Study on the Design of Variable Lane Demarcation in Urban Tunnels

Abstract

In order to alleviate the influence of low-speed vehicles on tunnel safety, this paper discusses the setting method of variable lane boundaries in urban tunnels. VISSIM simulation software is used to analyze the influence of low-speed vehicles on tunnel traffic flow when lane changes are allowed and when lane changes are prohibited. The results show that the influence of low-speed vehicles on the average speed of traffic flow in urban tunnels is the greatest, and the influence of low-speed vehicles on the average speed of traffic flow can be significantly alleviated when lane changes are allowed in the lane dividing line. When the speed of low-speed vehicles is 40 km/h and the variable lane is set, the average delay time is reduced by 30–50%. The existence of low-speed vehicles significantly increased the average delay time of the local lane, and the lower the vehicle speed and the greater the road traffic volume, the longer the average delay time. When the speed of low-speed vehicles is 40 km/h and the traffic volume is 1200 pcu/h, the traffic density of the right-hand lane decreases by 43.5% after the variable lane is set. While lane changing is prohibited, the presence of low-speed vehicles causes a backlog of vehicles in the rear of the lane, which leads to a significant increase in traffic density. Setting lane-changing permits can alleviate the impact of low-speed vehicles on traffic flow. The research results can provide a scientific basis for the operation and management of urban tunnels.

1. Introduction

Some of urban expressway tunnels cross mountains, lakes, or river bottoms, and generally have long cavities. The lane dividers inside the tunnel are painted as solid white lines to prevent traffic accidents caused by drivers changing lanes at will. However, drivers have different experiences, personalities, and driving skills, and individual drivers′ low speeds in the tunnel can lead to a backlog of vehicles lining up behind them, especially during the morning and evening rush hours, when waves of congestion can continuously propagate to the rear, seriously affecting the efficiency of tunnel traffic. Ref. [1] investigates the risk of travelling in the right-hand lane of an urban expressway with a mobile working zone. As the lane divider of the open section of the expressway is a dashed line, allowing lane changes for overtaking, the presence of the right-hand lane mobile working zone has a greater impact on this lane, and the impact on the other two lanes is governed by the speed of the mobile working zone and the volume of road traffic. The lane dividers in urban tunnels are generally solid lines, prohibiting lane changes and overtaking. The presence of a mobile working area in the right-hand lane poses a greater risk to the right-hand lane inside the tunnel and to the middle and left-hand lanes of the tunnel exit. The working hours and conditions of the mobile working area can be controlled by the tunnel management, while the impact of low-speed vehicles (commonly known as “turtle” vehicles, where a driver is travelling at a speed significantly below the road speed limit when there are no vehicles or other obstructions in sight on the road ahead) on the traffic flow, which often occurs on the actual road, is not yet effectively controlled. According to the statistics, low-speed vehicles appear during almost every hour section, seriously affecting the tunnel′s efficiency; however, due to the lane divider and the tunnel lane change capture system, the rear drivers can only choose to bear with the car driving, and current laws and regulations are ineffective measures for dealing with this issue.

With the development of intelligent transportation, using intelligent control technology for real-time intelligent adjustments of urban tunnel lane boundaries can maximize the use of urban tunnel road resources and alleviate the impact of low-speed vehicles on urban tunnel traffic, as well as the tunnel backlog of queuing vehicles, which can lead to road tunnel safety risks caused by other drivers performing unauthorized lane changes. In this paper, low-speed vehicles in urban tunnels are taken as the research object, the influence of low-speed vehicles on tunnel traffic flow under different conditions is analyzed using a simulation method, and the setting method of a variable lane boundary is proposed in order to provide theoretical support for traffic management in urban tunnels.

2. Literature Review

The influence of low-speed vehicles on road traffic flow is studied by the method of experimental measurement and traffic simulation. The research objects mainly include low-speed trucks or road maintenance vehicles, and the selected parameters mainly include average vehicle delay, average speed of traffic flow, and road efficiency.

Gao et al. [2] used a laser roadside traffic survey instrument with automatic vehicle type recognition to collect cross-sectional traffic flow data to calculate the V/C (ratio of maximum service traffic volume to basic capacity), slow-moving vehicle admixture rate, and average traffic speed for each dataset, to predict the effect of slow-moving vehicles on the average speed of traffic flow. Dong [3] used the meta-cellular transport model and combined it with the three-phase traffic flow theory to study the impact of low-speed vehicles on the traffic flow of current highways. Yan [4] modeled and simulated low-speed vehicles on the highway to reveal the law of their influence on traffic flow efficiency. Based on the two-lane NaSch model, Wang [5] established a meta-automata model for heavy-duty trucks by considering the differences in the dynamic and braking performance of trucks and cars, as well as the formation mechanism of low-speed vehicles. Ji et al. [6] mapped the traffic flow of each lane of the road by establishing a meta-cellular automaton model, and analyzed the impact of the operational behavior of two types of low-speed vehicles, sweepers and sprinklers, on the road traffic flow through the average vehicle speed, average vehicle delay, average traffic density, and road traffic efficiency curves.

The most obvious low-speed vehicles on urban roads are road work vehicles, i.e., mobile work areas. In order to minimize the impact of highway operating areas on traffic, Helen Waleczek et al. [7] proposed a reversible lane system. Du and Saiedeh Razavi [8] proposed a control strategy improvement method for highway maintenance work zones based on a nonlinear traffic flow model. Huimin [9] and Wu et al. [10] proposed a method to determine the length of a road maintenance operation area. Wu et al. [11] constructed a multiple regression model of single-vehicle travel risk and traffic flow parameters in fixed-operation areas of highways. Peng et al. [12] established a VISSIM simulation model of a highway maintenance work area and proposed a method to determine the length of the maintenance work area of a four-lane highway. Based on the prediction of traffic accidents’ impact level in maintenance construction zones, Wu et al. [13] established a highway construction zone-layout optimization model, with traffic accident cost control as the goal. Zhou et al. [14] established a VISSIM simulation model for the construction operation area of the Shanghai–Nanjing Expressway, and conducted a comprehensive analysis of the factors affecting traffic organization, establishing a prediction model for the number of traffic delays and traffic conflicts. Meng et al. [15] proposed a reasonable length value for the upstream transition section of a construction zone, based on vehicle queuing characteristics, by studying the traffic conflict characteristics of the half-closed construction zone of a two-way four-lane highway.

Considering that vehicle lane changing is an indispensable part of the driving process, a real-time planned lane-changing path method is proposed to ensure the safety and comfort of self-driving cars during the driving process [16]. Zhang [17] addresses the problem of path curvature jumps encountered by smart cars during lane changing and proposes a new lane-changing path with an X-Sin function. Yang [18] proposed a novel dynamic lane-change trajectory-planning model to solve the problem that the speed of adjacent vehicles in real traffic changes dynamically. Bai [19] used vehicle–vehicle cooperation to generate the trajectory of vehicle acceleration lane changes, and constructed a simulation model of acceleration lane changes with different collaboration degrees of front and rear vehicles under different driving environments. Luo [20] proposed a model for dynamic lane changes with vehicle–vehicle communication to eliminate potential collision risks during lane changes.

Wang [21] applied the vehicle-following model to the study of the lane-change behavior of vehicles in six lanes in both directions on urban roads, taking into account the safety distance and speed difference of vehicles, and constructed a set of rules for vehicle lane changes. Gan [22] constructed a spatial-temporal coefficient of variation model using trajectory data of vehicle lane changes to study the influencing factors of vehicle lane changes. Li [23] proposed a symmetric two-lane cellular automaton model, considering that a vehicle’s lane-change behavior is influenced by the different types of vehicles ahead. Ma [24] applied potential field theory to an urban tunnel-intertwined zone section to construct a vehicle lane-change time model. Wu [25], in order to be closer to the actual scenario of vehicle lane changes, focused on the acceleration changes of vehicles during the lane change process and derives a reasonable vehicle-following model for lane changes. Huang [26] used the time destination of vehicle lane changes and the relative distance to surrounding vehicles as input parameters to construct a neural network-based operation-level lane-change model.

To verify the impact of the freeway on local traffic, a dynamic simulation using simulation software was used to set up a specific freeway on a highway with high transportation intensity, and the most recent traffic census data was used as input data to compare the average speed, delay time, and queue length for both scenarios. Simulation results show the positive impact of the scenario on local traffic [27]. Vadim Mavrin [28] constructed simulation models to analyze problem areas of street and roadway networks based on a discrete-event approach. Using data from field studies and incident cluster analyses as source data, the model is able to predict the impact of changes in roadway configuration on traffic flow parameters and, thus, give suggestions for improvements based on the simulation results. Ihab Kaddoura [29] considers the shift from ICEV to BEV in a simulation-based emission calculation methodology that quantifies GHG and air pollutants as different BEV shares. The results show that the decarbonization of the transportation sector is effective in reducing emissions, but non-exhaust emissions remain.

Researchers at home and abroad have completed a lot of research work on the division, traffic flow characteristics, driving risks, and management and control strategies of expressway maintenance operation areas. However, the research objects mainly focus on fixed-operation areas, and the influence of mobile operation areas common in urban roads on traffic flow has not attracted attention. In addition, there is still a lack of effective measures to deal with the impact of low-speed vehicles on traffic flow.

3. Methodology

VISSIM is a microscopic, time-interval, and driving behavior-based simulation modeling tool for urban and public transport operations. It can analyze all kinds of traffic conditions, such as lane setting, traffic composition, traffic signals, bus stops, urban traffic, and public transportation operation conditions, etc., which is an effective tool for evaluating traffic engineering design and urban planning schemes.

3.1. Road Parameters

The road studied here features three lanes in each direction, before and after the tunnel and in the tunnel, with a lane width of 3.5 m. The lane dividers inside the tunnel are set as solid lines and dashed lines, representing the two states in which lane changing is prohibited and allowed, respectively, inside the tunnel. The length of the road section and the desired speed setting parameters are shown in

Table 1. Section setting parameters.

	Length (m)	Speed Limit (km/h)
Pre-tunnel section	100	80
Transition section	100	80
Inside the tunnel	600	60
Post-tunnel section	100	80

.

3.2. Driving Behavior Parameters

The driver′s reaction time is around 600 ms, and with the transfer delay of the vehicle braking system, the total reaction time for the driver takes a value of 1 s in general. In the transition section of urban tunnels, the driver′s reaction time is suitably prolonged due to the difference in illumination between the inside and outside of the cavern. The dark-adaptation time is generally longer, and can be taken as 1 s. The bright-adaptation time is taken as 0.6 s. The total driver reaction time is, therefore, 2 s for the entrance section of the city tunnel, and 1.6 s for the exit section.

3.3. Simulation of Working Conditions

The level of service classification of urban expressways is used as a benchmark, with input road traffic volumes of 600 pcu/h (standard traffic flow per hour), 1200 pcu/h, 1600 pcu/h, and 2000 pcu/h, respectively. The simulation speed input variables for low-speed vehicles are set to 40 km/h, 50 km/h, and 60 km/h, respectively. Three evaluation indicators, namely, the average speed of traffic flow, the average delay time, and the traffic density, were selected to analyze the impact of low-speed vehicles on the traffic flow in the two states of permitted and prohibited lane changes inside the tunnel.

4. Results

4.1. Average Speed of Traffic Flow

From Figure 1, Figure 2 and Figure 3, it can be seen that when the input traffic volume is 1200 pcu/h, vehicles are allowed to change lanes inside the tunnel, that low-speed vehicles travel at 40 km/h, and that the average speeds of the traffic flow in the left, middle, and right lanes are 83.70 km/h, 82.94 km/h, and 74.61 km/h, respectively, which are all within 10 km/h above and below the design speed of 80 km/h. The average speed fluctuates within the range of 80 km/h of the design speed. When the speed of low-speed vehicles is increased to 50 km/h, the average speeds of traffic flow in the left, middle, and right lanes are 84.72 km/h, 82.86 km/h, and 79.18 km/h, respectively; when the speed of low-speed vehicles is further increased to 60 km/h, the average speeds of traffic flow in the left, middle, and right lanes are 84.50 km/h, 83.76 km/h, and 81.10 km/h, respectively. The presence of low-speed vehicles has almost no effect on the average speed of traffic flow in each lane.

In the tunnel interior, where lane changes are permitted, the average speed of the traffic flow in each lane decreases significantly as the volume of road traffic increases, especially in the right-hand lane. A comparison of the average speed of the traffic flow in the left and middle lanes of the tunnel under various operating conditions between switchable and non-switchable lanes shows that the difference is very small, with the average speed of the traffic flow in the left and middle lanes of the non-switchable lane being even slightly higher than that in the switchable lane at low speeds of 40 km/h and 50 km/h. This is presumably because the presence of low-speed vehicles in the right-hand lane in a non-transferable condition only affects vehicles behind this lane, and has no effect on the other two lanes. In the lane-changeable state, the right lane of low-speed vehicles behind the queue of vehicles will partly choose to change lanes to overtake, thus forming a disruption to the left and middle lanes’ traffic flow, especially when the road traffic volume is large; that low-speed vehicles travel at lower speeds is most obvious, as shown in Figure 1, when there is a road traffic volume of 2000 pcu/h.

The provision of interchangeable or non-interchangeable lanes in a tunnel has the greatest impact on the average speed of traffic flow in the right-hand lane, as shown in Figure 1. The average speed of the traffic flow in the right-hand lane in the non-transferable state is below 55 km/h, with a difference of more than 25 km/h from the design speed of the road, which poses a certain risk to traffic safety. After being set up as an interchangeable lane, the average speed of the traffic flow in the right-hand lane increased significantly, all above 65 km/h, alleviating the risk of traffic in the tunnel to a certain extent. When the speed of low-speed vehicles is increased to 50 km/h and 60 km/h, as shown in Figure 2 and Figure 3, respectively, the average speed of the traffic flow in the right-hand lane is significantly increased when the tunnel interior is set to switchable lanes, compared to the non-switchable lane state, alleviating the impact of low-speed vehicles on the traffic flow in the right-hand lane.

4.2. Average Delay

As can be seen in Figure 4, Figure 5 and Figure 6, the presence of low-speed vehicles in the right-hand lane significantly increases the average delay time in this lane when comparing the left and middle lanes; the lower the speed of low-speed vehicles, the higher the volume of road traffic and the longer the average delay.

As shown in Figure 4, when the low-speed vehicle speed is 40 km/h and the road traffic volume is 1200 pcu/h, the average delay time for the right-hand lane in the tunnel in the non-changeable lane state reaches 16.94 s; after introducing a variable lane, the average delay time decreases to 7.89 s, which is more than 50% shorter. The average delay time in the right-hand lane is reduced by more than 30% when the lane divider inside the tunnel changes from a non-changeable to a changeable lane state at an input road traffic volume of 1600 pcu/h and 2000 pcu/h. The same trend can be seen in Figure 5 and Figure 6. As the volume of road traffic increases, the contribution of having variable lanes in the tunnel to reducing the average delay in the right-hand lane decreases.

4.3. Traffic Density

As can be seen in Figure 7, when the low-speed vehicle speed is 40 km/h and the road traffic volume is 1200 pcu/h, the traffic density in the right-hand lane in the non-changeable state is significantly greater than that in the other lanes, indicating that the low-speed vehicle causes a queuing backlog of vehicles behind the right-hand lane. After the installation of the variable lane, the traffic density in the right-hand lane drops rapidly, by 43.5%, indicating that a significant proportion of the affected traffic behind the low-speed vehicles chooses to change lanes at this point. The comparison revealed that the traffic density in both the left and middle lanes was greater in the variable lane condition than in the non-variable lane condition, further confirming the lane-changing behavior of vehicles in the right lane. As the volume of road traffic increases, the above trends are basically the same, but after the installation of variable lanes, the traffic density in the right-hand lane decreases gradually, indicating that the volume of road traffic has a greater influence on drivers′ choice of lane-change behavior; the same trend is seen in Figure 8 and Figure 9.

A comparative analysis of Figure 7, Figure 8 and Figure 9 shows that as the operating speed of low-speed vehicles increases, their influence on traffic density gradually decreases, showing that the traffic density in the right-hand lane is not significantly different from that in the left-hand and middle lanes. In addition, in line with the aforementioned phenomenon in Figure 7, the traffic density in the right-hand lane decreases in both Figure 8 and Figure 9 after the variable lane setting, while the traffic density in the other two lanes increases to varying degrees, further supporting the notion that the presence of low-speed vehicles in the right-hand lane causes the rear-end vehicles to change lanes.

4.4. Variable Lane Divider Setting

The key point in setting the variable lane divider is to accurately determine the presence of low-speed vehicles in the tunnel and to control the change of a lane divider from a solid line to a dashed line where conditions permit, allowing the rear queue of vehicles to change lanes to overtake and alleviate the impact of low-speed vehicles on the efficiency of tunnel traffic.

The design of the variable lane divider in urban tunnels is divided into two parts, one for the infrared detection device above the lane, the main purpose of which is to determine whether the moving vehicle is a low-speed vehicle. The other part is the lane divider of the variable markings, which is normally displayed as a solid white line, prohibiting overtaking, or as a dashed line when a low-speed vehicle is judged to be present in the system, allowing vehicles to change lanes to overtake.

The infrared detection device is positioned directly above the center of the lane, as shown in Figure 10. The infrared unit receives a signal value for every vehicle that passes in the lane. The spacing between the infrared devices is based on the minimum headway value, calculated according to the design speed, and taking into account the convenience of construction; the recommended value is 10 m, as shown in Figure 11.

Variable lane dividers shall be capable of the following functions: lane dividers in tunnels under normal conditions are shown as solid white lines, representing the prohibition of lane changing for overtaking purposes. When the system detects the presence of low-speed vehicles in the tunnel, the lane divider is displayed as a white dashed line, allowing the vehicle behind to change lanes to overtake, in order to mitigate the impact of low-speed vehicles on the efficiency of tunnel traffic. Therefore, the lane dividers were designed as white LED light boxes. The dimensions refer to the provisions of the Road Traffic Signs and Markings (GB5768): each LED indicator is 400 cm in length and 15 cm in width (as shown in Figure 12). Under normal circumstances, the LED light box is fully illuminated, i.e., the display is in the state of solid white lines, prohibiting lane changing and overtaking. When the system detects a low-speed vehicle, the LED box is lit at intervals, i.e., it shows a white dashed line state, allowing lane changes for overtaking purposes.

N infra-red detectors are installed side-by-side, directly above the middle of each lane in the city tunnel, while a lane demarcation line with variable markings is installed on the corresponding lane demarcation line, formed by m LED indicators in sequence. Both the infrared detection device and the LED indicator are connected to a power supply system and a control system. The power supply system is used to supply real-time power to the infrared detection device and the LED indicator, and the control system is used to receive real-time signals from the infrared detection device and to control the real-time adjustment of the lighting status of the LED indicator. This system must not be triggered when low-speed vehicles are in the transition section of the tunnel entrance/exit, or when the distance between them and the normal traffic ahead is not sufficient to ensure safe lane changing for overtaking by the vehicle behind, so as not to cause dangerous lane-changing behavior by the driver behind. In order to fully guarantee the safety of tunnel traffic, the system is set to allow lane-change overtaking with a lane-change gap of 50 m, i.e., the lane-change gap is used as the activation threshold for the system. Therefore, the signal detection states of five consecutive infrared detectors are considered. When the infrared device X₀ detects the passage of a vehicle, the direction of travel is delayed, and the adjacent infrared devices X₁, X₂, X₃, X₄, and X₅ detect, within time t whether there is a vehicle passing, if no vehicle passes the signal, the vehicle is judged to be a low-speed vehicle, and the LED indicators that are all lit are changed to be lit at intervals, i.e., the white solid line is changed to a white dashed line, allowing lane changes for overtaking purposes. Otherwise, the LEDs remain fully illuminated, i.e., the display shows a solid white line and changing lanes to overtake is prohibited. The time t is set to avoid misjudgments, e.g., if at a certain moment the vehicles in front are in the middle of two adjacent IR detectors and no signal is detected, while the first vehicle sends a signal that it is a low-speed vehicle. Therefore, t should satisfy the following formula:

$$\frac{L-h}{v/3.6}<t<\frac{L-h}{v_m/3.6}$$

(1)

where $v_m$ is the speed at which the “turtle” vehicle is travelling (40~60 km/h). $v$ is the tunnel design speed (60~80 km/h). $h$ is the vehicle length (3~6 m). L is the infrared device arrangement spacing (8~15 m).

Assuming a tunnel design speed of 80 km/h, a low-speed vehicle speed of 40 km/h, and a body length of 4 m, the value of t can be calculated as 0.5 s.

The high risk of traffic safety in the transition section at the entrance and exit of the city tunnel and the setting of variable lane dividers can cause the phenomenon of vehicle lane changing and incur a certain risk of lane-changing behavior. Variable markings should, therefore, be avoided in the transition sections at the entrance and exit of tunnels, where the risk of traffic is high, and should be considered in areas where the risk of traffic inside the tunnel is relatively low.

5. Discussion

The research on low-speed vehicles in this paper is based on the common slow-speed vehicles on urban roads, and the driving speed is within the range of 40~60 km/h. The conclusions obtained are applicable to traffic planning and the management of urban roads. However, whether their effects on traffic flow apply to vehicles at lower speeds, such as speeds below 20 km/h, remains to be studied. For example, the speed of common moving work areas on roads is generally 5–20 km/h. The setting of variable lanes may have little effect on alleviating the driving risks caused by moving work areas. More attention should be paid to the road traffic volume in moving work areas. In extreme cases, the speed of low-speed vehicles is 0, which is equivalent to fixed-operation areas or obstacles on the road; how the driving risk caused by them can be measured is a question that remains unanswered. Whether we can find a general means to study the impact of low-speed vehicles on traffic flow is also a goal that needs our constant efforts.

The results of Ref. [2] were obtained through the analysis of experimental data, which showed a negative logarithmic linear relationship between the average traffic speed and the mixing rate of large vehicles, which is consistent with the conclusion of this paper. However, the influence of low-speed vehicles on the average speed of traffic flow needs further analysis. Ref. [3] found that a traffic flow with low average speed and high traffic density was formed behind the moving bottleneck, which was similar to the phenomenon of backlog of vehicles behind low-speed vehicles in this paper. Ref. [4] considered that mobile bottlenecks had little influence on traffic flow in medium–low density areas, while having great influence on traffic flow in high-density areas. However, this phenomenon is not obvious in this study, which may be because there is only a single low-speed vehicle in the model. Through simulation analysis in [6], it was found that road operation vehicles had an obvious movement bottleneck effect, resulting in the formation of a vehicle congestion zone in the upstream region. As a result, the average density of vehicle flow increases, the vehicle delay increases, and the road traffic flow, average vehicle speed, and road traffic efficiency all decrease significantly, a conclusion which is also consistent with this paper.

In this paper, the influence of factors such as vehicle proportions and driver heterogeneity have not been taken into account in the simulated working conditions, and the safety risks of lane changing for low-speed vehicles have not been analyzed; further research will be conducted later. How to quantify the financial value of variable lane settings, namely, the value of saving time, is also the next step for research.

6. Conclusions

This paper draws the following conclusions from the simulation analysis of traffic flow in urban tunnels:

• Low-speed vehicles in urban tunnels have the greatest impact on the average speed of traffic flow in the right-hand lane and a smaller impact on the average speed of traffic flow in the other two lanes;
• The impact of low-speed vehicles on the average speed of traffic flow can be significantly mitigated when lane dividers in urban tunnels are set to allow lane changes;
• The presence of low-speed vehicles in the right-hand lane in urban tunnels significantly increases the average delay time in that lane. The lower the speed of low-speed vehicles, the higher the volume of road traffic, and the longer the average delay;
• The traffic density in the right-hand lane in urban tunnels is significantly greater than in other lanes in the non-changeable condition, and the presence of low-speed vehicles causes queues to build up behind vehicles in the right-hand lane. After being set to allow lane changes, the traffic density in the right-hand lane dropped rapidly, suggesting that a significant proportion of affected vehicles behind low-speed vehicles chose to change lanes at this point.