Parallel independent replicated simulation (PIRS) is an effective approach to speed up the simulation processes. In a PIRS, a single simulation run is executed by multiple computers in parallel. The statistical properties for a PIRS may be affected by the scheduling policies. For an unbiased PIRS scheduling policy, a reliable distributed computing environment is required. We consider an unbiased PIRS scheduling policy on a distributed platform such as a network of workstations. We observe that including more computing resources may degrade the performance of PIRS. Simple rules are proposed to select processors for PIRS.