Process arrival pattern, which denotes the timing when different processes arrive at an MPI collective operation, can have a significant impact on the performance of the operation. In this work, we characterize the process arrival patterns in a set of MPI programs on two common cluster platforms, use a micro-benchmark to study the process arrival patterns in MPI programs with balanced loads, and investigate the impacts of the process arrival pattern on collective algorithms. Our results show that (1) the differences between the times when different processes arrive at a collective operation are usually sufficiently large to significantly affect the performance; (2) application developers in general cannot effectively control the process arrival patterns in their MPI programs in cluster environments: balancing loads at the application level does not balance the process arrival patterns; and (3) the performance of the collective communication algorithms is sensitive to process arr...