for each $a\in A_t(i,u)$ do
10	$i^{\prime }\leftarrow i+u+a$, $u^{\prime }\leftarrow u+a$
11	if $(t+1,\hspace{0.17em}{i}^{\prime },\hspace{0.17em}{u}^{\prime })$ is feasible then
12	$c\leftarrow c(t,i,u,a)$
13	if $DP(t+1,\hspace{0.17em}{i}^{\prime },\hspace{0.17em}{u}^{\prime })>DP\left(t,i,u\right)+c$, then
14	$DP(t+1,\hspace{0.17em}{i}^{\prime },\hspace{0.17em}{u}^{\prime })\leftarrow DP\left(t,i,u\right)+c$
15	$\mathrm{pred}(t+1,i^{\prime },u^{\prime })\leftarrow (t,i,u,a)$
16	end if
17	end if
18	end for
19	end for
20	end for
21	Termination and backtracking
22	$\left(t^{*},i^{*},u^{*})\leftarrow \mathrm{a}\mathrm{r}\mathrm{g} \mathrm{m}\mathrm{i}\mathrm{n} DP(t,i,u\right)$ over feasible terminal states
23	Recover the optimal trajectory and control sequence by backtracking via $\mathrm{pred}(\cdot )$

5.2. Control Framework

The control process for ART eco-driving and dedicated lane sharing is illustrated in Figure 8. The system first identifies the vehicle type. If the vehicle is ART, an eco-driving trajectory is re-optimized and executed when safety risks are detected or a trajectory replanning period is reached. The replanning strategy helps address emerging risks in a timely manner [34]. If unexpected situations occur that require manual takeover, ART switches from the eco-driving controller to a baseline car-following mode (IDM) for operation. Once the ART state is updated, the length of the dynamic block zone is adjusted accordingly.

For non-ART, the system checks whether the vehicle is within the dynamic block zone. If it is, a mandatory lane change is triggered; otherwise, the non-ART vehicle proceeds in its current lane. However, mandatory lane changes may not always be immediately feasible due to insufficient lane gaps. In such cases, the non-ART vehicle continues to travel within the dedicated lane until a suitable lane-changing opportunity becomes available, as specified in Equation (10).

6. Simulation Experiments

6.1. Parameter Settings

To evaluate the effectiveness of the proposed control framework, a simulation-based approach is adopted. The experimental scenario is based on a representative intersection along the Yibin ART T1 line, with an upstream control distance of $l$= 600 m. To avoid introducing additional traffic flow complexity, only the adjacent through lane next to the ART lane is considered for sharing. Lane changing is prohibited within 60 m before the section and 100 m before the intersection. From the inside to the outside, the lane configuration consists of an ART dedicated lane and a conventional lane for non-ART vehicles. The signal cycle length is T = 60 s, with a 30 s green time for the through movement. A similar setup is also used in other studies [35]. Based on the field survey, the through traffic volume is set to $D$ = 780 veh/h/ln. To highlight the benefits of ART lane sharing, the ART arrival interval is set to 60 s—shorter than actual operating conditions—so as to demonstrate the potential for additional lane resources to be shared. In general, longer ART headways would provide more idle capacity for non-ART vehicles, resulting in greater efficiency gains.

The motion behavior of non-ART vehicles is modeled using the intelligent driver model. The desired speed of non-ART vehicles is set to 18 m/s, with a vehicle length $l_v$= 5 m. The desired time headway is set to 2 s. The desired speed of ART vehicles is 15 m/s, and the vehicle length $l_{ART}$ is 31.64 m. These values are determined based on the field survey. All vehicles are subject to maximum acceleration and deceleration limits of 2 m/s² and −3 m/s², respectively [36,37]. The comfortable deceleration for ART is set to $b_{\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{t}}$ = −1.5 m/s², and the braking delay, including actuator and communication latency, is $t_d$ = 1 s [38]. Based on field investigations and system-specific design considerations, $L_s$ = 5 m is adopted as the minimum standstill safety distance. The simulation step size is 1 s, and the total simulation duration is 600 s. All simulations are implemented on the Matlab 2024b platform using a system equipped with an AMD Ryzen 9 8945HX CPU and 32 GB of RAM. For clarity and reproducibility, the main simulation parameters used in the experiments are summarized in

Table 3. Simulation parameters and settings.

Category	Parameter	Symbol	Value
Signal	Cycle length	$T$	60 s
	Green time	-	30 s
Vehicles	Traffic volume	$D$	780 veh/h/ln
	ART arrival interval (headway)	-	60 s
	Desired speed (non-ART vehicles)	$V_{\mathrm{m}\mathrm{a}\mathrm{x}}^{veh}$	18 m/s
	Desired headway (non-ART vehicles)	-	2 s
	Desired speed (ART)	$V_{\mathrm{m}\mathrm{a}\mathrm{x}}^{ART}$	15 m/s
	Vehicle length (non-ART vehicles)	$l_{veh}$	5 m
	Vehicle length (ART)	$l_{ART}$	31.64 m
	Max acceleration	$a_{\mathrm{m}\mathrm{a}\mathrm{x}}$	2 m/s2
	Max deceleration (all vehicles)	$b_{\mathrm{m}\mathrm{a}\mathrm{x}}$	−3 m/s2
	Comfortable deceleration (ART)	$b_{\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{t}}$	−1.5 m/s2
	Braking delay (ART)	$t_d$	1 s
	Minimum standstill safety distance	$L_s$	5 m
Simulation	Time step	-	1 s
	Simulation duration	-	600 s

.

6.2. Evaluation of ART Lane-Sharing Effectiveness

To evaluate the effectiveness of the proposed framework, a comparative analysis is conducted across multiple control scenarios in terms of vehicle delay and energy consumption. The following three control strategies are evaluated: (1) ART-dedicated: the ART lane is reserved exclusively for ART vehicles, with no access permitted to non-ART vehicles; (2) Lane sharing without ART priority: non-ART vehicles are allowed to freely enter and exit the ART lane without any block-based clearance or priority control; (3) Lane sharing with ART priority: a moving block control mechanism is enforced to ensure ART operational priority. To ensure comparability among these control strategies, all non-ART vehicles are generated from the regular lane.

Figure 9 illustrates the vehicle trajectories under the three control scenarios. The simulation results reveal the following insights: (1) In the ART-dedicated scenario, the ART lane remains underutilized for prolonged periods, resulting in inefficient use of the valuable spatiotemporal road resources. In contrast, the adjacent regular lane is saturated, but due to the exclusive access rule, non-ART vehicles are prohibited from using the ART lane. This results in increased congestion and delay for non-ART traffic. The imbalance in lane utilization reveals significant issues related to traffic inefficiency and inequitable resource allocation, potentially contributing to public criticism of ART priority policies. (2) In the lane-sharing without ART priority scenario, the ART lane accommodates a considerable number of non-ART vehicles, effectively easing congestion in the adjacent lane. However, this also causes notable delays for ART vehicles, thereby compromising their operational efficiency, as detailed in Figure 10. (3) In the lane-sharing with ART priority scenario, the ART lane is effectively utilized to absorb overflow traffic from the saturated regular lane, while ART vehicles experience minimal delay, demonstrating a balance between priority protection and resource sharing.

Figure 10 presents the delay and energy consumption results under the three control strategies. The results indicate that: (1) In the ART-dedicated policy, non-ART vehicles experience the highest levels of delay and energy consumption, with an average delay of 45.1 s and fuel usage of 73.2 mL. ART operations are efficient, but the dedicated lane remains underutilized. (2) Lane sharing without ART priority reduces the delay and fuel usage of non-ART vehicles by 76.2% and 20.5%, respectively. However, ART vehicles suffer a 40.1% increase in delay and a 10.0% increase in energy consumption, indicating compromised operational efficiency. (3) Compared with the ART-dedicated strategy, the proposed ART-priority lane-sharing strategy effectively reduces the delay and energy consumption of non-ART vehicles by 72.6% and 24.6%, respectively, while maintaining almost unchanged delay and energy performance for ART vehicles. These findings demonstrate that ART-priority lane sharing improves lane utilization and overall traffic efficiency. It should be noted that the delay of ART vehicles remains approximately 20 s, which is mainly determined by their arrival interval. The effects of different arrival intervals will be further investigated in subsequent analyses.

6.3. Sensitivity Analysis of Traffic Demand

To evaluate the performance of the proposed control strategy under different traffic demand conditions, a baseline demand of D = 780 veh/h/ln is used, and the demand is varied from 0.8D to 1.2D with a step of 0.1D. Figure 11 illustrates the delay and energy consumption results under different demand levels, where the bars represent non-ART vehicles and the lines correspond to ART.

It can be observed that as traffic demand increases, the ART-dedicated strategy exhibits the most significant growth in both delay and energy consumption for non-ART vehicles. In particular, when the demand exceeds 0.9D, the increase in delay becomes exponential. In contrast, both lane-sharing strategies maintain relatively stable performance. Notably, the ART-Priority Shared strategy yields the lowest energy consumption for non-ART vehicles. This improvement is twofold: first, the moving-block control in the ART lane reduces unnecessary red-light waiting for non-ART vehicles, as illustrated in Figure 9c, where non-ART vehicles in the ART lane can proceed without stopping. Second, the leading effect of ART further enhances the overall energy efficiency of the mixed traffic flow.

It is also observed that the delay and energy consumption of ART vehicles remain optimal under the ART-Priority Shared strategy. In particular, the ART delay under this strategy almost coincides with that of the ART-Dedicated scheme, indicating that the priority control effectively preserves ART operational efficiency. Moreover, the ART energy consumption is even lower than in the ART-Dedicated case, which may result from the trajectory re-optimization process enabled by the lane-sharing mechanism.

A potential concern is whether the ART-Priority Shared strategy remains effective under oversaturated conditions and whether non-ART vehicles may become trapped in the ART lane. Figure 12 illustrates the performance of the two lane-sharing strategies under oversaturated traffic. It can be observed that the ART-Priority Shared strategy effectively protects non-ART vehicles while maintaining ART operational efficiency. No “trapped-in-lane” situations occur, which can be attributed to the design of the moving-block control that focuses on entry authorization for non-ART vehicles rather than forced clearance. In contrast, in the fully shared scenario, ART vehicles experience noticeably higher delays.

6.4. Sensitivity Analysis of ART Arrival Interval

As discussed earlier, the arrival interval of ART vehicles can influence their delay, as it may cause periodic interactions with the signal cycle. In this section, the impact of different ART arrival intervals on vehicle delay is evaluated. The arrival time interval of ART vehicles at the intersection detection zone varies from 40 s to 80 s with a step of 10 s. The traffic demand is set to 780 veh/h/ln, and all other parameters remain unchanged. Figure 13 presents the vehicle delay results under different arrival intervals. It can be observed that regardless of the ART arrival interval, the proposed ART-Priority Shared strategy consistently achieves a significant reduction in delay for non-ART vehicles, while maintaining the same delay level for ART vehicles as in the ART-Dedicated case. These results demonstrate the robust performance of the proposed strategy under varying ART arrival intervals.

One concern is whether the proposed ART-Priority Shared strategy remains effective when multiple ART vehicles pass through the intersection within the same green time window. This situation frequently occurs when the ART arrival interval is 40 s, as illustrated in Figure 14. The results indicate that the proposed strategy can stably manage such scenarios without compromising traffic performance.

6.5. Sensitivity Analysis of Non-ART Compliance

A key concern in opening the ART lane is whether non-ART vehicles will comply with the moving block control rules. Non-compliance may affect the delay and energy consumption of ART operations. Therefore, this section evaluates the impact of varying non-ART compliance levels on overall system performance.

Compliance refers to the willingness of non-ART to obey moving-block instructions. Non-compliant vehicles ignore the lane control signals and intrude into the ART dynamic block zone. In the simulation, the compliance rate is defined as the proportion of non-ART that follow block rules. During vehicle generation, non-ARTs are randomly assigned compliance attributes based on the specified compliance rate. Figure 15 illustrates the effect of non-ART compliance on ART vehicle delay and energy consumption. The results show that when the compliance rate exceeds 0.6, the performance of ART operations is only marginally affected.

6.6. Computational Efficiency Analysis

To apply the proposed strategy in real-world scenarios, a key challenge lies in the computational burden of the system. Since the moving-block control and lane-sharing updates mainly involve simple mathematical operations, the analysis of computational efficiency focuses on the ART-led eco-driving trajectory optimization. Two widely adopted trajectory optimization methods were selected for comparison with the proposed algorithm: the Gaussian Pseudospectral Method (GPOPS) [39] and the segmentation method [40]. The former employs a direct collocation framework discretized into a nonlinear programming and solved using the general-purpose solver SNOPT. The latter simplifies the optimization process by dividing the trajectory into several predefined segments—typically including deceleration, cruising, and acceleration—thereby reducing the number of decision variables.

Table 4. Computational efficiency comparison.

Indicator	GPOPS	Segmentation Method	This Paper
Energy consumption (kWh)	1.32	1.52	1.26
Computation time (s)	0.15	0.56	0.05

presents the comparative results of the three algorithms. The GPOPS algorithm demonstrates higher computational efficiency but results in relatively greater energy consumption. The segmentation-based method requires a longer computation time (0.56 s), which limits its suitability for real-time control applications. This is mainly due to the additional time required to integrate the nonlinear energy consumption function. In contrast, the proposed algorithm achieves significant advantages in both computational efficiency (0.05 s) and solution optimality. These improvements stem from the time–space–state network formulation, which transforms the original nonlinear optimization problem into a finite-state search framework. When combined with the state-space reduction algorithm, the proposed approach achieves both high computational efficiency and accuracy.

7. Conclusions and Future Work

This study proposed a moving-block-based lane-sharing strategy for ART systems with a leading eco-driving approach. The lane-sharing strategy focuses on granting lane-access authorization to conventional vehicles rather than relying on forced lane clearance or signal coordination. Furthermore, an efficient and accurate trajectory optimization algorithm is developed to generate eco-driving trajectories for ART vehicles, which in turn indirectly improve the performance of following vehicles. A series of simulation experiments were conducted to evaluate the effectiveness of the proposed strategy, and the following conclusions can be drawn:

(1)

The proposed control framework achieves a balance between operational efficiency and the performance of non-ART vehicles, reducing the delay and energy consumption of non-ART vehicles by 72.6% and 24.6%, respectively, without increasing the delay or energy consumption of ART operations.

(2)

The strategy demonstrates strong adaptability under varying traffic demand levels and ART arrival intervals.

(3)

When the non-ART vehicles’ compliance rate with the moving block control exceeds 0.6, the operational efficiency of ART remains largely unaffected.

Although this study verifies the effectiveness of the proposed moving-block lane-sharing strategy for ART lane management, the communication of block information to non-ART vehicles warrants further investigation. As shown in Figure 3, LED light strips provide effective lane-access authorization but are not standardized traffic control devices. Future work may explore using connected vehicle communication for block control or converting dense LED strips into fixed roadside signals to improve implementation feasibility. Moreover, extending the strategy to multi-intersection scenarios represents another promising direction for future work.