Traffic flow theory-based modeling of bike-vehicle interactions for enhanced safety and mobility

This paper introduces an innovative approach to enhancing active transportation analysis and decision support by addressing the notable research gap of integrating traffic flow analysis, spatio-temporal trajectory models, and an input-output (moving queue) diagram. We establish a unique four-stage method for assessing bike-vehicle traffic interaction on designated road links: 1) Given the input of volume, we convert it to speed and density using the fundamental diagram and Q-K curves under different congestion conditions. 2) We analyze vehicle trajectories and utilize an input-output (moving queue) diagram to calculate the total exposures between bikes and vehicles as a function of speed difference and the product of bike and vehicle volume, ensuring the balance equations for both vehicle and bike exposure individually. 3) Beginning at the moment a vehicle enters a shared facility, we apply an illustrative method to determine the duration of individual exposure time, adjusting Newell's car-following model to accommodate for various phases of driver reactions, transitioning from anticipation to overtaking/yield phase. 4) We measure the overall impact of exposure on mobility and safety using a multimodal semi-dynamic traffic assignment that focuses on both delay and exposure-based utility across various facility types and development scenarios. Our research underscores that controlling the flow of bikes and vehicles is a pivotal factor in determining the relative bike exposure to risk, offering valuable insights for the future development of transportation models and safety improvement strategies using a case study from Gilbert, AZ.