Summary: Recent studies show that MPI processes in real applications could arrive at an MPI collective operation at different times. This imbalanced process arrival pattern can significantly affect the performance of the collective operation. MPI\_Alltoall() and MPI\_Allgather() are communication-intensive collective operations that are used in many scientific applications. Therefore, their efficient implementations under different process arrival patterns are critical to the performance of scientific applications running on modern clusters. In this paper, we propose novel RDMA-based process arrival pattern aware MPI\_Alltoall() and MPI\_Allgather() for different message sizes over InfiniBand clusters. We also extend the algorithms to be shared memory aware for small to medium size messages under process arrival patterns. The performance results indicate that the proposed algorithms outperform the native MVAPICH implementations as well as other non-process arrival pattern aware algorithms when processes arrive at different times. Specifically, the RDMA-based process arrival pattern aware MPI\_Alltoall() and MPI\_Allgather() are 3.1 times faster than MVAPICH for 8 KB messages. On average, the applications studied in this paper (FT, RADIX, and N-BODY) achieve a speedup of 1.44 using the proposed algorithms.