Individual Path Recommendation Under Public Transit Service Disruptions Considering Behavior Uncertainty

Abstract

Public transit passengers need guidance during service disruptions. This study proposes an individual-based path (IPR) recommendation model. The model decides which paths to recommend for each passenger with the objective of minimizing system travel time and respecting passengers' path choice preferences. We assume the recommendations could affect passengers' path choice probabilities, but their actual choices are uncertain. This behavior uncertainty makes the problem a stochastic optimization with decision-dependent distributions. We propose a single-point approximation method to eliminate the expectation operator by introducing two new concepts: epsilon-feasibility and Gamma-concentration, which control the mean and variance of path flows in the optimization problem. The approximation yields a tractable single-stage mixed integer linear formulation, which can be solved efficiently with Benders decomposition. The approximation gap is approved to be bounded from the above. Additional theoretical analysis shows that epsilon-feasibility and Gamma-concentration are strongly connected to expectation and chance constraints in a typical stochastic optimization formulation, respectively. The model is implemented in a real-world case study using data from an urban rail disruption in the Chicago Transit Authority system, and a synthetic case study with varied network sizes and incident locations. In the real-world case study, results show that the proposed IPR model reduces the average travel times in the system by 6.6% compared to the status quo and by 4.2% compared to a capacity-based benchmark model. In the synthetic case study, the proposed model shows 15.0% to 1.8% lower system travel time compared to the capacity-based benchmark, depending on the network sizes and demand situations.