Models and algorithms for addressing travel time variability: Applications from optimal path finding and traffic equilibrium problems

Abstract

Optimal path finding problems under uncertainty have many important real-world applications in various science and engineering fields. In this study, we propose an adaptive α-reliable path finding problem, which is to adaptively determine a reliable path with the minimum travel time budget required to meet the user-specified reliability threshold. The problem is formulated as a chance constrained model, where the chance constraint describes the travel time reliability requirement under a dynamic programming framework. The properties of the proposed model are explored to examine its relationship with the stochastic on-time arrival (SOTA) path finding model. A discrete-time solution algorithm is developed to find the adaptive α-reliable path. Convergence of the algorithm is provided along with numerical results to demonstrate the proposed formulation and solution algorithm.