# Evaluation of Mixed Traffic Flow Efficiency and Safety on Hard-Shoulder-Running Freeways
## 1 Introduction  
Hard shoulder running (HSR) is regarded as a pivotal measure within active traffic management strategies for optimizing freeway utilization during periods of high congestion [1; 2; 3]. By utilizing the existing hard shoulder for driving, HSR is more economically efficient for increasing freeway capacity than the traditional methods (such as building more roads, constructing more lanes, etc.) [4; 5]. Currently, a deeper understanding of HSR has been gained across a wide range of fields. [PERSON] analyzed the implementation of shoulder use during peak hours on a section of the A86 highway in northern Paris and found that the road capacity increased by 16%, while the speed was augmented by 25% compared to the conditions without shoulder opening [6]. [PERSON] pointed out that the temporary use of shoulders can significantly alleviate traffic congestion when control measures such as lower speed limits and prohibitions on overtaking are implemented [7]. [PERSON] et al. proposed a methodological framework based on simulation to assess the impacts of HSR on congested freeways during instances of non-recurring congestion [8]. Some studies also analyzed the relationship between the implementation of HSR and road safety [9; 10]. [PERSON] et al. revealed that while the accident rate remained unchanged when the flow rate of the road segment increased within a certain range due to shoulder opening, it would significantly increase when the speed and density exceeded certain thresholds [11]. [PERSON] et al. found that opening shoulders was applicable in cases of accidents involving only property damage, and that the road flow could be increased by 15% to 40% after opening the shoulders [12]. Previous studies have focused on HSR with traffic flow including only human-driven vehicles (HDVs). Recently, significant advancements have been achieved in the connected automated vehicles (CAVs) industry, primarily due to the advancements in advanced information and communication technologies (ICT) and on-board sensing systems [13; 14; 15]. The freeway will gradually witness the transformation of traffic flow from purely HDVs to fully CAVs. During the evolutionary period, a mixed traffic paradigm will emerge, featuring the coexistence of CAVs alongside HDVs [16; 17]. The characteristics of such mixed traffic flows are supposed to be quite different from those of regular ones that involve only HDVs [18; 19]. [PERSON] et al. developed a dynamic hard-shoulder opening strategy, utilizing a hidden Markov model framework within a hybrid network environment, to alleviate the impacts associated with the varying penetration rate of CAVs [20]. [PERSON] et al. [21] and [PERSON] et al. [22] employed a microscopic simulation to assess the impact of different market penetration levels of CAVs on highway capacity and concluded that the freeway capacity would increase significantly after the market penetration of CAVs reached moderate-to-high percentages; conversely, the introduction of CAVs could potentially have a negligible effect at lower penetration levels. For the safety aspect, [PERSON] et al. [23] observed that a significant reduction in traffic safety risks occurs when the proportion of CAVs exceeds 50%. However, few studies have systematically examined the impact of mixed traffic flow with various penetration rates to the HSR on freeways. In this article, we employed a microscopic simulation model integrated with a factorial experimental design to detect the impact of mixed traffic flow on freeway HSR. First, we depict the characteristics of the traffic efficiency and safety of pure HDVs under various levels of service after the HSR activated. Then, the patterns of the mixed traffic flow with various penetration rates are also recorded under the same simulated conditions. Finally, through statistical analyses of the simulation results, the novel findings are obtained.