###### Abstract
[12] proposed the concept of green wave bandwidth coordination rate to analyze the mapping relationship between adjacent intersections and then established a multi-path green wave control model with the objective of maximizing the total green wave bandwidth coordination rate. [PERSON] et al. [13] proposed an arterial green wave control model named Pband, whose main highlight is the ability to choose the optimal phase scheme from the NEMA phase scheme and the splitting phase scheme. [PERSON] et al. [14] combined the advantages of the AM-BAND model [3] and the PBAND model [13] to propose an asymmetric multi-bandwidth model with phase optimization, named the AM-BAND-PBAND model. [PERSON] et al. [15] conducted an in-depth study on the essential principles of green wave control by proposing a series of new concepts, such as characteristic points, lines, and equations of the traffic signal progression trajectory, and applied them to arterial green wave control. [PERSON] and [PERSON] [16] proposed an arterial partitioning technique based on OD data provided by connected vehicles to improve the green wave control effect of a long-distance arterial. Aiming at the problem that the green wave is easily destroyed under saturated traffic conditions, [PERSON] et al. [17] proposed the method of real-time adjustment of signal timing scheme and speed guidance to improve the arterial green wave control effect based on the vehicle-road cooperative technology. Research on the arterial green wave control for two traffic modes is summarized as follows. [PERSON] et al. [18] developed the INTEBAND, which is an integrated model capable of coordinating cars and buses. [PERSON] et al. [19] proposed an arterial green wave control model for straight and left-turning terms as well as social vehicles. [PERSON] et al. [20] proposed the Lmband, which can solve the inconsistency problem of intersection grouping arising from buses and cars on long-distance arterials. [PERSON] et al. [21] specifically considered the stochastic nature of bus dwell time and proposed an arterial green wave control model for cars and social vehicles. Due to its advantages, such as ease of use, flexibility, and low cost, the electric bicycle is one of the most commonly used travel tools for urban residents in China. Therefore, it is necessary to take into account the green wave coordination demand for electric bicycles. However, because there are significant differences in speeds between electric bicycles and motor vehicles, existing arterial green wave control methods, which mainly focus on motor vehicles, cannot solve the green wave control problem of both motor vehicles and electric bicycles. To address the limitations of existing methods, this paper proposes an arterial multi-path green wave control model that considers both motor vehicles and electric bicycles. The main innovations of this paper are summarized as follows. (1) A novel arterial green wave control model for multiple traffic modes is proposed, which can simultaneously generate multi-path green wave bands for motor vehicles (cars, buses) and electric bicycles on an arterial. (2) By introducing 0/1 variables, the connection between the phase sequence and coordination path in the symmetrical phase scheme is established, enabling synchronous optimization of the phase sequence and coordination path. The reason for introducing 0/1 variables to optimize the phase sequence and the coordinated path is that 0/1 variables have clear, logical meanings and are simple to model.