## 1 Background  
To increase the service levels and optimize the linear designs of expressways, the proportions of tunnels therein are increasing in China. In mountainous areas in particular, road tunnels are far more prevalent than they are in flat areas [1]. At the end of 2018, there were 17,738 road tunnels in China, with a combined length of 17,236 km; of those tunnels, more than 70% were either long or extra-long ones. Because the inside of a road tunnel is a closed strip [2; 3; 4], the driving environment changes suddenly at the tunnel entrance and exit (e.g., the \"black hole\" and \"white hole\" phenomena [5; 6]). This causes some drivers to be nervous and afraid, thereby increasing greatly the possibility of driving errors [7; 8]. [PERSON] [9] investigated traffic accidents in Norway in 2008-2011 and found that a collision in a tunnel is twice as likely to cause fatalities than one is elsewhere. [PERSON] [10] also indicated that the rate of dying in a traffic accident in a tunnel is almost twice that elsewhere, and regardless of whether the traffic flow is two-way or one-way, the probability of a traffic accident at the tunnel entrance is higher than that elsewhere in the tunnel. As a bottleneck in an expressway, when an accident happens in a tunnel, it can easily lead to secondary accidents [11]. Therefore, it is very important to make tunnel traffic safer. To reduce the rates of traffic accidents in tunnels, it is necessary to study the mechanisms for such accidents and find the key factors affecting the safety levels at the entrances and exits of expressway tunnels. Most of the relevant studies show that the tunnel traffic safety has close relationship with the road conditions, traffic conditions, traffic management level, and weather conditions, and these conditions interact with each other at the same time. [PERSON] [12] and [PERSON] [13] studied the impact of road friction and roughness on the traffic safety in winter, which had a significant impact on the vehicle performance, acceleration, braking, steering, and motion stability. Another important factor affecting traffic safety is the vehicle speed. From the previous research work [14; 15], the traffic accidents become more prevalent with increasing vehicle speed, but the relationship between vehicle speed and the probability traffic accidents is not a simple linear one. When the speed limit is higher, vehicles tend to travel faster, thereby increasing the rate and severity of accidents significantly. The accident risk of vehicles increases rapidly with increasing speed [10]. [PERSON] [16] investigated how vehicle speed difference (the difference in speed between the fastest vehicle and the slowest one) affects traffic accidents, and the results indicated that the rate of traffic accidents increases exponentially with increasing speed difference. However, even when all vehicles have the same speed, there is still one accident happening in every 10 million kilometers, indicating that only controlling the speed difference is insufficient to prevent all traffic accidents [17]. Additionally, the lower speed limit is not necessarily better: a speed limit that is too low leads to reduced driver compliance and inefficient road traffic. Therefore, for safer traffic in a long downhill tunnel, the vehicle speeds should be controlled in a reasonable range so that they are neither too high nor too low and have a relatively small difference. Speed management is an important aspect to improve the level of tunnel traffic safety. Most of the research focuses on setting up the traffic engineering facilities (such as the signs and line marking, lighting facilities, etc.) to increase the stimulus to drivers, so as to reduce fatigue and take the initiative to reduce speed. [PERSON] [18] conducted a fatigue test for drivers in the bypass tunnel (FFS) in Stockholm, Sweden, with and without decorative lights on the ceiling of the tunnel.