Urban–rural public transport accessibility evaluation based on improved gravity model with actual time

Accessibility represents a paramount metric for assessing the service level of public transportation systems. Current research predominantly focuses on urban intra-system accessibility, with limited holistic studies encompassing small- to medium-sized cities, adjacent towns, and rural areas. Traditional metrics like bus mode share, route length, and road density inadequately quantify urban–rural transportation supply. Existing methods rely on travel distance and assumed bus speeds, neglecting actual time-based assessments. Building upon the gravity model, this study proposes a regional bus accessibility model, using real travel time as impedance and supply–demand ratio as a weighting factor, and visualises results through ArcGIS spatial analysis. Leveraging Python scraping technology and the Gaode Map Open Platform, we obtain actual bus travel durations between origins and destinations. Taking 16 traffic zones in Tengzhou County as examples, we analyse temporal–spatial differences in bus travel between urban and rural village zones. The accessibility results intuitively reveal the level of bus accessibility from urban centres to surrounding villages, providing quantitative information crucial for site selection analysis and public transport optimisation.