Stochastic shortest path problems (SSPPs) have many applications in practice and are subject of ongoing research for many years. This paper considers a variant of SSPPs where times or costs to pass an edge in a graph are, possibly correlated, random variables. There are two general goals one can aim for, the minimization of the expected costs to reach the destination or the maximization of the probability to reach the destination within a given budget. Often one is interested in policies that build a compromise between different goals which results in multi-objective problems. In this paper, an algorithm to compute the convex hull of Pareto optimal policies that consider expected costs and probabilities of falling below given budgets is developed. The approach uses the recently published class of PH-graphs that allow one to map SSPPs, even with generally distributed and correlated costs associated to edges, on Markov decision processes (MDPs) and apply the available techniques for MDPs to compute optimal policies.

随机最短路径问题（SSPP）在实践中有许多应用，并且是正在进行的研究多年的主题。本文考虑了SSPP的一种变体，其中通过图形边缘的时间或成本可能是相关的随机变量。一个目标可以达到两个总体目标，即在给定的预算内将到达目的地的预期成本最小化或将到达目标的概率最大化。人们常常对在不同目标之间建立折衷方案的政策感兴趣，这会导致多目标问题。在本文中，开发了一种计算帕累托最优策略的凸包的算法，该算法考虑了预期成本和低于给定预算的概率。该方法使用了最近发布的一类PH图，可以用来映射SSPP，