We propose a model for the estimation of query execution time in an environment supporting bushy and pipelined parallelism. We consider a parallel architecture of processes having private main memories, accessing a shared secondary storage and communicating to each other via a network. For this environment, we compute the cost of query operators when processed in isolation and when in pipeline mode. WE use those formulae to incrementally compute the cost of a query execution plan from its components. Our cost model can be incorporated to any optimizer for parallel query processing that considers parallel and pipelined execution of the query operators.