Robust Transit Frequency Setting Problem With Demand Uncertainty

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, limited studies have considered demand uncertainties when designing transit schedules. To better address demand uncertainty issues inherent in public transit systems, this paper utilizes the robust optimization (RO) framework 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 the RO-based formulation to incorporate demand uncertainty, which has not been considered in the literature. The large-scale origin-destination (OD) matrices for real-world transit problems bring computational challenges in solving the optimization problem. To efficiently generate robust transit schedules, a Transit Downsizing (TD) approach is proposed to reduce the dimensionality of the problem. The proposed models are tested with real-world transit lines and data from the Chicago Transit Authority (CTA). Meanwhile, a stochastic programming (SP) framework is used to construct a benchmark stochastic TFSP model. Compared to the current transit schedule implemented by the 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 transit schedules outperform the benchmark stochastic transit schedules by reducing both wait and in-vehicle travel times when demand is significantly uncertain.