Robust path recommendations during public transit disruptions under demand uncertainty

When there are significant service disruptions in public transit systems, passengers usually need guidance to find alternative paths. This paper proposes a path recommendation model to mitigate congestion during public transit disruptions. Passengers with different origins, destinations, and departure times are recommended with different paths such that the system travel time is minimized. We model the path recommendation problem as an optimal flow problem with uncertain demand information. To tackle the lack of analytical formulation of travel times due to capacity constraints, we propose a simulation-based first-order approximation to transform the original problem into a linear program. Uncertainties in demand are modeled using robust optimization to protect the path recommendation strategies against inaccurate estimates. A real-world rail disruption scenario in the Chicago Transit Authority (CTA) system is used as a case study. Results show that even without considering uncertainty, the nominal model can reduce the system travel time by 9.1% (compared to the status quo), and outperforms the benchmark capacity-based path recommendation. The average travel time of passengers in the incident line (i.e., passengers receiving recommendations) is reduced more (−20.6% compared to the status quo). After incorporating the demand uncertainty, the robust model can further reduce system travel times. The best robust model can decrease the average travel time of incident-line passengers by 2.91% compared to the nominal model. The improvement of robust models is more prominent when the actual demand pattern is close to the worst-case demand.