Efficient ways to implement space-time parallel applications based on the parareal-in-time algorithm are studied with a pipelined communication pattern. After analyzing the standard one, a simplified implementation of the parareal-in-time algorithm is introduced for scientific computing problems, where an identity transformation is used as a coarse solver and the pipelined communications are used to resolve dependencies. Based on analysis of the convergence property and expected performance, it is shown that this new implementation is valid for explicit time-evolution calculations. Through performance measurements of time-parallel applications, strategies for the further tuning toward postpeta-scale computing is discussed.