A modified social force model for high-density through bicycle flow at mixed-traffic intersections
Introduction
As a main mode of transportation, cycling has been widely promoted by many countries due to its public health and environmental benefits [1]. However, accompanied by increasing cycling demand, it also brings many issues that are mainly related to traffic management at bottlenecks [2]. The signalized intersection is one of the most common bottlenecks in urban traffic networks. In most cases, there are no lane markings within intersections, and the operation space for different road users is vague and commonly shared by motorized vehicles and bicycles. It leads to frequent interactions among heterogeneous traffic users, which would obviously restrict traffic safety and efficiency [3], [4], [5]. Therefore, precise evaluation is required to support the management of bicycle and mixed flows. In addition to design guidelines, microscopic bicycle traffic simulation models are helpful tools that can fulfill this need [6].
At mixed-traffic intersections with high-density bicycle flow, through bicycles commonly show the tendency of dispersion in the lateral direction during the crossing process [5]. This phenomenon frequently occurs and can be worldwide found in many areas, like China, and countries in Europe with bicycle popularity, as shown in Fig. 1. Initially, cyclists wait for a green period at the entrance (Fig. 2(a)). When the signal lights turn green, through bicycles enter the inner intersection and gradually disperse outside their expected riding area (Fig. 2(b)). Then, the outer cyclists find occasions to return to their expected riding area for safely entering the exiting bicycle lane (Fig. 2(c)), i.e. the merging behavior named in this paper. Previous studies have pointed out that frequent interactions among through bicycles and other road users is the core reason for the lateral dispersion [9], [10]. Besides, the lateral dispersion extent is commonly affected by the dynamic traffic context in each cycle [5], as well as by the types of the adjacent vehicle lane on the approach (i.e. an exclusive right-turn vehicle lane or a shared right-turn and through vehicle lane) [11]. For that, models concerning the through bicycle flow and, more specifically, the simulation of the lateral dispersion characteristics, and interactions, is crucial to understand how through bicycles with high-density impacts traffic efficiency and safety and improve simulation modelling performance.
To the authors’ knowledge, despite several efforts have been put on modelling through bicycles, however, they cannot be considered as a good representation of behavioral realism to some extent. Early microscopic models such as Cellular Automata (CA) models and most of the simulation software such as VISSIM, Transmodeller, etc., depict the lateral dispersion with the hypothesis of constant extent by fixed operation space settings and fail to capture interactions between through bicycles and motorized vehicles due to their virtual lane-based or discrete-based assumptions [12], [13]. The performance of these models is generally not satisfied with bicycle movements [12]. In addition to these, the original social force model (SFM) stemming from pedestrian dynamics modelling [14], [15] was introduced to model some cycling behaviors in recent due to its ability to explain movements on the continuous space [16], [17], [18]. Attempts were also made in through bicycle modelling [19]. However, since the motion controlled by social forces is essentially considered as responses of stimulus from nearby traffic users, the original SFM still needs to integrate additional elements to resolve the description of behaviors and their decision process [20], [21].
To deal with these shortages, a modified SFM model of through bicycles has been designed in this study. It integrates cyclists’ interactions considering behavior decisions and the dynamic characteristics of lateral dispersion with continuous motions under no lane assumption of through bicycles. The main contributions of this study are as follows. In this modified model, we first establish a dynamic boundary model to describe the dynamic scope and extent of the lateral dispersion of the through bicycle flow. Secondly, the behavior force model is introduced, which is involved in four common interactive behaviors of through bicycles, i. e. freely moving, following, overtaking, and merging behavior. Embedded with the behavior force model, two rule-based behavior decision models are established to capture different traffic behavior patterns with the decision process. The model is tested with trajectory data collected in Shanghai, China, and also compared with the original SFM, with satisfactory performances obtained.
The paper is structured as follows. In Section 2, we provide a review of existing models of through bicycles and identify the research gaps. Section 3 introduces the proposed simulation model from each component. Section 4 presents the results of the case study and the comparison of simulation results. Finally, Section 5 concludes the research and presents directions for future study.
Section snippets
Literature review
In regard to the theoretical modelling, microscopic simulation models of through bicycles in literature can be classified into two categories, CA and force-based models. To compare the different modelling ideas and analyze their strengths and weaknesses, each method is discussed successively throughout this section.
CA model is a time and space discrete model proposed by Nagel and Schreckenberg [22], [23], [24]. Several extensions of the original CA have been proposed to describe bicycle traffic
Methods
In this section, we first discuss the overall idea and structure of the proposed model in Section 3.1, followed by the description of the specific methods in the rest of this section.
Study site
Since the simulation model proposed in this paper is used to reproduce the dynamics of through bicycles, test at a mixed-traffic intersection with frequent interactions is necessary. Therefore, an intersection in Shanghai, China called Jianhe-Xianxia intersection is selected as the study site. The site is a typical two-phase intersection where the through bicycle flow always consists of e-bikes and regular bikes (r-bikes), as shown in Fig. 10. Bicycles frequently ride out of the expected riding
Conclusions
At mixed-traffic intersections with high-density bicycle traffic flow, the through bicycle flow shows an obvious lateral dispersion tendency and frequent interactions with other road users within the shared space. Its negative impacts greatly influence traffic safety and efficiency. Therefore, precise evaluation tools are required to fulfill the urgent demand for facility planning, infrastructure designs, and traffic management, while the microscopic simulation model is agreed to be powerful.
Acknowledgements
This work was supported by the National Key Research and Development Program of China (2019YFB1600204), and the Natural Science Foundation of China (52072262). The authors are also grateful to the editor, anonymous reviewers and the people who helped us for their suggestions and comments of this paper.
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