# Median U-Turn Intersection Critical Parameter Research and Operational Performance Evaluation
## 1 Introduction  
As a key node of road networks, signalized intersections usually serve as the most important way to manage and control urban transportation and vehicle movements [1]. With the increase in vehicle ownership in urban areas, signalized intersections are becoming increasingly busy and congested [2]. Generally, the left-turn traffic within intersections is considered as one of the crucial factors that may cause traffic congestion [3], because it is a real possibility that left-turn traffic passing the intersections collides with the traffic from other directions [4, 5]. The crossings of different vehicle movement trajectories within the intersections are called conflict points [6, 7]. The existence of conflict points normally causes higher accident rates and severe casualties in the intersections [8]. Given the data from the National Highway Traffic Safety Administration (NHTSA) and Fatality Analysis and Reporting System (FARS), there are almost 9000 fatalities and about 1.5 million injuries caused by left-turn movements occurring annually in the United States [9]. Therefore, to ensure that intersections can operate more safely and efficiently, left-turn traffic should be regularized scientifically. In recent years, shifting and reorganizing the conflict points outside intersections to reduce their number has become a major concern in many unconventional intersection designs [10]. Among them, these unconventional intersection designs include median U-turns, restricted crossing U-turns (RCUTs), and displaced left-turns (DLTs). Oneof the better-known and more widely used intersections is the median U-turn (MUT) intersection. The concept of the MUT intersection first emerged in the United States, particularly in Michigan, where it has been widely adopted. This innovative intersection is removing the direct left-turn movements of vehicles to accommodate indirect left-turn movements through median U-turns. It only allows the through traffic from major and minor roads to pass through the unclosed median. Figure 1 shows an example of a signalized MUT intersection in Michigan. To some extent, the signalized MUT intersection is considered to have the potential to improve driving safety and reduce unnecessary delays for vehicles at intersections by decreasing the number of conflict points. It would be of considerable value to evaluate the safety benefits for traffic performance operation [11]. Figure 2 illustrates how an MUT intersection can effectively reduce the number of conflict points from 32 to 16. Relevant studies have confirmed that MUT intersections increase safety and reduce accidents because there is no opportunity for direct left-turns or head-on collisions. Compared with conventional intersections, the implements of MUT intersections are expected to  
Figure 1: The operation of a signalized median U-turn (MUT) intersection in Michigan (adapted from Google Earth). Figure 2: Conventional and media U-turn (MUT) intersection conflict points. result in total crash reductions ranging from 20% to 50% [12; 13]. [PERSON] et al. conducted a safety evaluation and concluded that MUT intersections can reduce head-on crashes by more than 80% and rear-end left-turn crashes by 48% [14]. [PERSON] and [PERSON] used CORSIM to analyze the traffic performance of MUT intersections and found that the implementation of MUT intersections resulted in overall reductions in rear-end, angle, and sideswipe crashes by 17%, 96%, and 61%, respectively [15; 16]. Although many studies have concluded that MUT intersections offer significant benefits to traffic capacity and efficiency, there are various areas that remain unexplored in studies of MUT intersections. Specifically, there is no widely accepted theory for calculating the critical parameters of MUT intersections, such as the distance between unclosed median and median U-turns (separation distance), or the gap and width of median U-turns. The following studies address these parameters. Firstly, in terms of the separation distance, [PERSON] et al.