This paper is based on (Mombelli et al., 2022). In their article, they dealt with a fleet of autonomous vehicles which is required to perform internal logistics tasks in some protected areas. This fleet is supposed to be ruled by a hierarchical supervision architecture which, at the top level, distributes and schedules Pick up and Delivery tasks, and, at the lowest level, ensures safety at the crossroads and controls the trajectories. They presented the problem of finding a shortest path under risk constraints and proposed a way to compute speed functions along the path. In this paper, we present some theoretical results and focus on the fixed path problem. We propose several new ways of computing speed functions including a couple with reinforcement learning.