Trajectories representing the motion of moving objects are typically obtained via location sampling, e.g. using GPS or road-side sensors, at discrete time-instants. In-between consecutive samples, nothing is known about the whereabouts of a given moving object. Various models have been proposed (e.g., sheared cylinders; spacetime prisms) to represent the uncertainty of the moving objects both in unconstrained Euclidian space, as well as road networks. In this paper, we focus on representing the uncertainty of the objects moving along road networks as time-dependent probability distribution functions, assuming availability of a maximal speed on each road segment. For these settings, we introduce a novel indexing mechanism - UTH (Uncertain Trajectories Hierarchy), based upon which efficient algorithms for processing spatio-temporal range queries are proposed. We also present experimental results that demonstrate the benefits of our proposed methodologies.