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Public transit systems are the backbone of urban mobility systems in the eraof urbanization. The design of transit schedules is important for the efficientand sustainable operation of public transit. However, previous studies usuallyassume fixed demand patterns and ignore uncertainties in demand, which maygenerate transit schedules that are vulnerable to demand variations. To addressdemand uncertainty issues inherent in public transit systems, this paper adoptsboth stochastic programming (SP) and robust optimization (RO) techniques togenerate 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 thenextended to SP-based and RO-based formulations to incorporate demanduncertainty. The large-scale origin-destination (OD) matrices for real-worldtransit problems make the optimization problems hard to solve. To efficientlygenerate robust transit schedules, a Transit Downsizing (TD) approach isproposed to reduce the dimensionality of the problem. We prove that the optimalobjective function of the problem after TD is close to that of the originalproblem (i.e., the difference is bounded from above). The proposed models aretested with real-world transit lines and data from the Chicago TransitAuthority (CTA). Compared to the current transit schedule implemented by CTA,the nominal TFSP model without considering demand uncertainty reducespassengers' wait times while increasing in-vehicle travel times. Afterincorporating demand uncertainty, both stochastic and robust TFSP models reducepassengers' wait times and in-vehicle travel times simultaneously. The robustTFSP model produces transit schedules with better in-vehicle travel times andworse wait times for passengers compared to the stochastic TFSP model.

Transit Frequency Setting Problem with Demand Uncertainty