Robust adaptive strategies for the guidance of users in road networks
  We present an algorithm for optimal guidance of users in road networks. It is a "stochastic-on-time-arrival (SOTA)"-like algorithm which calculates optimal guidance strategies with reliable paths, for road network origin-destination pairs. Our contribution consists here in extending an existing SOTA algorithm, in order to include robustness of the guidance strategy, towards path failures. The idea of SOTA algorithms is to calculate the maximum probability of reaching a destination node, starting from any node of a road network, and given a time budget. This calculus gives the optimal path for every origin-destination pair of nodes in the network, with an associated optimal adaptive guidance strategy. We propose here an extension of this approach in order to take into account the existence and the performance of alternative detours of the selected paths, in the calculus of the guidance strategy. We take into account the fact that one or many links of the selected optimal path may fail during the travel. We then consider that users may be sensitive to path changing. That is to say that they may prefer paths with efficient alternative detours, with respect to paths without, or with less efficient detours, even with a loss in the average travel time, and/or in its reliability. In order to take into account such behaviors, we propose a model that includes the existence as well as the performance of detours for selected paths, in the calculus of the travel time reliability. This new way of calculating travel time reliability guarantees a kind of robustness of the guidance strategies. 
Farida Manseur, Nadir Farhi, Habib Haj-Salem, Jean-Patrick Lebacque
math.OC