Understanding traffic bottlenecks of long freeway tunnels based on a novel location-dependent lighting-related car-following model

https://doi.org/10.1016/j.tust.2023.105098Get rights and content

Highlights

  • A novel location-dependent lighting-related car-following model is developed.

  • Traffic efficiency is related to luminance levels of tunnel lighting and daylight.

  • Periodic oscillations are proved to exist under visual adaptation occurrence.

  • Recommending lighting control strategy adaptive to daylight based on traffic oscillation.

Abstract

To understand the formation of lighting-related traffic bottlenecks along the long freeway tunnels in the daytime, this study develops an intelligent driver model incorporating the location-dependent lighting-related desired speed (IDM-LLDS). This car-following model associates desired speed variations with the lighting-transition-incurred visual adaptation in the portal areas and low illumination in the interior zone of the tunnel, such that how the impact of location-heterogeneous lighting conditions on driver’s car-following behavior propagates through car platoons is described. The model is validated, and numerical examples are presented to illustrate the traffic patterns related to tunnel lighting and daylight. The results demonstrate that periodic oscillations in traffic patterns are presented under visual adaptation occurrence if traffic flow density is not significantly high. Adaptive tunnel lighting and implementation of sunscreens at tunnel portals can both improve the traffic conditions in strong daylight. The former performs better in improving traffic efficiency, while the latter excels in smoothing visual-adaptation-based traffic oscillation. With the objective of minimizing the magnitude of traffic oscillation, the tunnel lighting strategies adaptive to daylight are recommended under different traffic volumes and travel speeds where majority of cars can avoid obvious trajectory oscillation traversing the tunnel.

Introduction

A tunnel is a traffic bottleneck compared with normal road segments, where the capacity considerably drops. Specifically, the entrance is a bottleneck, as observed in traffic volume and travel speed fluctuation in the Tsuburano and Kobotoke tunnels, Japan (Koshi et al., 1992). Nearly 20 % of traffic congestion occurs at tunnel entrances on intercity expressways in Japan (Xing et al., 2014). The exit and interior of a long tunnel are also bottlenecks, as observed on expressways and freeways in China (Shui et al., 2015, Sun et al., 2018, Yang et al., 2022). The bottlenecks in the long freeway tunnel have drawn freeway operators’ attention since the bottleneck effect is amplified by the adjacent upstream interchange where heavy traffic merges from a nearby county or freeway network and therefore queues on both ramp and mainline stretches for several kilometers (Liao et al., 2018).

The mechanism of the bottleneck formation should be investigated before implementing traffic control strategies to mitigate the congestion from the bottlenecks along the long freeway tunnels. Unlike bottlenecks in the work zone, merging, diverging, and weaving segments, which are triggered by lane-changing behaviors (Chen and Ahn, 2015, Chen and Ahn, 2018), traffic bottlenecks in long freeway tunnels are mainly derived from car-following (CF) behaviors affected by location-heterogeneous lighting conditions along the tunnel. To be specific, in most of China’s freeway tunnels, roads are designed with solid lane marking and lane changing is prohibited for drivers (JTG, 2009), such that drivers decelerate or accelerate according to the driving behavior of leading cars. The CF behaviors in tunnel are presented as different speeds and spacings compared to the normal road segment (Jin, 2018, Wada et al., 2020) due to lighting condition variations along the tunnel. Tunnel is a semi-enclosed space where the lighting changes from bright to dark at the entrance zone and from dark to bright at the exit zone in the daytime. The abrupt lighting transition in the entrance and exit zones incurs visual oscillations for drivers, who need an adaptation time to clearly discern the targets and objects, that is, visual adaptation (Qin et al., 2017, Mehri et al., 2019). When a car enters and leaves the tunnel, the driver tends to slow the car as a result of visual adaptation (Sun et al., 2020, Yu et al., 2023). Additionally, in long freeway tunnels, drivers nevertheless maintain relatively low speed, driving carefully in the interior zone due to low illumination, although they have less discomfort after visual adaptation in the entrance zone (Yeung and Wong, 2014, Yu et al., 2022). However, to the best of our knowledge, few research efforts have incorporated the impact of location-heterogeneous lighting conditions on CF behaviors into traffic flow models in the literature. Additionally, there is no specific tunnel scenario in commercial microscopic traffic simulation software, i.e., tunnel is always considered as the normal road segment from the perspective of traffic flow modelling.

Hence, the aim of this study is to understand the formation of traffic bottlenecks along the long freeway tunnels in the daytime based on a novel CF model considering location-dependent lighting conditions.

Several studies have attempted to quantify the impact of lighting conditions on drivers’ behaviors based on experiments in real tunnels or simulated scenarios in laboratory. In these studies, drivers’ behaviors fall into two categories: visual performances and driving behaviors (Zhang et al., 2016).

The studies on the relationship between lighting conditions and visual performance can date back to 1910s when Piéron’s Law was initiated (Piéron, 1914). Piéron’s Law reveals the relationship between the intensity of luminous object in a dark environment and the visual reaction times of observers in laboratory (Pins and Bonnet, 1996, Pins and Bonnet, 1997, van Maanen et al., 2012). Visual reaction time is defined as the duration between the emergence of the visual stimulus (i.e., luminous object) and the detection of a response from an observer, which is critical for road safety whether road users can immediately recognize hazardous obstacles especially in dark environment (Donkin and van Maanen, 2014, Peña-García et al., 2010, Peña-García et al., 2016). Similar experiment methods were utilized in driving simulators for traffic safety problem on the open road at night or under mesopic conditions (Alferdinck, 2006, Hunter et al., 2017, Cao et al., 2021) and the interior zones of tunnels (Zhao et al., 2012, Kircher and Ahlstrom, 2012, Domenichini et al., 2017, He et al., 2020, Liang et al., 2020). In the interior zones of tunnels, visual performance measures are extended from visual reaction time to miss target rate, fixation time and so forth. The appropriate lighting conditions are investigated where even visually distracted drivers are able to observe the presence of obstacles in time.

However, in the CF scenario, drivers are always attentive to the leading car and environment in the interior zone of tunnel. Therefore, more direct measures substituted for visual performance to describe the drivers’ behaviors, that is, driving behaviors. For an individual car, driving behaviors were evaluated based on experiments in real tunnels or driving simulator with different lighting conditions, including desired/mean and standard deviation of speeds (Pritchard and Hammett, 2012, Jägerbrand and Sjöbergh, 2016, Gilandeha et al., 2018, Liu et al., 2020, Zhao et al., 2022a, Zhao et al., 2022b), mean and standard deviation of lateral positions (Kircher and Ahlstrom, 2012, Domenichini et al., 2017), spacing (Zhang et al., 2021) and minimum time to collision (Kircher and Ahlstrom, 2012) to the leading car. In these measures, desired/mean speed is easily observed and recorded for an individual car.

In the portal areas (i.e., entrance and exit zones) of tunnels where the environment brightness transits between higher daylight and lower tunnel lighting in the daytime, visual adaptation time were widely used to describe the impact of lighting transition on drivers’ behaviors from the perspective of traffic safety. Visual adaptation time is measured by variation in pupil size/area (Du et al., 2014, He et al., 2017a, Yan et al., 2017, Wang et al., 2020, Yan et al., 2022), fixation time (He et al., 2017a, Yan et al., 2017), missed target rates (He et al., 2017b) or reaction time for targets (He et al., 2020). The former two measures are recorded during the naturalistic driving experiments in real tunnels, while the latter two are obtained in simulated scenarios of laboratory.

Speed is a critical parameter in CF scenario. However, to the best of our knowledge, the speed variation during visual adaptation is nevertheless missing in prior studies, even though it is feasible to record both the driver’s pupil size/area and the car’s speed simultaneously in the naturalistic driving experiments. In addition, the impacts of lighting conditions on drivers’ behaviors are mostly evaluated from the perspective of an individual car in the literature. It needs to be further investigated how the impact of lighting conditions on drivers’ behaviors propagates in car platoon, or how the impact of lighting conditions on the speed variation propagates through traffic flow, equivalently.

To describe how the impact of location-heterogeneous lighting conditions on the speed variation propagates through traffic flow, a location-dependent traffic flow model is needed. In commercial microscopic traffic simulation software such as the Paramics and VISSIM, there is no specific tunnel scenario, i.e., tunnel is always considered as the normal road segment from the perspective of traffic flow modelling. In the literature, macroscopic and microscopic traffic flow models have been developed. The macroscopic model is Jin (2018)’s location-dependent kinematic wave model. Assuming location-dependent time gaps and bounded acceleration stationary states in the entrance zone of tunnel, the model presents a location-dependent triangular fundamental diagram and Lighthill-Whitham-Richards (LWR) stationary states (Lighthill and Whitham, 1955, Richards, 1956) in the entrance zone, demonstrating that bounded acceleration leads to capacity drop. The microscopic model (Wada et al., 2020) was further developed to reveal the dynamic properties of the capacity drop formation in the entrance zone of tunnel based on the same assumptions: bounded acceleration and inhomogeneous fundamental diagrams with location-dependent time gaps. The model incorporates the location-dependent features into Jin and Laval (2018)’s continuum CF model with bounded acceleration, equivalent to the second-order LWR model.

However, the limitations of the location-dependent continuum CF model are twofold, although the model can interpret the bottleneck in the entrance zone of tunnel. First, only the bottleneck in the entrance is evaluated, while the interior and exit bottlenecks cannot be ignored, especially for long tunnels. Second, the assumption for location-dependent time gaps is based on the observation that drivers drive more carefully under different lighting conditions inside a tunnel. However, how lighting conditions affect time gaps or other drivers’ behaviors, such as the desired speed at different locations is missing in existing CF models which are not suitable for traffic flow modelling in tunnel. To be specific, the speed variations during visual adaptation due to lighting transition in the portal areas and under low illuminance in the interior zone should be integrated into location-dependent CF model.

Among the most popular CF models using desired measures is Treiber et al. (2000)’s intelligent driver model (IDM). The desired measure is the desired speed, i.e., the average/mean speed when no car surrounds the subject car. This model was improved by incorporating power cooperation with the front car (Li et al., 2015), fluctuation of time gaps (Jiang et al., 2014), varying behavior between high and low speeds (Tian et al., 2016), task-capability interfaces (Saifuzzaman et al., 2015), and traffic oscillations (Treiber and Kesting, 2018), and applied in simulations of emerging technologies (Kesting et al., 2010, He et al., 2015, Zhou et al., 2017a, Zhou et al., 2017b, Zhu et al., 2018, Liu and Fan, 2020, Sharath and Velaga, 2020, Yu et al., 2021, Makridis et al., 2021, Shi and Li, 2021, Du et al., 2022, Chen et al., 2023, Ji et al., 2023). These extensions demonstrate the broad extrapolation of IDM. In IDM-formed models, both a maximum acceleration and a comfortable deceleration rate are introduced, such that unrealistically high accelerations or decelerations are avoided, and traffic bottlenecks can be well described. In this study, incorporating the relationship between location-dependent lighting conditions and desired speed, an IDM-formed CF model is developed to understand the formulation of traffic bottlenecks along the long freeway tunnels.

The objective of this study is to understand lighting-related bottlenecks along the long freeway tunnels in the daytime, and a novel CF model, IDM incorporating the location-dependent lighting-related desired speed (IDM-LLDS) is developed. The model can also be promoted to specific one-way long road tunnels where lane-changings are prohibited.

The model presented in this study is an improvement over the microscopic traffic flow modelling in tunnel scenario with integrating the impact of lighting conditions into description of driver’s CF behavior. The contributions are threefold. First, how the impact of lighting condition variations on driver’s CF behavior propagates through car platoons is described. Second, traffic efficiency in a tunnel is related to the tunnel lighting and daylight, which are often used to evaluate the driver’s safety. Third, the traffic oscillation is evaluated in terms of lighting conditions, recommending appropriate tunnel lighting control strategies adaptive to the luminance levels of daylight.

The rest of this paper is organized as follows: IDM-LLDS is formulated in Section 2. In Section 3, the proposed model is validated with actual data. Section 4 provides numerical examples to describe the features of traffic patterns along the tunnel with different lighting conditions and evaluates the countermeasures for eliminating traffic oscillation. The conclusions of this paper and avenues for future research are presented in Section 5. The Appendix demonstrates the derivations of the lighting-related parameters of IDM-LLDS based on experiments to calibrate the proposed model.

Section snippets

Notations and assumptions

Given a long freeway tunnel with length D. Road surface luminance is assumed as driver visual luminance. Let Lx denote the road surface luminance (cd/m2) with respect to location x in the daytime where the beginning of the section is at x=0, as Fig. 1 demonstrates. A tunnel section is divided into four main zones with different luminance characteristics in the daytime: exterior, entrance, interior, and exit zones, denoted as Zo, Zet, Zin, and Zex, respectively. The exterior zone is the open

Validation of IDM-LLDS

In this section, we validated IDM-LLDS by collecting the trajectories of the car platoon in the right hole of the Longfengshan tunnel of Freeway G65, which has two lanes in each direction. Longfengshan tunnel is a typical long freeway tunnel with length 2.9 km, as presented in Fig. A.1, where roads are designed with solid lane marking, and lane changing is prohibited for drivers. Consequently, the traffic in the outer lane is mixed with cars and trucks, while the traffic in the inner lane

Numerical examples

Recurrent traffic congestion occurs along the Longfengshan tunnel of Freeway G65, Chongqing, on weekend afternoons during the summer vacation. As explained in Section 3, the inner lane of the right hole of the Longfengshan tunnel was selected as the studied area for numerical examples. Based on the measured tunnel lighting of the Longfengshan tunnel on June 25th, 2020, the lamps in the tunnel have faded through years of operation compared with standard designed lighting, as presented in Fig. 5.

Conclusions

An intelligent driver model incorporating the location-dependent lighting-related desired speed (IDM-LLDS) was developed to describe the formation of traffic bottlenecks along long freeway tunnels in the daytime. This novel car-following (CF) model associated desired speed variations with the lighting-transition-incurred visual adaptation in the portal areas and low illumination in the interior zone of the tunnel, describing how the impact of location-heterogeneous lighting conditions on

CRediT authorship contribution statement

Shanchuan Yu: Conceptualization, Writing – original draft, Methodology, Funding acquisition. Cong Zhao: Resources, Validation, Writing – review & editing. Lang Song: Software, Data curation. Yishun Li: Investigation. Yuchuan Du: Project administration.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work has been supported by the National Natural Science Foundation of China (Grant No.71901190). The authors would like to thank the insightful comments from anonymous reviewers which helped us substantially improve this paper. The first author thanks his wife Mrs. Maojiao Wang and daughter Ms. Muyan Yu for their solid supports when writing this paper.

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