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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 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 arrival patterns. These results indicate that the process arrival pattern is an important factor that must be taken into consideration in developing and optimizing MPI collective routines. We propose a scheme that achieves high performance with different process arrival patterns, and demonstrate that by explicitly considering process arrival pattern, more efficient MPI collective routines than the current ones can be obtained.