An analytic investigation into the fundamental aspects of scheduling “Dial-a-Ride” transportation systems is conducted. Based upon simple mathematical models that focus on the combinatorial nature of the problem, a class of algorithms is derived for which performance can be measured in a precise asymptotic probabilistic sense. The approach yields many qualitative insights and the resulting transportation schemes have many attractive practical features. For example, they have modest computational requirements, are decentralized, and are easy to visualize and implement.