The pervasive use of cloud computing has led to many concerns, such as performance challenges in communication- and computation-intensive services on virtual cloud resources. Most evaluations of the infrastructural overhead are based on standard benchmarks. Therefore, the impact of communication issues and infrastructure services on the performance of parallel MPI-based computations remains unclear. This paper presents the performance analysis of communication- and computation-intensive software based on the discrete element method, which is deployed as a service (SaaS) on the OpenStack cloud. The performance measured on KVM-based virtual machines and Docker containers of the OpenStack cloud is compared with that obtained by using native hardware. The improved mapping of computations to multicore resources reduced the internode MPI communication by 34.4% and increased the parallel efficiency from 0.67 to 0.78, which shows the importance of communication issues. Increasing the number of parallel processes, the overhead of the cloud infrastructure increased to 13.7% and 11.2% of the software execution time on native hardware in the case of the Docker containers and KVM-based virtual machines of the OpenStack cloud, respectively. The observed overhead was mainly caused by OpenStack service processes that increased the load imbalance of parallel MPI-based SaaS.