# A Study on a Prediction Model of E-Bike Expansion Degree at Irregular Signalized Intersections
## 1 Introduction  
In recent years, there have been an increasing number of e-bikes on the urban roads. As of 2019, the global market value of e-bikes reached 57.5 billion yuan (7.475 billion euros) and is expected to grow to 73.9 billion yuan (9.607 billion euros) in 2026. Among them, China has more than 300 million e-bikes, ranking first in the world [1]. Due to the popularity of e-bikes, traffic problems in cities are complex and the operation efficiency and safety of intersections are facing challenges. In Poland, an adaptive signal control method was adopted to adjust the length of vehicle queue [2]. In China, the number of public transportation vehicles per 10,000 persons in the city is positively associated with commuting by non-motor transport (by walking or cycling) [3]. Moreover, contraflow left-turn lane (which dynamically uses a portion of the opposing through lanes as additional left-turn lanes) was used to meet the demand of left-turns [4]. However, most of the optimization strategies are only for motor vehicle flow. The purpose of intersection signal control is to separate the traffic conflicts in the time distribution, but it cannot completely solve the traffic conflicts in the space distribution. [PERSON] et al. [5] showed that the rate of accidents involving e-bikes at intersections has been increasing year by year, especially in developing countries. E-bike accidents are generally attributed to two causes. Firstly, at signalized intersections, e-bike riders exhibit dangerous riding behavior, leading to a much higher violation rate of e-bikes than that of traditional bikes [6]. Secondly, due to the swinging, grouping, and transcendence characteristics of e-bikes [7], the expansion effect is significant whencrossing an intersection. E-bikes occupy the driving space of motor vehicles at intersections and therefore significantly disturb the normal running of motor vehicles. Moreover, there are many factors that affect the expansion effect of e-bikes. [PERSON] et al. [8] reported that the higher the speed of an e-bike, the greater the transverse distance required. In addition, [PERSON] et al. [9] found that e-bikes had twice the risk of being involved in traffic accidents in intersections as compared with conventional bikes. According to [10], the number of e-bike accidents in Jiangsu Province accounted for about 70% of the total traffic accidents from January to June in 2016, especially near irregular intersections. Compared with typical signalized intersections, the traffic flow directions of irregular signalized intersections are irregular [11]. The vehicle driving trajectory is different from that of regular signalized intersections [12]. Therefore, the uncertainty of the expansion effect of e-bikes is more obvious. The expansion effect of e-bikes is the most important release characteristic. [PERSON] et al. [13] studied the factors that influence the expansion effect of straight-going e-bikes at typical intersections and determined the influence degree of different factors on the expansion effect. [PERSON] et al. [14] found that the number and direction of e-bikes arriving during a red light had a significant impact on the dispersion width of left-turn e-bikes. In addition, in intersections, the impact of e-bikes on motor vehicles has also been reflected in the expansion effect of e-bikes. [PERSON] et al. [15] reported that e-bike riders usually set out in advance and occupy adjacent roads. These violations have affected the normal passage of motor vehicles. Considering this, most researchers have established simulation models to evaluate the influence of the expansion effect of e-bikes on motor vehicles. For example, a mixed traffic flow signal timing model that considers the advance release of e-bikes has been established. The analysis of [PERSON] et al. [16] showed that when the proportion of e-bikes was 40-60%, the influence of e-bikes on the expansion of motor vehicles could be considered to be in the signal control timing.