We propose a massively parallel framework termed a parallel-pipeline model of execution that can be employed on a homogeneous computational cluster. We show that speedups near-linear in the number of processors are achievable for applications involving reduction operations based on a novel, parallel-pipeline model of execution. As computational clusters become viable alternative platforms for solving large computational problems, the research community acknowledges that the cluster environment can be used effectively when adaptive resource management is employed. This requires the ability to estimate the resource requirements of applications before scheduling decisions are made. We propose a resource estimation model for applications executed in the parallel-pipeline model of execution. We develop a performance model that predicts the resource utilization (i.e., computation and communication complexity) for applications executing under the parallel-pipeline model on a homogeneous computational cluster. This performance prediction model can provide information to a cluster scheduler.