Subline frequency setting for autonomous minibusses under demand uncertainty

Over the last years, there have been initiated several pilots with autonomous minibusses. Unlike regular bus services, autonomous minibusses serve a limited number of stops and have more flexible schedules since they do not require bus drivers. This allows the operation of a line through a flexible combination of sublines, where a subline serves a subset of consecutive stops in the same order as the original line. This paper studies the subline frequency setting (SFS) problem under uncertain passenger demand. We present a frequency setting model that assigns autonomous minibusses to sublines in order to exploit the available resources as much as possible and minimize the operational and passenger waiting time costs. Passenger waiting time costs may depend on the combination of several lines whose frequencies cannot be perfectly aligned for each passenger journey. We present a new estimation of the expected waiting time for passengers to improve the accuracy of the passenger waiting time costs in the case of sublines. Our SFS model is originally formulated as a MINLP and reformulated as a MILP that can be solved to global optimality. Further, we explicitly consider the uncertainty of passenger demand in the optimization process by formulating a stochastic optimization model. The performances of our stochastic and deterministic models that assign minibusses to sublines are tested under various passenger demand scenarios in the 14-stop autonomous minibus line in Eberbach, Germany and a fictional bus line with 20 bus stops. Results show potential improvements in operational costs in the range of 10%–40% depending on the passenger demand profile.