Tractable Pathfinding for the Stochastic On-Time Arrival Problem

We present a new technique for fast computation of the route that maximizes the probability of on-time arrival in stochastic networks, also known as the path-based stochastic on-time arrival (SOTA) problem. We utilize the solution to the policy-based SOTA problem, which is of pseudopolynomial time complexity in the time budget of the journey, as a heuristic for efficiently computing the optimal path. We also introduce Arc-Potentials, an extension to the Arc-Flags pre-processing algorithm, which improves the efficiency of the graph pre-processing and reduces the computation time. Finally, we present extensive numerical results demonstrating the effectiveness of our algorithm and observe that its running time when given the policy (which can be efficiently obtained using pre-processing) is almost always linear in the length of the optimal path for our test networks. ∗Electrical Engineering and Computer Science, University of California, Berkeley. †Systems Engineering, University of California, Berkeley. ‡Electrical Engineering and Computer Science, University of California, Berkeley. 1 ar X iv :1 40 8. 44 90 v1 [ cs .D S] 1 9 A ug 2 01 4