Online Predictive Optimization Framework for Stochastic Demand-Responsive Transit Services

This study develops an online predictive optimization framework for dynamically operating a transit service in an area of crowd movements. The proposed framework integrates demand prediction and supply optimization to periodically redesign the service routes based on recently observed demand. To predict demand for the service, we use Quantile Regression to estimate the marginal distribution of movement counts between each pair of serviced locations. The framework then combines these marginals into a joint demand distribution by constructing a Gaussian copula, which captures the structure of correlation between the marginals. For supply optimization, we devise a linear programming model, which simultaneously determines the route structure and the service frequency according to the predicted demand. Importantly, our framework both preserves the uncertainty structure of future demand and leverages this for robust route optimization, while keeping both components decoupled. We evaluate our framework using a real-world case study of autonomous mobility in a university campus in Denmark. The results show that our framework often obtains the ground truth optimal solution, and can outperform conventional methods for route optimization, which do not leverage full predictive distributions.Comment: 34 pages, 12 figures, 5 table

Modeling Overlapping and Heterogeneous Perception Variance in Stochastic User Equilibrium Problem with Weibit Route Choice Model

In this study, a new SUE model using the Weibull random error terms is proposed as an alternative to overcome the drawbacks of the multinomial logit (MNL) SUE model. A path-size weibit (PSW) model is developed to relax both independently and identically distributed assumptions, while retaining an analytical closed-form solution. Specifically, this route choice model handles route overlapping through the path-size factor and captures the route-specific perception variance through the Weibull distributed random error terms. Both constrained entropy-type and unconstrained equivalent MP formulations for the PSW-SUE are provided. In addition, model extensions to consider the demand elasticity and combined travel choice of the PSW-SUE model are also provided. Unlike the logit-based model, these model extensions incorporate the logarithmic expected perceived travel cost as the network level of service to determine the demand elasticity and travel choice. Qualitative properties of these minimization programs are given to establish equivalency and uniqueness conditions. Both path-based and link-based algorithms are developed for solving the proposed MP formulations. Numerical examples show that the proposed models can produce a compatible traffic flow pattern compared to the multinomial probit (MNP) SUE model, and these models can be implemented in a real-world transportation network