  Public transit systems are the backbone of urban mobility systems in the era
of urbanization. The design of transit schedules is important for the efficient
and sustainable operation of public transit. However, previous studies usually
assume fixed demand patterns and ignore uncertainties in demand, which may
generate transit schedules that are vulnerable to demand variations. To address
demand uncertainty issues inherent in public transit systems, this paper adopts
both stochastic programming (SP) and robust optimization (RO) techniques to
generate robust transit schedules against demand uncertainty. A nominal
(non-robust) optimization model for the transit frequency setting problem
(TFSP) under a single transit line setting is first proposed. The model is then
extended to SP-based and RO-based formulations to incorporate demand
uncertainty. The large-scale origin-destination (OD) matrices for real-world
transit problems make the optimization problems hard to solve. To efficiently
generate robust transit schedules, a Transit Downsizing (TD) approach is
proposed to reduce the dimensionality of the problem. We prove that the optimal
objective function of the problem after TD is close to that of the original
problem (i.e., the difference is bounded from above). The proposed models are
tested with real-world transit lines and data from the Chicago Transit
Authority (CTA). Compared to the current transit schedule implemented by CTA,
the nominal TFSP model without considering demand uncertainty reduces
passengers' wait times while increasing in-vehicle travel times. After
incorporating demand uncertainty, both stochastic and robust TFSP models reduce
passengers' wait times and in-vehicle travel times simultaneously. The robust
TFSP model produces transit schedules with better in-vehicle travel times and
worse wait times for passengers compared to the stochastic TFSP model.
