directed acyclic graph completion time distribution

For a workflow application (directed acyclic graph), suppose each vetex is a computing task and each edge is a communication between vetexs (with dependencies, parent - child). If we can model the computing time at each vetex as a distribution (normal or beta), what is the completion time of the whole DAG (or its disbribution)? Communication time can be considered later. Is it possible to know a bound X on the completion time for a given probability Y? It also helps if I could know Y for a given X. Thanks. suggestions and references appreciated.