The Boltzmann transport equation is solved by means of a parallel explicit algorithm known as parallel sweep, and a source iteration procedure to solve the coupling between different angular directions. Using an explicit solver implies that the nodes have to be visited in a specific order. Factors that influence the scalability of the algorithm have been analysed, namely the different strategies to group the tasks to be done at the calculation stage, and how deep should the task graph be worked prior to the communication stage. Two and three dimensional unstructured meshes have been considered. With relatively small meshes, good weak and strong speedup results are obtained, using up to ≈ 900 processors.