In this paper, we present a method for overlapping communications on parallel computers for pipelined algorithms. We first introduce a general theoretical model which leads to a generic computation scheme for the optimal packet size. Then, we use the OPIUM library, which provides an easy-to-use and efficient way to compute, in the general case, this optimal packet size, on the column $LU$ factorization; the implementation and performance measures are made on an Intel Paragon.