A multi-valued DAG model and an optimal PERT-like Algorithm for the Distribution of Applications on Heterogeneous Computing Systems

In this paper, we study the following theoretical scheduling problem: the tasks of a given application have to be statically distributed and executed on the heterogeneous servers of a multi-user system on a wide area, heterogeneous network, such as Internet. The application is divided into a set of communicating tasks that may be executed on at least one, and possibly several, servers. The processing time of each task depends on the server processing it, and the communication delay between two tasks depends on the communicating servers. Task duplication is allowed. We propose an efficient algorithm that first uses a PERT-like algorithm to compute the earliest execution dates of each task and then build an optimal static solution for this scheduling problem, with a low number of tasks duplications.