Designing the master schedule for demand-adaptive transit systems

Demand-Adaptive Systems (DASs) display features of both traditional fixed-line bus services and purely on-demand systems such as dial-a-ride, that is, they offer demand-responsive services within the framework of traditional scheduled bus transportation. A DAS bus line serves a given set of compulsory stops according to a predefined schedule, which specifies the time windows associated with each stop, and thus provides the traditional use of a transit line without reservation. On the other hand, passengers may issue requests for transportation between two optional stops, inducing detours in the vehicle routes. The design of a DAS line is a complex planning process that requires to select the compulsory stops and to determine its master schedule in terms of the time windows associated with the compulsory stops. In this paper, we focus on determining the master schedule for a single DAS line. We propose a mathematical description and a solution method based on probabilistic approximations of several DAS line core characteristics. Results of numerical experiments are also given and analyzed.