Critical Demand Density Thresholds for Public Transit Mode Transition: A Study on Fixed-Route and Demand-Responsive Systems Under Financial Subsidies

As urban mobility trends shift toward greater customization and flexibility, selecting between Fixed-Route Transit (FRT) and Demand-Responsive connector (DRC) systems remains a key challenge, particularly in low-density areas. This study develops a dual-perspective service quality model that integrates passenger utility and operator cost to determine the Critical Demand Density (CDD)—the threshold at which switching between FRT and DRT becomes optimal. The model captures core components of travel time (walking, waiting, riding) and operational characteristics. Under non-subsidized conditions, FRT is more suitable in compact, high-demand regions, while DRT better serves decentralized, low-demand areas, with the CDD threshold at approximately 13 passengers/hour/km2. Incorporating fiscal subsidies, the model reformulates utility functions to include passenger-based marginal subsidies. Results show that subsidies significantly shift the mode transition threshold, increasing the CDD to 22 passengers/hour/km2 and improving DRC’s competitiveness. Sensitivity analyses reveal that factors such as service area geometry, walking time importance, and subsidy magnitude markedly affect CDD values. The model provides a practical, policy-relevant tool for optimizing transit mode decisions based on spatial demand and financial support. This work highlights the strategic role of subsidies in enhancing DRT viability and contributes to sustainable and inclusive urban mobility planning.