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Cycling has emerged as one of the most important green transport modes in recent years, with cities increasingly prioritizing cycling in their sustainable policy agenda. However, the associated traffic dynamics, especially the evolution of bicycle flow at bottlenecks, have not been extensively studied. In this study, real-world experiments were conducted to investigate the dynamics of bicycle flow at bottlenecks under various cycling demands generated by the cyclist unloading and loading processes. Upon the activation of the bottleneck, its capacity remained largely constant. For the same physical system, the bottleneck capacity of the cyclist loading process exceeded that of the unloading process, indicating the occurrence of capacity drop and hysteresis. Statistical analyses demonstrated that the capacity drop was attributable to the difference in speeds of the two processes for the same cycling demands after the bottleneck activation. These findings could potentially be explained by behavioral inertia. Further analysis revealed that, compared with the unloading process, the cyclist loading process was associated with higher cycling speeds owing to the higher overtaking rates. The outcomes of this study can advance our understanding of the physics of bicycle flow dynamics and provide valuable insights for transport planning professionals involved in facility planning and control of existing networks. Funding: This work was supported by National Natural Science Foundation of China [Grants 71931002 and 72288101], the University of Hong Kong [Francis S Y Bong Professorship to S. C. Wong], the Guangdong-Hong Kong-Macau Joint Laboratory Program of the 2020 Guangdong New Innovative Strategic Research Fund, Guangdong Science and Technology Department [Grant 2020B1212030009], and Fundamental Research Funds for the Central Universities [Grant JZ2023YQTD0073]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/trsc.2023.0193. [ABSTRACT FROM AUTHOR]

We consider a heterogeneous two-dimensional space where a given set of competitive facilities is located. Customers are assumed to be scattered continuously over the space, and each customer is assumed to choose a facility to minimize individual total cost of receiving service. The total cost consists of both the congested travel time to the facility and a cost associated with the congestion externality at the facility. Furthermore, customer demand at any location is assumed to be a function of the total cost of receiving service. Given these assumptions, it is of interest to estimate the market areas and market shares captured by each competitive facility. This problem is formulated here as a calculus of variations problem, and its optimality conditions are shown to be equivalent to the spatial customer choice equilibrium conditions with elastic demand and market externality. The model is solved by an efficient finite element method and illustrated with a numerical example. [ABSTRACT FROM AUTHOR]