  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.
