Multimodal dynamic and stochastic routing

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Speeding up Martins' algorithm for multiple objective shortest path problems

The latest transportation systems require the best routes in a large network with respect to multiple objectives simultaneously to be calculated in a very short time. The label setting algorithm of Martins efficiently finds this set of Pareto optimal paths, but sometimes tends to be slow, especially for large networks such as transportation networks. In this article we investigate a number of speedup measures, resulting in new algorithms. It is shown that the calculation time to find the Pareto optimal set can be reduced considerably. Moreover, it is mathematically proven that these algorithms still produce the Pareto optimal set of paths

Dynamic and stochastic routing for multimodal transportation systems

The authors present a case study of a multimodal routing system that takes into account both dynamic and stochastic travel time information. A multimodal network model is presented that makes it possible to model the travel time information of each transportation mode differently. This travel time information can either be static or dynamic, or either deterministic or stochastic. Next, a Dijkstra-based routing algorithm is presented that deals with this variety of travel time information in a uniform way. This research focuses on a practical implementation of the system, which means that a number of assumptions were made, like the modelling of the stochastic distributions, comparing these distributions, and so on. A tradeoff had to be made between the performance of the system and the accuracy of the results. Experiments have shown that the proposed system produces realistic routes in a short amount of time. It is demonstrated that routing dynamically indeed results in a travel time gain in comparison to routing statically. By making use of the additional stochastic travel time information even better (i.e. faster), more reliable routes can be calculated. Moreover, it is shown that routing in the multimodal network may have its advantages over routing in a unimodal network, especially during rush hours