# Exploring the Relationship Between Mixed Non-Motorized Traffic Flow Width and Other Parameters
## 1 Introduction  
As a general rule, the width of a bicycle lane depends on the standard specification of road construction. For vehicles, the width of a lane is decided based on vehicle traffic flow characteristics. But for a bicycle lane, bicycle flow characteristics are completely neglected. Even the standard specifications of road construction are not uniform [1]. Therefore, this paper focuses on the characteristics of bicycle traffic flow and their relationship with bicycle traffic flow width. Many studies have focused on modeling vehicle traffic flow, which motivates us to develop a bicycle traffic flow model based on the same principle. We also need to consider a mixed bicycle traffic flow, which refers to a traffic flow composed of both mechanical and electric bicycles. Traffic flow models can generally be divided into macroscopic and microscopic models [2]. Macroscopic traffic flow is the study of the relationships among density, flow, and speed under different conditions. Microscopic traffic flow models are employed to characterize the interactions between individual vehicles. For instance, the car-following model--a typical example of microscopic traffic flow models--describes the microscopic movements of adjacent vehicles operating within the same lane. In contrast, this paper focuses on macroscopic traffic flow models. Currently, there are numerous studies on macroscopic traffic flow models for bicycles. [PERSON]. [3] investigated the relationships among the flow, density, and speed of bicycles. [PERSON] [4] experimentally studied the speed-flow relationship of bicycles. In the research realm of bicycle traffic inChina, [PERSON] and [PERSON] [5] established the first bicycle traffic flow model. [PERSON] and [PERSON] [6] defined the density of vehicles in a lane of unit area as the density of mixed bicycle traffic flow. This definition played a crucial role in subsequent studies on bicycle traffic flow in China. [PERSON] et al. [7] conducted statistical analysis on vehicle speeds on actual road segments, and constructed a traffic flow model. [PERSON] [8] used mathematical and statistical methods to study the speed-flow relationship of mechanical bicycles, electric bicycles, and mixed bicycles on physically separated road sections, with varying proportions of mixed electric bicycles. Based on the characteristics of mixed bicycle traffic flow, [PERSON] et al. [9] introduced a logistic model and established mathematical models for describing the flow-density relationship of mixed bicycle traffic. [PERSON] et al. [10] used video analysis systems to analyze the characteristics of mixed bicycle traffic in bicycle lanes in peak periods. These studies enriched the theory of macroscopic bicycle traffic flow. However, the above studies rarely described any variation in the width of bicycle traffic flow under different conditions. In vehicle traffic flow, the three primary variables, also known as the three macroscopic parameters, are flow, speed, and density. Through observation, it was found that under high bicycle traffic flow density, cyclists do not exhibit distinct queuing behavior as motor vehicles do. Instead, when encountering slower-moving vehicles ahead, some cyclists deviate from the designated non-motor-vehicle lane by crossing the isolation line to utilize motor vehicle lanes for overtaking, thereby inducing lateral variations in traffic flow patterns. Therefore, it is necessary to consider the width of the bicycle traffic flow. This parameter is crucial for analyzing the relationship between bicycle traffic flow and bicycle lane width. [PERSON] investigated the relationship between capacity and path width through a controlled bottleneck experiment in Delft in the Netherlands. A key finding of their study was the positive linear correlation between bicycle lane capacity and lane width. Specifically, within the width range of 0.50 to 1.50 m, each additional meter of bicycle lane width corresponds to a capacity increase of 1.11 bicycles per second [11].