•Overarching framework that covers non-shared taxi, paratransit, and ridesharing.•Systematic quantification of cost and performance in approximate closed-form formulas.•Insights that could be used to explore operating, pricing, and regulatory strategies.•Analytical results are corroborated by agent-based simulations. The paper presents a general analytic framework to model transit systems that provide door-to-door service. The model includes as special cases non-shared taxi and demand responsive transportation (DRT). In the latter we include both, paratransit services such as dial-a-ride (DAR), and the form of ridesharing (shared taxi) currently being used by crowd-sourced taxi companies like Lyft and Uber. The framework yields somewhat optimistic results because, among other things, it is deterministic and does not track vehicles across space. By virtue of its simplicity, however, the framework yields approximate closed form formulas for many cases of interest.